What are the factors of this expression?

Question

the quadratic expression x^2+7x+6 is modeled
what are the factors of this expression?
A.(x+3) and (x+2)
B.(x+1) and (x+6)
C.(x-6) and (x-1)
D.(x+5) and (x+1)

Answer 1

The quadratic expression : x² + 7x + 6

Rewrite the factors

x² + x + 6x + 6

Take out common term x and 6

x(x + 1) + 6(x + 1)

Take out common term x + 1

(x + 1)(x + 6)

Therefore B is the right choice.

 

Answer 2

The trinomial is x² + 7x + 6.

Compare the equation x² + 7x + 6 with ax² + bx + c.

a = 1, b = 7 and c = 6.

We need to find two numbers with a sum of  7 (b = 7) and a product of 1 · 6 or 30 (a = 1 and c = 6). Make an organised list of the factors of 6 and look for the pair of factors with the sum of 7.

Factors of 6 | Sum of Factors

      1, 6          |          7

     2 , 3          |          5

The correct factors are m = 1 and n = 6.

The pattern form of x² + 7x + 6

= x² + mx + nx + 6

= x² + 1x + 6x + 6          (Substitute m = 1 and n = 6)

= (x² + 1x) + (6x + 6)    (Group terms with common factors)

= x(x + 1) + 6(x + 1)       (Factor the GCF from each grouping)

= (x + 1)(x + 6)               (x + 1 is the common factor)

The factor form of x² + 7x + 6 = (x + 1)(x + 6).

Option B is correct choice.