FACTORING QUADRATIC EXPRESSIONS WORKSHEET

Factor each of the following quadratic expressions.

Question 1 :

x² + 6x + 8

Question 2 :

x² + 9x + 18

Question 3 :

x² + 3x -18

Question 4 :

x² - 2x - 15

Question 5 :

x² - 4x + 3

Question 6 :

3x² + 10x + 8

Question 7 : 

3x² – 5x – 12

Question 8 : 

x² – 9

Question 9 : 

9x² - 49

Question 10 : 

(x + 2)² - 25

Answers

1. Answer :

= x² + 6x + 8

Multiply the coefficient x², 1 and the constant term 8.

= 1 x 8

= 8

Find two numbers such that the product is equal to 8 and the sum is equal to the coeffient of x, 6.

The two numbers satisfy the above condition are 2 and 4.

Split the middle term 6x using the two numbers 2 and 4.

= x² + 2x + 4x + 8

Factor by grouping.

= (x² + 2x) + (4x + 8)

= x(x + 2) + 4(x + 2)

= (x + 2)(x + 4)

2. Answer :

= x² + 9x + 18

Multiply the coefficient x², 1 and the constant term 18.

= 1 x 18

= 18

Find two numbers such that the product is equal to 18 and the sum is equal to the coeffient of x, 9.

The two numbers satisfy the above condition are 3 and 6.

Split the middle term 9x using the two numbers 3 and 6.

= x² + 3x + 6x + 18

Factor by grouping.

= (x² + 3x) + (6x + 18)

= x(x + 3) + 6(x + 3)

= (x + 3)(x + 6)

3. Answer :

= x² + 3x - 18

Multiply the coefficient x², 1 and the constant term -18.

= 1 x (-18)

= -18

Find two numbers such that the product is equal to -18 and the sum is equal to the coeffient of x, 3.

The two numbers satisfy the above condition are -3 and 6.

Split the middle term 3x using the two numbers -3 and 6.

= x² - 3x + 6x - 18

Factor by grouping.

= (x² - 3x) + (6x - 18)

= x(x - 3) + 6(x - 3)

= (x - 3)(x + 6)

4. Answer :

= x² - 2x - 15

Multiply the coefficient x², 1 and the constant term -15.

= 1 x (-15)

= -15

Find two numbers such that the product is equal to -15 and the sum is equal to the coeffient of x, -2.

The two numbers satisfy the above condition are -5 and 3.

Split the middle term -2x using the two numbers -5 and 3.

= x² - 5x + 3x - 15

Factor by grouping.

= (x² - 5x) + (3x - 15)

= x(x - 5) + 3(x - 5)

= (x - 5)(x + 3)

5. Answer :

= x² - 4x + 3

Multiply the coefficient x², 1 and the constant term 3.

= 1 x 3

= 3

Find two numbers such that the product is equal to 3 and the sum is equal to the coeffient of x, -4.

The two numbers satisfy the above condition are -3 and -1.

Split the middle term -4x using the two numbers -3 and -1.

= x² - 3x - x + 3

Factor by grouping.

= (x² - 3x) + (-x + 3)

= x(x - 3) - 1(x - 3)

= (x - 3)(x - 1)

6. Answer :

= 3x² + 10x + 8

Multiply the coefficient x², 3 and the constant term 8.

= 3 x 8

= 24

Find two numbers such that the product is equal to 24 and the sum is equal to the coeffient of x, 10.

The two numbers satisfy the above condition are 3 and 8.

Split the middle term 10x using the two numbers 3 and 8.

= 3x² + 3x + 8x + 8

Factor by grouping.

= (3x² + 3x) + (8x + 8)

= 3x(x + 1) + 8(x + 1)

= (x + 1)(3x + 8)

7. Answer :

= 3x² – 5x – 12

Multiply the coefficient x², 3 and the constant term -12.

= 3 x (-12)

= -36

Find two numbers such that the product is equal to -36 and the sum is equal to the coeffient of x, -5.

The two numbers satisfy the above condition are -9 and 4.

Split the middle term -5x using the two numbers -9 and 4.

= 3x² - 9x + 4x - 12 

Factor by grouping.

= (3x² - 9x) + (4x - 12) 

= 3x(x - 3) + 4(x - 3)

= (x - 3)(3x + 4)

8. Answer :

The quadratic expression x² – 9 can be factored using the following algebraic identity.

a² - b² = (a + b)(a - b)

= x² – 9

= x² – 3²

= (x + 3)(x - 3)

9. Answer :

= 9x² - 49

= 3²x² – 7²

= (3x)² – 7²

= (3x + 7)(3x - 7)

10. Answer :

= (x + 2)² - 25

= (x + 2)² – 5²

= (x + 2 + 5)(x + 2 - 5)

= (x + 7)(x - 3)

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