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Factorisation of a Polynomial

check whether...

Question

check whether g(x) is a factor of p(x)

p(x)= 8x³-6x²-4x+3

g(x)= x/3-1/4

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Solution

p(x)= 8x³-6x²-4x+3
g(x)= x/3-1/4
that is, x=3/4
put value of x in p(x)
p(3/4)=8(27/64)-6(9/16)-4*(3/4)+3
=(27/8)-(27/8)-3+3
=0
therefore g(x) is a factor of p(x)

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Q. Question 15
Check whether p(x) is a multiple of g(x) or not:

(i)

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

p (x) = 2 x^{3} - 11 x^{2} - 4 x + 5, g (x) = 2 x + 1

Check whether p(x) is a multiple of g(x) or not :

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

Q. Question 14
By Remainder theorem, find the remainder when p(x) is divided by g(x).

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

p (x) = x^{3} - 3 x^{2} + 4 x + 50, g (x) = x - 3

p (x) = 4 x^{3} - 12 x^{2} + 14 x - 3, g (x) = 2 x - 1

p (x) = x^{3} - 6 x^{2} + 2 x - 4, g (x) = 1 - \frac{3}{2} x

Q. Question 14
By Remainder theorem, find the remainder when p(x) is divided by g(x).

(i)

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

p (x) = x^{3} - 3 x^{2} + 4 x + 50, g (x) = x - 3

p (x) = 4 x^{3} - 12 x^{2} + 14 x - 3, g (x) = 2 x - 1

p (x) = x^{3} - 6 x^{2} + 2 x - 4, g (x) = 1 - \frac{3}{2} x

Q. Question 15
Check whether p(x) is a multiple of g(x) or not:

(i)

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

p (x) = 2 x^{3} - 11 x^{2} - 4 x + 5, g (x) = 2 x + 1

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Factorisation of a Polynomial

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