Find the value of a, if x - a is a factor of x³ - ax² + 2x + a - 1

Solution:

Given, the polynomial is x³ - ax² + 2x + a - 1.

Also, x - a is a factor of the given polynomial.

We have to find the value of a.

Let g(x) = x³ - ax² + 2x + a - 1.

x - a = 0

x = a

Put x = a in g(x)

g(a) = 0

(a)³ - a(a)² + 2(a) + a - 1 = 0

a³ - a³ + 2a + a - 1 = 0

3a - 1 = 0

3a = 1

Therefore, a = 1/3

✦ Try This: Find the value of a, if x + 1 is a factor of ax³ + x² - 2x + 4a - 9.

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

NCERT Exemplar Class 9 Maths Exercise 2.3 Sample Problem 2

Find the value of a, if x - a is a factor of x³ - ax² + 2x + a - 1

Summary:

Factors of a number can be referred to as numbers or algebraic expressions that evenly divide a given number/expression. The value of a if x - a is a factor of x³ - ax² + 2x + a - 1 is 1/3

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