How do you use the remainder theorem to find the remainder for the division $(x^{4} + 5 x^{3} - 14 x^{2}) \div (x - 2)$ $(x^4+5x^3-14x^2)div(x-2)$ ?

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How do you use the remainder theorem to find the remainder for the division $(x^{4} + 5 x^{3} - 14 x^{2}) \div (x - 2)$ $(x^4+5x^3-14x^2)div(x-2)$ ?

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Answer 1 · 2016-09-08T14:37:50

$f (2) = 0$ $f(2) = 0$ There is no remainder.
$x - 2$ $x-2$ is a factor.

Explanation:

If we have $f (x) = x^{4} + 5 x^{3} - 14 x^{2}$ $f(x) = x^4 +5x^3-14x^2$

Let $x - 2 = 0 \to x = 2$ $x-2 = 0 rarr x =2$

The remainder of $x^{4} + 5 x^{3} - 14 x^{2} \div (x - 2)$ $x^4 +5x^3-14x^2 div(x-2)$
is found from $f (2)$ $f(2)$

$f (2) = 2^{4} + 5 {(2)}^{3} - 14 {(2)}^{2}$ $f(2) = 2^4 +5(2)^3-14(2)^2$

= $16 + 40 - 56 = 0$ $16+40-56 =0$

The fact that the remainder is 0, (ie there is no remainder), means that $(x - 2)$ $(x-2)$ is a factor of $x^{4} + 5 x^{3} - 14 x^{2}$ $x^4 +5x^3-14x^2$

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How do you use the remainder theorem to find the remainder for the division $(x^{4} + 5 x^{3} - 14 x^{2}) \div (x - 2)$ $(x^4+5x^3-14x^2)div(x-2)$ ?

1 Answer

Explanation:

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How do you use the remainder theorem to find the remainder for the division (x4+5x3−14x2)÷(x−2)(x^4+5x^3-14x^2)div(x-2)?

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Explanation:

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How do you use the remainder theorem to find the remainder for the division $(x^{4} + 5 x^{3} - 14 x^{2}) \div (x - 2)$ $(x^4+5x^3-14x^2)div(x-2)$ ?