Worksheet on Factoring Simple Quadratics is for those who are seriously searching to learn factorization problems. We have given different problems along with solutions on our Factorization Worksheets. Therefore, anyone who wants to start their practice immediately to learn factorization problems can utilize our Factoring Quadratic Equations Worksheet With Answers and get good marks. Concentrate on the areas you are lagging and improve your performance in the exams. Practice with Factoring Simple Quadratics Worksheet those have equations like x^2 + ax + b.

1. Factorize the following expression:

(i) a^{2} + 9a + 20

(ii) m^{2} + 15m + 54

(iii) y^{2} + 3y – 4

(iv) n^{2} + 2n – 24

(v) x^{2} – 5x + 4

(vi) a^{2} – 15a + 14

## Solution:

(i) The Given expression is a^{2} + 9a + 20.

By comparing the given expression a^{2} + 9a + 20 with the basic expression x^2 + ax + b.

Here, a = 1, b = 9, and c = 20.

The sum of two numbers is m + n = b = 9 = 5 + 4.

The product of two number is m * n = a * c = 1 * (20) = 20 = 5 * 4

From the above two instructions, we can write the values of two numbers m and n as 5 and 4.

Then, a^{2} + 9a + 20 = a^{2} +5a + 4a + 20.

= a (a+ 5) + 4(a + 5).

Factor out the common terms.

(a + 5) (a + 4)

Then, a^{2} + 9a + 20 = (a + 5) (a + 4).

(ii) The Given expression is m^{2} + 15m + 54.

By comparing the given expression m^{2} + 15m + 54 with the basic expression x^2 + ax + b.

Here, a = 1, b = 15, and c = 54.

The sum of two numbers is m + n = b = 15 = 6 + 9.

The product of two number is m * n = a * c = 1 * (54) = 54 = 6 * 9

From the above two instructions, we can write the values of two numbers m and n as 6 and 9.

Then, m^{2} + 15m + 54 = m^{2} + 6m + 9m + 54.

= m (m + 6) + 9(m + 6).

Factor out the common terms.

(m + 6) (m + 9)

Then, m^{2} + 15m + 54 = (m + 6) (m + 9).

(iii) The Given expression is y^{2} + 3y – 4.

By comparing the given expression y^{2} + 3y – 4 with the basic expression x^2 + ax + b.

Here, a = 1, b = 3, and c = -4.

The sum of two numbers is m + n = b = 3 = 4 – 1.

The product of two number is m * n = a * c = 1 * (-4) = -4 = 1 * -4

From the above two instructions, we can write the values of two numbers m and n as 1 and -4.

Then, y^{2} + 3y – 4 = y^{2} + 4y -y – 4.

= y (y + 4) – 1(y + 4).

Factor out the common terms.

(y + 4) (y – 1)

Then, y^{2} + 3y – 4 = (y + 4) (y – 1).

(iv) The Given expression is n^{2} + 2n – 24.

By comparing the given expression n^{2} + 2n – 24 with the basic expression x^2 + ax + b.

Here, a = 1, b = 2, and c = -24.

The sum of two numbers is m + n = b = 2 = 6 – 4.

The product of two number is m * n = a * c = 1 * (-24) = -24 = 6 * -4

From the above two instructions, we can write the values of two numbers m and n as 6 and -4.

Then, n^{2} + 2n – 24 = n^{2} + 6n – 4n – 24.

= n (n + 6) – 4(n + 6).

Factor out the common terms.

(n + 6) (n – 4)

Then, n^{2} + 2n – 24 = (n + 6) (n – 4).

(v) The Given expression is x^{2} – 5x + 4.

By comparing the given expression x^{2} – 5x + 4 with the basic expression x^2 + ax + b.

Here, a = 1, b = -5, and c = 4.

The sum of two numbers is m + n = b = -5 = -1 – 4.

The product of two number is m * n = a * c = 1 * (4) = 4 = -1 * -4

From the above two instructions, we can write the values of two numbers m and n as -1 and -4.

Then, x^{2} – 5x + 4 = x^{2} – x – 4x + 4.

= x (x – 1) – 4(x – 1).

Factor out the common terms.

(x – 1) (x – 4)

Then, x^{2} – 5x + 4 = (x – 1) (x – 4).

