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

p(x) = x³ - 5x² + 4x - 3 ; g(x) = x – 2

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Solution

In order to check if g(x) is a multiple of p(x), let us check if g(x) is a factor of p(x).

Let, x - 2 = 0

x = 2

p(x) = x³ - 5x² + 4x - 3
p(2) = 2³ - 5(2)² + 4(2) - 3
= 8 - 5(4) + 8 - 3
= 8 - 20 + 8 - 3
= 16 -23
= -7 ≠ 0

Hence, (x - 2) is a not a factor of p(x).

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Similar questions

If $p (x) = x^{3} - 5 x^{2} + 4 x - 3$ and $g (x) = x - 2$ , show that p(x) is not multiple of g(x).

g (x)

p (x)

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

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

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

If $p (x) = 2 x^{3} - 11 x^{2} - 4 x + 5$ and $g (x) = 2 x + 1$ , show that g(x) is not multiple of p(x).

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

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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