Question

Is x + 9 a factor of the polynomial P(x) = x^3 + 11x^2 + 15x -27? If so, write the polynomial as a product of two factors. If not, explain how you know.

Answer 1

Answer:

(x + 9) (x² + 2x - 3)

Yes, x+9 a factor of p(x)

Step-by-step explanation:

x³ + 11x² + 15x -27 = x² (x + 9) + (2x² + 15x -27)

= x² (x + 9) + (x + 9) (2x - 3)

= (x + 9) (x² + 2x - 3)

Answer 2

Factored form of the polynomial will be (x + 9)(x² + 2x - 3).

   Given in the question,

• Polynomial → P(x) = x³ + 11x² + 15x - 27
• One factor of the given polynomial → (x + 9)

Use synthetic division to find the other factor,

Since, (x + 9) is a factor,

(x + 9) = 0 ⇒ x = -9

So the divisor will be (-9).

-9 |     1     11       15      -27

          -    -9     -18        27

          1     2      -3         0

So the other factor will be (x² + 2x - 3).

       Therefore, factored form of the polynomial will be (x + 9)(x² + 2x - 3).

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