(vi) The Given expression is a^{2} – 15a + 14.

By comparing the given expression a^{2} – 15a + 14 with the basic expression x^2 + ax + b.

Here, a = 1, b = -15, and c = 14.

The sum of two numbers is m + n = b = -15 = -1 – 14.

The product of two number is m * n = a * c = 1 * (14) = 14 = -1 * -14

From the above two instructions, we can write the values of two numbers m and n as -1 and -14.

Then, a^{2} – 15a + 14 = a^{2} – a – 14a + 14.

= a (a – 1) – 14(a – 1).

Factor out the common terms.

(a – 1) (a – 14)

Then, a^{2} – 15a + 14 = (a – 1) (a – 14).

2. Resolve into factors

(i) a^{2} + 3a – 10

(ii) m^{2} – 18m – 63

(iii) a^{2} + 6a + 8

(iv) a^{2} + 12a + 32

(v) x^{2} – 8x + 15

(vi) m^{2} – 12m + 35

## Solution:

(i) The Given expression is a^{2} + 3a – 10.

By comparing the given expression a^{2} + 3a – 10 with the basic expression x^2 + ax + b.

Here, a = 1, b = 3, and c = -10.

The sum of two numbers is m + n = b = 3 = 5 – 2.

The product of two number is m * n = a * c = 1 * (-10) = -10 = 5 * -2

From the above two instructions, we can write the values of two numbers m and n as 5 and -2.

Then, a^{2} + 3a – 10 = a^{2} + 5a – 2a – 10.

= a (a + 5) – 2(a + 5).

Factor out the common terms.

(a + 5) (a – 2)

Then, a^{2} + 3a – 10 = (a + 5) (a – 2).

(ii) The Given expression is m^{2} – 18m – 63.

By comparing the given expression m^{2} – 18m – 63 with the basic expression x^2 + ax + b.

Here, a = 1, b = -18, and c = -63.

The sum of two numbers is m + n = b = -18 = 3 – 21.

The product of two number is m * n = a * c = 1 * (-63) = -63 = 3 * -21

From the above two instructions, we can write the values of two numbers m and n as 3 and -21.

Then, m^{2} – 18m – 63 = m^{2} + 3m – 21m – 63.

= m (m + 3) – 21(m + 3).

Factor out the common terms.

(m + 3) (m – 21)

Then, m^{2} – 18m – 63 = (m + 3) (m – 21).

(iii) The Given expression is a^{2} + 6a + 8.

By comparing the given expression a^{2} + 6a + 8 with the basic expression x^2 + ax + b.

Here, a = 1, b = 6, and c = 8.

The sum of two numbers is m + n = b = 6 = 2 + 4.

The product of two number is m * n = a * c = 1 * (8) = 8 = 2 * 4

From the above two instructions, we can write the values of two numbers m and n as 2 and 4.

Then, a^{2} + 6a + 8 = a^{2} + 2a + 4a + 8.

= a (a + 2) + 4(a + 2).

Factor out the common terms.

(a + 2) (a + 4)

Then, a^{2} + 6a + 8 = (a + 2) (a + 4).

(iv) The Given expression is a^{2} + 12a + 32.

By comparing the given expression a^{2} + 12a + 32 with the basic expression x^2 + ax + b.

Here, a = 1, b = 12, and c = 32.

The sum of two numbers is m + n = b = 12 = 8 + 4.

The product of two number is m * n = a * c = 1 * (32) = 32 = 8 * 4

From the above two instructions, we can write the values of two numbers m and n as 8 and 4.

Then, a^{2} + 12a + 32 = a^{2} + 8a + 4a + 32.

= a (a + 8) + 4(a + 8).

Factor out the common terms.

(a + 8) (a + 4)

Then, a^{2} + 12a + 32 = (a + 8) (a + 4).

(v) The Given expression is x^{2} – 8x + 15.

By comparing the given expression x^{2} – 8x + 15 with the basic expression x^2 + ax + b.

Here, a = 1, b = -8, and c = 15.

The sum of two numbers is m + n = b = -8 = – 3 – 5.

The product of two number is m * n = a * c = 1 * (15) = 15 = -3 * -5

From the above two instructions, we can write the values of two numbers m and n as -3 and -5.

