Question

find the vlaue of k if x-1 is the factor of p(x)=4x^3+3x^2-4x+k

Answer 1

Answer:

k = -3

Step-by-step explanation:

P(x) = 4x³+3x²-4x+k

g(x) = x-1

∴ P(1) = 4(1)³+3(1)²-4(1)+k  = 0

         = 4+3-4+k = 0

         = k = -3  

Answer 2

Solution :

The given polynomial is

  p(x) = 4x³ + 3x² - 4x + k

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

  p(1) = 0

  ⇒ 4 (1)³ + 3 (1)² - 4 (1) + k = 0

  ⇒ 4 + 3 - 4 + k = 0

  ⇒ k = - 3

Therefore, the value of k is (- 3)

••• Extra •••

  Let's factorize the given polynomial with the value of k = - 3

Then, p(x) = 4x³ + 3x² - 4x - 3

  = 4x³ - 4x + 3x² - 3

  = 4x (x² - 1) + 3 (x² - 1)

  = (x² - 1) (4x + 3)

  = (x + 1) (x - 1) (4x + 3) ,

which is the factorization of the given polynomial p(x)