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If x + 1 is a factor of ax³ + x² - 2x + 4a - 9, find the value of a.

Solution:

Given, x + 1 is a factor of ax³ + x² - 2x + 4a - 9.

We have to find the value of a.

Let the polynomial be p(x) = ax³ + x² - 2x + 4a - 9

Let the factor of g(x) = x + 1

Let g(x) = 0

x + 1 = 0

x = -1

Substitute x = -1 in p(x),

Since g(x) is a factor of p(x), p(-1) = 0

p(-1) = ax³ + x² - 2x + 4a - 9 = 0

a(-1)³ + (-1)² - 2(-1) + 4a - 9 = 0

-a + 1 + 2 + 4a - 9 = 0

-a + 4a - 9 + 3 = 0

3a - 6 = 0

3a = 6

a = 6/3

a = 2

Therefore, the value of a is 2.

✦ Try This: Find the value of m, so that 2x -1 be a factor of 8x⁴ +4x³ -16x² +10x+7.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2

NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 22

If x + 1 is a factor of ax³ + x² - 2x + 4a - 9, find the value of a

Summary:

Factorization of polynomials is the process by which we decompose a polynomial expression into the form of the product of its irreducible factors, such that the coefficients of the factors are in the same domain as that of the main polynomial. If x + 1 is a factor of ax³ + x² - 2x + 4a - 9, the value of a is 2

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