Divide P(x) by g(x)
P(x) $= x^{4} - 3 x^{2} - 4$
g(x) $= x + 2$

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Solution

$p (x) = x^{4} - 3 x^{2} - 4$
$g (x) = x + 2$
Since divisor, we can divide the polynomial by synthetic division.

$∴$ Quotient $: x^{3} - 2 x^{2} + x - 2.$
Hence, the answer is $x^{3} - 2 x^{2} + x - 2.$

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Similar questions

Q. Divide

p (x)

g (x)

in the following case and verify division algorithm.

p (x) = x^{4} - 3 x^{2} - 4; g (x) = x + 2

Q. Divide the polynomial

p (x)

by the polynomial

g (x)

and find the quotient and remainder in each of the following:
(i)

p (x) = x^{3} - 3 x^{2} + 5 x - 3, g (x) = x^{2} - 2

(ii)

p (x) = x^{4} - 3 x^{2} + 4 x + 5, g (x) = x^{2} + 1 - x

(iii)

p (x) = x^{4} - 5 x + 6, g (x) = 2 - x^{2}

Q. Find the remainder when

p (x) = x^{4} - 3 x^{2} + 4 x + 5

, is divided by

g (x) = x^{2} + 1 - x

Question 1 (ii)
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following: $p (x) = x^{4} - 3 x^{2} + 4 x + 5, g (x) = x^{2} + 1 - x$

Q. Apply the division algorithm to find the remainder on dividing

p (x) = x^{4} - 3 x^{2} + 4 x + 5

g (x) = x^{2} + 1 - x .

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Divide P(x) by g(x)P(x) =x4−3x2−4g(x)=x+2

p(x)=x4−3x2−4g(x)=x+2Since divisor, we can divide the polynomial by synthetic division.∴ Quotient :x3−2x2+x−2.Hence, the answer is x3−2x2+x−2.

Divide P(x) by g(x)
P(x) $= x^{4} - 3 x^{2} - 4$
g(x) $= x + 2$

$p (x) = x^{4} - 3 x^{2} - 4$
$g (x) = x + 2$
Since divisor, we can divide the polynomial by synthetic division.

$∴$ Quotient $: x^{3} - 2 x^{2} + x - 2.$
Hence, the answer is $x^{3} - 2 x^{2} + x - 2.$