If x + 2a is a factor of x⁵ - 4a²x³ + 2x + 2a + 3, find a.

Solution:

Given, the polynomial is x⁵ - 4a²x³ + 2x + 2a + 3

x + 2a is a factor of the polynomial.

We have to find the value of a.

Let p(x) = x⁵ - 4a²x³ + 2x + 2a + 3

Let g(x) = x + 2a

So, g(x) = 0

x + 2a = 0

x = -2a

Put x = -2a in p(x),

Given, g(x) is a factor of p(x).

p(-2a) = x⁵ - 4a²x³ + 2x + 2a + 3 = 0

(-2a)⁵ - 4a²(-2a)³ + 2(-2a) + 2a + 3 = 0

-32a⁵ - 4a²(-8a³) - 4a + 2a + 3 = 0

-32a⁵ + 32a⁵ - 2a + 3 = 0

-2a + 3 = 0

-2a = -3

a = 3/2

Therefore, the value of a is 3/2.

✦ Try This: Find the value of k if (x-2)is a factor of polynomial p(x) = 2x³ - 6x² + 5x + k.

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

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NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 20

If x + 2a is a factor of x⁵ - 4a²x³ + 2x + 2a + 3, find a

Summary:

The process of factoring polynomials involves expressing the polynomial as the product of its factors. If x + 2a is a factor of x⁵ - 4a²x³ + 2x + 2a + 3, the value of a is 3/2

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