FACTORING QUADRATIC EXPRESSIONS EXAMPLES

Example 1 :

Factor the following :

(i)  x² + 10x + 24

Solution :

In the quadratic expression above, the coefficient of x² is 1.

Decompose the constant term +24 into two factors such that the product of the two factors is equal to +24 and the addition of two factors is equal to the coefficient of x, that is +10. 

Then, the two factors of +24 are 

+4 and +6

Factor the given quadratic expression using +4 and +6. 

x² + 10x + 24  =  (x + 4)(x + 6)

Therefore, the factors of the given quadratic expression are

(x + 4) and (x + 6)

(ii)  z² + 4z - 12

Solution :

In the quadratic expression above, the coefficient of z² is 1.

Decompose the constant term -12 into two factors such that the product of the two factors is equal to -12 and the addition of two factors is equal to the coefficient of z, that is +4. 

Then, the two factors of -12 are 

-2 and +6

Factor the given quadratic expression using -2 and +6. 

z² + 4z - 12  =  (z - 2)(z + 6)

Therefore, the factors of the given quadratic expression are

(z - 2) and (z + 6)

(iii)  p² - 6p - 16

Solution :

In the quadratic expression above, the coefficient of p² is 1.

Decompose the constant term -16 into two factors such that the product of the two factors is equal to -16 and the addition of two factors is equal to the coefficient of p, that is -6. 

Then, the two factors of -16 are 

-8 and +2

Factor the given quadratic expression using -8 and +2. 

p² - 6p - 16  =  (p - 8)(p + 2)

Therefore, the factors of the given quadratic expression are

(p - 8) and (p + 2)

(iv)  t² - 17t + 72

Solution :

In the quadratic expression above, the coefficient of t² is 1.

Decompose the constant term +72 into two factors such that the product of the two factors is equal to +72 and the addition of two factors is equal to the coefficient of t, that is -17. 

Then, the two factors of +72 are 

-8 and -9

Factor the given quadratic expression using -8 and -9. 

t² - 17t + 72  =  (t - 8)(t - 9)

Therefore, the factors of the given quadratic expression are

(t - 8) and (t - 9)

(v)  y² - 16y - 80

Solution :

In the quadratic expression above, the coefficient of y² is 1.

Decompose the constant term -80 into two factors such that the product of the two factors is equal to -80 and the addition of two factors is equal to the coefficient of y, that is -16. 

Then, the two factors of -80 are 

-20 and +4

Factor the given quadratic expression using -20 and +4. 

y² - 16y - 80  =  (y - 20)(y + 4)

Therefore, the factors of the given quadratic expression are

(y - 20) and (y + 4)

(vi)  a² + 10a - 600

Solution :

In the quadratic expression above, the coefficient of a² is 1.

Decompose the constant term -600 into two factors such that the product of the two factors is equal to -600 and the addition of two factors is equal to the coefficient of a, that is +10. 

Then, the two factors of -600 are

+30 and -20

Factor the given quadratic expression using +30 and -20. 

a² + 10a - 600  =  (a + 30)(a - 20)

Therefore, the factors of the given quadratic expression are

(a + 30) and (a - 20)

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