Question

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Answer 1

well, "Write an equation in which the quadratic expression 2x^2 - 2x - 12 equals 0" really just implies 2x^2 - 2x - 12 = 0 as your equation

when they say "divide each term by the gcf" we can divide every term by the gcf 2, then write a 2 on the outside

Answer 2

2(x^2 - x - 6) = 0 is your "factored form" after the gcf is factored out

then just factor this

Answer 3

as a hint: focus on this part (x^2 - x - 6)

pick two numbers that: add up to -1 and multiply to get -6

Answer 4

that's the factored equation yes

Answer 5

2x^2 - 2x - 12 = 0 should be your starting equation

Answer 6

the values of x that make the equation 2(x^2 - x - 6) = 0 true

Answer 7

first two lines are good

the next pieces of information do not yield any useful information - distributing terms doesn't get us closer to finding what x equals

Answer 8

start with this:

(x^2 - x - 6)

factor this expression. as a hint, find two numbers that add up to -1 and multiply to get -6

Answer 9

awesome, so

2(x-3)(x+2) = 0

what are your solutions for the values of x?

Answer 10

almost

(x+2) = 0 gives us x = -2

so starting from the top:

Answer 11

original equation: 2x^2 - 2x - 12 = 0
factoring out gcf: 2(x^2 - x - 6)
factoring the polynomial: 2(x-3)(x+2) = 0
solving for x: x = 3 and x = -2

meaning: x = 3 and x = -2 are two values that will make the equation true. (I am not sure how detailed they want but you could also mention these are the roots of the quadratic expression)

Answer 12

yes