Question

Factor: x2 + 12x + 35 *
O (x+5)(x+7)
(x+7)(x-5)
O (x+4)(x+3)
O Prime

Answer 1

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`x {}^(2) + 12x + 35`

`x {}^(2) + 7x + 5x + 35`

`x(x + 7) + 5(x + 7)`

`(x + 5)(x + 7)`

Answer 2

(x+5)(x+7)

Explanation:

We need to find two binomials of the form (x+a) and (x+b) such that their product gives
`x^2+12x+35`

So, notice that the values for "a" and for "b" in the binomials to factor should verify that :

1) a * b = 35

and 2) a+b = 12

Since the product (x+a) times (x+b) =
`x^2+ax+bx+a*b= x^2+(a+b)x +a*b`

The pair of values 7 and 5 satisfy such conditions.

Therefore (x+5) (x+7) =
`x^2+12x+35`

and then (x+5) and (x+7) are binomial factors of the original trinomial.