Then, x^{2} – 8x + 15 = x^{2} – 3x – 5x + 15.

= x (x – 3) – 5(x – 3).

Factor out the common terms.

(x – 3) (x – 5)

Then, x^{2} – 8x + 15 = (x – 3) (x – 5).

(vi) The Given expression is m^{2} – 12m + 35.

By comparing the given expression m^{2} – 12m + 35 with the basic expression x^2 + ax + b.

Here, a = 1, b = -12, and c = 35.

The sum of two numbers is m + n = b = -12 = – 5 – 7.

The product of two number is m * n = a * c = 1 * (35) = 35 = -5 * -7

From the above two instructions, we can write the values of two numbers m and n as -5 and -7.

Then, m^{2} – 12m + 35 = m^{2} – 5m – 7m + 35.

= m (m – 5) – 7(m – 5).

Factor out the common terms.

(m – 7) (m – 5)

Then, m^{2} – 12m + 35 = (m – 7) (m – 5).

3. Factor the middle term

(i) m^{2} – 4m – 12

(ii) a^{2} – 4a – 45

(iii) x^{2} + 15x + 56

(iv) p^{2} – 13p + 36

(v) q^{2} + 5q – 24

(vi) r^{2} + 17r – 84

(vii) a^{2} – 15a + 44

(viii) m^{2} – 5m – 24

(ix) x^{2} – 4x – 77

(x) a^{2} – 12a + 20

## Solution:

(i) The Given expression is m^{2} – 4m – 12.

By comparing the given expression m^{2} – 4m – 12 with the basic expression x^2 + ax + b.

Here, a = 1, b = -4, and c = -12.

The sum of two numbers is m + n = b = -4 = 2 – 6.

The product of two number is m * n = a * c = 1 * (-12) = -12 = 2 * -6

From the above two instructions, we can write the values of two numbers m and n as 2 and -6.

Then, m^{2} – 4m – 12 = m^{2} – 2m + 6m – 12.

= m (m – 2) + 6(m – 2).

Factor out the common terms.

(m – 2) (m + 6)

Then, m^{2} – 4m – 12 = (m – 2) (m + 6).

(ii) The Given expression is a^{2} – 4a – 45.

By comparing the given expression a^{2} – 4a – 45 with the basic expression x^2 + ax + b.

Here, a = 1, b = -4, and c = -45.

The sum of two numbers is m + n = b = -4 = 5 – 9.

The product of two number is m * n = a * c = 1 * (-45) = -45 = 5 * -9

From the above two instructions, we can write the values of two numbers m and n as 5 and -9.

Then, a^{2} – 4a – 45 = a^{2} + 5a – 9a – 45.

= a (a + 5) – 9(a + 5).

Factor out the common terms.

(a + 5) (a – 9)

Then, a^{2} – 4a – 45 = (a + 5) (a – 9).

(iii) The Given expression is x^{2} + 15x + 56.

By comparing the given expression x^{2} + 15x + 56 with the basic expression x^2 + ax + b.

Here, a = 1, b = 15, and c = 56.

The sum of two numbers is m + n = b = 15 = 8 + 7.

The product of two number is m * n = a * c = 1 * (56) = 56 = 8 * 7

From the above two instructions, we can write the values of two numbers m and n as 8 and 7.

Then, x^{2} + 15x + 56 = x^{2} + 8x + 7x + 56.

= x (x + 8) + 7(x + 8).

Factor out the common terms.

(x + 8) (x + 7)

Then, x^{2} + 15x + 56 = (x + 8) (x + 7).

(iv) The Given expression is p^{2} – 13p + 36.

By comparing the given expression p^{2} – 13p + 36 with the basic expression x^2 + ax + b.

Here, a = 1, b = -13, and c = 36.

The sum of two numbers is m + n = b = -13 = -9 – 4.

The product of two number is m * n = a * c = 1 * (36) = 36 = -9 * -4

From the above two instructions, we can write the values of two numbers m and n as -9 and -4.

Then, p^{2} – 13p + 36 = p^{2} – 9p – 4p + 36.

= p (p – 9) – 4(p – 9).

Factor out the common terms.

(p – 9) (p – 4)

Then, p^{2} – 13p + 36 = (p – 9) (p – 4).

