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F(X) = X5 + 3x4 − X3 − 3x2 + 5x + 15, G(X) = X + 3 - Mathematics

Answer in Brief

f(x) = x5 + 3x4 − x3 − 3x2 + 5x + 15, g(x) = x + 3

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Solution

It is given that f(x) = x5 + 3x4 − x3 − 3x2 + 5x + 15 and g(x) = x+3 

By the factor theorem, g(x) is the factor of polynomial f(x).

i.e. x+3 =0

 `f(-3) = (-3)^5 + 3(-3)^4 - (-3)^3 - 3(- 3)^2 + 5(-3) + 15`
(−3) = 0

Hence, g(x) is the factor of polynomial f (x).

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 6 Factorisation of Polynomials
Exercise 6.4 | Q 3 | Page 24
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