Factor -3x^2+8x+16

Problem

−3*x2+8*x+16

Solution

1. Factor out the negative sign from the entire expression to make the leading coefficient positive.

−1*(3*x2−8*x−16)

2. Identify the coefficients for the quadratic expression a*x2+b*x+c inside the parentheses, where a=3 b=−8 and c=−16

3. Find two numbers that multiply to a⋅c=3⋅(−16)=−48 and add to b=−8 These numbers are −12 and 4

4. Rewrite the middle term −8*x using the two numbers found in the previous step.

−1*(3*x2−12*x+4*x−16)

5. Factor by grouping the terms inside the parentheses.

−1*((3*x2−12*x)+(4*x−16))

6. Extract the greatest common factor from each group.

−1*(3*x*(x−4)+4*(x−4))

7. Factor out the common binomial (x−4)

−1*(3*x+4)*(x−4)

8. Distribute the negative sign back into one of the binomials to simplify the final expression.

(3*x+4)*(4−x)

Final Answer

−3*x2+8*x+16=(3*x+4)*(4−x)

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