What is the remainder when x³ + 3x² +5x + 1 is divided by x + 3?. Created by DRAGONGIRL9271. Math

What is the remainder when x³ + 3x² +5x + 1 is divided by x + 3?...

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October 2022 1 3 Report

What is the remainder when x³ + 3x² +5x + 1 is divided by x + 3?

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✏️REMAINDER THEOREM

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$\underline{\mathbb{PROBLEM:}}$

What is the remainder when (x³ + 3x² + 5x + 1) is divided by (x + 3)?

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$\underline{\mathbb{ANSWER:}}$

$\qquad\LARGE\rm» \:\: \green{P(\text-3)=\text-14}$

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$\underline{\mathbb{SOLUTION:}}$

- Represent the polynomial function as P(x) and let (x + 3) equate to zero. The value of P(-3) be the remainder.

$\rm P(x) = {x}^{3} + {3x}^{2} + 5x + 1 \: \: ; \: \: x = \text - 3$

$\rm P( \text - 3) =( \text - 3)^{3} + 3( \text - 3)^{2} + 5( \text - 3) + 1$

$\rm P( \text - 3) =\text - 27 + 3(9) + 5( \text - 3) + 1$

$\rm P( \text - 3) =\text - 27 + 27 + ( \text - 15) + 1$

$\rm P( \text - 3) =\text - 15 + 1$

$\rm P( \text - 3) =\text - 14$

$\therefore$ The remainder after dividing polynomial into (x + 3) is -14.

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✏️REMAINDER THEOREM

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