Given the polynomial P(x) = 2x3 - x2 - 13x – 6 and one of its factors: x + 2.?

Question

Given the polynomial P(x) = 2x^3 - x^2 - 13x – 6 and one of its factors: x + 2.

a. How many zeros will there be? How do you know that?

b. Find the remaining factors of the polynomial.

c. Please explain in words how you found the others.

Answer 1

a. The number of zeros is equal to the highest exponent in the equation. In your equation, the highest exponent x is raised to is 3, so there are 3 factors.

b. For this, divide the polynomial by x+2, either by synthetic or long division. Then factor the resulting polynomial, either by factoring or the quadratic formula. Another way would be to plug your polynomial into a graphing calculator and find each place the graph crosses the x axis, and write down the x coordinate for each one.

c. Refer to 'b' and write down what you did.

I hope I helped!