(v) The Given expression is q^{2} + 5q – 24.

By comparing the given expression q^{2} + 5q – 24 with the basic expression x^2 + ax + b.

Here, a = 1, b = 5, and c = -24.

The sum of two numbers is m + n = b = 5 = -3 + 8.

The product of two number is m * n = a * c = 1 * (-24) = -24 = -3 * 8

From the above two instructions, we can write the values of two numbers m and n as -3 and 8.

Then, q^{2} + 5q – 24 = q^{2} – 3q + 8q – 24.

= q (q – 3) + 8(q – 3).

Factor out the common terms.

(q – 3) (q + 8)

Then, q^{2} + 5q – 24 = (q – 3) (q + 8).

(vi) The Given expression is r^{2} + 17r – 84.

By comparing the given expression r^{2} + 17r – 84 with the basic expression x^2 + ax + b.

Here, a = 1, b = 17, and c = -84.

The sum of two numbers is m + n = b = 17 = 21 – 4.

The product of two number is m * n = a * c = 1 * (-84) = -84 = 21 * -4

From the above two instructions, we can write the values of two numbers m and n as 21 and -4.

Then, r^{2} + 17r – 84 = r^{2} + 21r -4r – 84.

= r (r + 21) – 4(r + 21).

Factor out the common terms.

(r + 21) (r – 4)

Then, r^{2} + 17r – 84 = (r + 21) (r – 4).

(vii) The Given expression is a^{2} – 15a + 44.

By comparing the given expression a^{2} – 15a + 44 with the basic expression x^2 + ax + b.

Here, a = 1, b = -15, and c = 44.

The sum of two numbers is m + n = b = -15 = -11 – 4.

The product of two number is m * n = a * c = 1 * (44) = 44 = -11 * -4

From the above two instructions, we can write the values of two numbers m and n as -11 and -4.

Then, a^{2} – 15a + 44 = a^{2} – 11a – 4a + 44.

= a (a – 11) – 4(a – 11).

Factor out the common terms.

(a – 11) (a – 4)

Then, a^{2} – 15a + 44 = (a – 11) (a – 4).

(viii) The Given expression is m^{2} – 5m – 24.

By comparing the given expression m^{2} – 5m – 24 with the basic expression x^2 + ax + b.

Here, a = 1, b = -5, and c = -24.

The sum of two numbers is m + n = b = -5 = 3 – 8.

The product of two number is m * n = a * c = 1 * (-24) = -24 = 3 * -8

From the above two instructions, we can write the values of two numbers m and n as 3 and -8.

Then, m^{2} – 5m – 24 = m^{2} + 3m – 8m – 24.

= m (m + 3) – 8(m – 3).

Factor out the common terms.

(m – 3) (m – 8)

Then, m^{2} – 5m – 24 = (m – 3) (m – 8).

(ix) The Given expression is x^{2} – 4x – 77.

By comparing the given expression x^{2} – 4x – 77 with the basic expression x^2 + ax + b.

Here, a = 1, b = -4, and c = -77.

The sum of two numbers is m + n = b = -4 = -11 + 7.

The product of two number is m * n = a * c = 1 * (-77) = -77 = -11 * 7

From the above two instructions, we can write the values of two numbers m and n as -11 and 7.

Then, x^{2} – 4x – 77 = x^{2} – 11x +7x – 77.

= x (x – 11) + 7(x – 11).

Factor out the common terms.

(x – 11) (x + 7)

Then, x^{2} – 4x – 77 = (x – 11) (x + 7).

(x) The Given expression is a^{2} – 12a + 20.

By comparing the given expression a^{2} – 12a + 20 with the basic expression x^2 + ax + b.

Here, a = 1, b = -12, and c = 20.

The sum of two numbers is m + n = b = -12 = -10 – 2.

The product of two number is m * n = a * c = 1 * (20) = 20 = -10 * -2

From the above two instructions, we can write the values of two numbers m and n as -10 and -2.

Then, a^{2} – 12a + 20 = a^{2} – 10a – 2a + 20.

= a (a – 10) – 2(a – 10).

Factor out the common terms.

(a – 10) (a – 2)

Then, a^{2} – 12a + 20 = (a – 10) (a – 2).