Question

by factor, theorem show that (x+3) and (2x-1) are factors of 2x^2+5x-3

Answer 1

Solution:

Here we need to prove whether (x + 3) and (2x - 1) are factors of the polynomial 2x² + 5x - 3 or not.

So, by applying factor theorem;

g(x) = (x + 3)

⇒ 0 = x + 3

⇒ x = -3

f(x) = 2x² + 5x - 3

Substitute the value of x in this equation.

f(-3) = 2(-3)² + 5(-3) - 3

⇒ f(-3) = 2(9) - 15 - 3

⇒ f(-3) = 18 - 18

⇒ f(-3) = 0

Since the value of f(-3) becomes zero,

∴ (x + 3) is a factor of 2x² + 5x - 3

For proving (2x - 1) is a factor of 2x² + 5x - 3:

g(x) = (2x - 1)

⇒ 0 = 2x - 1

⇒ 2x = 1

⇒ x = 1/2

Substitute the value of x in the given polynomial.

f(x) = 2x² + 5x - 3

⇒ f(1/2) = 2 (1/2)² + 5(1/2) - 3

⇒ f(1/2) = 1/2 + 5/2 - 3

⇒ f(1/2) = 6/2 - 3

⇒ f(1/2) = 3 - 3

⇒ f(1/2) = 0

Since value of f(x) becomes zero,

∴ (2x - 1) is a factor of 2x² + 5x - 3