Question

using factor theorem show that g(x) is a factor of p(x) when p(x)=2x³+7x²- 24x-45,gx=x-1​

Answer 1

Answer:

Step-by-step explanation:

Given polynomial = 2x³ + 7x² - 24x - 45

We have to prove that x-3 is a factor of the given polynomial.

x - 3 = 0

x = 3

Put x  = 3,

         = 2(3)³ + 7(3)² - 24(3) - 45

         = 2(27) + 7(9) - 72 - 45

         = 54 + 63 - 72 - 45

          = 117 - 117

          = 0

As the remainder is 0, x-3 is a factor of the given polynomial.

Hence proved

Answer 2

Correct Question

Using factor theorem show that g(x) is a factor of p(x) when p(x)=2x³+7x²- 24x-45,gx=x-3

Solution

• p(x) = 2x³ + 7x² - 24x - 45
• g(x) = (x - 3)

→ (x - 3) = 0

→ x = 3

Putting the value of x

p(x) = 2x³ + 7x² - 24x - 45

p(x) = 2(3)³ + 7(3)² - 24*3 - 45

p(x) = 2×27 + 7×9 - 72 - 45

p(x) = 54 + 63 - 117

p(x) = 117 - 117

p(x) = 0

Hence, (x - 3) is a of 2x³ + 7x² - 24x - 45

Note

** If f(x) is a polynomial of degree n ≥ 1 and ‘a’ is any real number, then

★ (x-a) is a factor of f(x), if f(a)=0

★ Its converse “ if (x-a) is a factor of the polynomial f(x), then f(a)=0”