Question

Which expression is a factor of both x^2 − 9 and x^2 + 8 x + 15

Answer 1

x + 3

Explanation:

x² - 9 ← is a difference of squares and factors as

x² - 9 = (x - 3)(x + 3)

To factor x² + 8x + 15

Consider the factors of the constant term (+ 15) which sum to give the coefficient of the x- term (+ 8)

The factors are + 5 and + 3, since

5 × 3 = 15 and 5 + 3 = 8, thus

x² + 8x + 15 = (x + 5)(x + 3)

Thus the factor (x + 3) is common to both

Answer 2

x+3

Explanation:

1. Use formula for the difference of squares:

`a^2-b^2=(a-b)(a+b)`

to factor

`x^2-9=(x-3)(x+3).`

2. Factor
`x^2+8x+15:`

`x^2+8x+15=x^2+3x+5x+15=x(x+3)+5(x+3)=(x+3)(x+5).`

Now you can see that
`x+3` is the common factor.