Question

One root of f(x) = 2x3 + 9x2 + 7x – 6 is –3. Explain how to find the factors of the polynomial.

Answer 1

Step-by-step explanation:

Given f(x) = 2x³ + 9x² + 7x – 6

Also given that -3 is a root, which means (x+3) is a factor of f(x).

In order to find the other factors, we need to divide f(x) by (x-3)

or  (2x³ + 9x² + 7x – 6) /  (x-3)

you can either use long division or synthetic division to perform this division, either way, you will end up with :

(2x³ + 9x² + 7x – 6) /  (x-3) = (2x² + 3x -2) which is also a factor of f(x)

Hence f(x) can be expressed

f(x) = 2x³ + 9x² + 7x – 6 = (x-3)(2x² + 3x -2)

We notice that for (2x² + 3x -2) you can further factor this using quadratic factoring (or your choice of method to solve quadratic equations).

By factoring, (2x² + 3x -2) = (2x-1) (x+2)

hence f(x) = (x-3)(2x² + 3x -2) = (x-3)(2x-1)(x+2)

Answer 2

Answer:

Identify the factor x+3 from the given root -3.

Use synthetic division to divide the polynomial by x+3.

Uses the bottom row of the synthetic division as coefficients in the quadratic 2x^2+3x-2.

Factor the quotient to find the two other factors: x+2 and 2x-1.

Step-by-step explanation:

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