How do you factor 5x^3-16x^2-41x-20 given that x – 5 is a factor?

Answer 1

Use synthetic division

Put the zero (x-5=0, so x=5) on the left, and write out the coefficients.

5| 5 -16 -41 -20

⇓ 25 45 20

---------------------

5 9 4 | 0

The "reduced polynomial" is seen in the coefficients under the dashed line.

5x² + 9x + 4

So the answer is:

5x³-16x²-41x-2 = (x-5)(5x²+9x+4) which can be further factored into

5x³-16x²-41x-2 = (x-5)(5x+4)(x+1)