Please help me matching and explain me the procedure of each one. Thank you

Question

Match each quadratic expression to its factored form.

2x^2+7x-15 A.(2x-3)(x+10)

2x^2+4x-30 B.(2x-3)(x+5)

2x^2+17x-30 C.2(x-3)(x+5)

Answer 1

factoring is just the reverse method of foiling (First, Outside, Inside ,Last)

You do this by finding combinations of numbers that will yeild the factors given, that when you foil them back give the original formulation.

for example 2x^2+4x-30

pull a 2 out of each term

2(x² + 2x - 15)

now factor the parenthesis. what two numbers MULTIPLY to get -15 and ADD to get 2. ou should see thats 5 and 3

( x 3) (x 5)

no we decide where to put the signs, because I need the 15 to be negative and the 2 to be positive. So to make this happen we get

( x - 3) (x + 5)

so final answer is 2( x - 3) (x + 5)