Factor the following polynomial equation. Then plot the series on the provided graph. y= x^3 -3x^2 -16x -12

Question

Factor the following polynomial equation. Then plot the series on the provided graph.

y= x^3 -3x^2 -16x -12

Answer 1

The key to starting off factoring polynomials is:

Factors of p (coefficient)/factors of q (leading coefficient)

For this problem that would be (factors of 12)/(factors of 1)

This would be (+/-1, +/-2, +/-3, +/-4, +/-6, +/-12)

From here it is a manner of testing each of these by synthetic division. You find that -2 works for a zero. So the factor that gives you this is (x+2)

The results of synthetic division are x²-5x-6. This can be factored to give the remaining 2 factors.

x²-5x-6 = (x-6)(x+1)

So the finished factorization is (x+2)(x-6)(x+1)

To graph this: https://www.desmos.com/calculator