Question

6 multiple choice 10 points what is one of the binomials when the expression is written in factored form: $2x^2 - 7x - 15$ $(x + 3)$ $(x + 5)$ $(2x + 3)$ $(2x - 5)$

Explanation:

Step1: Split middle term

Find two numbers that multiply to $2\times(-15)=-30$ and add to $-7$. These numbers are $3$ and $-10$.
Rewrite the expression: $2x^2 -10x +3x -15$

Step2: Group and factor pairs

Group terms: $(2x^2 -10x)+(3x -15)$
Factor out common terms: $2x(x-5)+3(x-5)$

Step3: Factor out binomial

Factor out $(x-5)$: $(2x+3)(x-5)$

Answer:

(2x + 3)