Question

I need help seeing what I did wrong

Answer 1

Answer:  The two roots are x = 3/2 and x = -2

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Explanation:

You have the right idea so far. But the two numbers should be 3 and -4 since

• 3*(-4) = -12
• 3+(-4) = -1

The -1 being the coefficient of the x term.

This means you need to change the -3x and 4x to 3x and -4x respectively. The other inner boxes are correct.

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Refer to the diagram below to see one way to fill out the box method, and that helps determine the factorization.

If we place a 2x to the left of -2x^2, then we need an -x up top because 2x*(-x) = -2x^2

Then based on that outer 2x, we need a -2 up top over the -4x. That way we get 2x*(-2) = -4x

So we have the factor -x-2 along the top

The last thing missing is the -3 to the left of 3x. Note how -3*(-x) = 3x in the left corner and -3*(-2) = 6 in the lower right corner.

We have the factor 2x-3 along the left side.

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The two factors are (2x-3) and (-x-2) which leads to the factorization (x+3)(-x+2)

The last thing to do is set each factor equal to 0 and solve for x

• 2x-3 = 0 solves to x = 3/2 = 1.5
• -x-2 = 0 solves to x = -2

The two roots are x = 3/2 and x = -2