Find the difference between $P (x) = x^{4} - {3 x}^{2} + 4 x + 5, g (x) = x^{2} + 1 - x$

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Solution

$P (x) - g (x) = x^{4} - 3 x^{2} + 4 x + 5 - x^{2} - 1 + x$

$= x^{4} - 4 x^{2} + 5 x + 4$

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Similar questions

Q. Divide

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

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

Q. Find the remainder when

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

, is divided by

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

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. 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 .

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

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Find the difference between P(x)=x4−3x2+4x+5,g(x)=x2+1−x

P(x)−g(x)=x4−3x2+4x+5−x2−1+x=x4−4x2+5x+4

Find the difference between $P (x) = x^{4} - {3 x}^{2} + 4 x + 5, g (x) = x^{2} + 1 - x$

$P (x) - g (x) = x^{4} - 3 x^{2} + 4 x + 5 - x^{2} - 1 + x$

$= x^{4} - 4 x^{2} + 5 x + 4$