Shakir asked in Science & MathematicsMathematics · 10 months ago

Use the Division Algorithm and synthetic division to express the polynomial function

P(x) = 7x^3 − 40x^2 − 9x − 18

in the form (divisor)(quotient) + remainder for the divisor.

x − 6

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• 10 months ago

P(x) = (x - 6)(7x² + 2x + 3) + 0

• ?
Lv 7
10 months ago

(See below for work and solution)

• 10 months ago

You need to *divide* the first polynomial (P(x)) by the binomial (x-6) using synthetic division. You seem to be multiplying.

When dividing a 3rd-degree polynomial by a 1st-degree polynomial, you would expect the result to be a 2nd-degree polynomial, not a 4th-degree polynomial.

Synthetic division:

7x^3 - 40x^2 - 9x - 18 --> coefficients 7, -40, -9, -18

x - 6 --> (x - 6) = 0 --> x = 6 --> divisor 6

6 | 7 . -40 . -9 . -18

.. | . . . 42 . 12 . 18

.. ------------------------

.... 7 . . . 2 . 3 | . . 0 <-- remainder

....^ coefficients

The resulting polynomial has coefficients of 7, 2, 3 with no remainder