Question

question 4 of 10
factor the trinomial below.
$x^2 - 2x - 35$

a. $(x + 5)(x + 7)$
b. $(x - 5)(x - 7)$
c. $(x + 5)(x - 7)$
d. $(x - 5)(x + 7)$

Explanation:

Step1: Recall factoring trinomial \(x^2 + bx + c\)

We need two numbers that multiply to \(c=-35\) and add to \(b = -2\).

Step2: Find the two numbers

Let the numbers be \(m\) and \(n\). So \(m\times n=-35\) and \(m + n=-2\). The numbers are \(5\) and \(-7\) since \(5\times(-7)=-35\) and \(5+(-7)=-2\).

Step3: Factor the trinomial

Using the numbers, we can factor \(x^2-2x - 35=(x + 5)(x-7)\) (because when we expand \((x + 5)(x-7)=x^2-7x+5x - 35=x^2-2x-35\)).

Answer:

C. \((x + 5)(x - 7)\)