Question

2. Find the value of k, if x + 5 is the factor of the polynomial.
P(x) = 4x 3 - 16 x2 + kx - 5​

Answer 1

CORRECT QUESTION :-

★ Find the value of k, If x + 5 is a factor of polynomial p(x) = 4x³ - 3 - 16 x² + kx - 5.

GIVEN :-

• x + 5 is a factor of polynomial p(x) = 4x³ - 3 - 16 x² + kx - 5.
• A polynomial p(x) = 4x³ - 3 - 16 x² + kx - 5.

TO FIND :-

• The value of k, If x + 5 is a factor of polynomial p(x) = 4x³ - 3 - 16 x² + kx - 5.

SOLUTION :-

• If x + 5 is a factor of polynomial p(x) = 4x³ - 3 - 16 x² + kx - 5. Then ,

★ x + 5 = 0

★ x = -5.

Now,

→ p(x) = 4x³ - 3 - 16 x² + kx - 5 = 0

→ p(-5) = 4 × (-5)³ - 16 (-5)² + k × (-5) - 5 = 0

→ 4 × (-125) - 16 × 25 + -5k - 5 = 0

→ -500 - 400 - 5 - 5k = 0

→ -900 - 5 - 5k = 0

→ -905 - 5k = 0

→ -5k = 0 + 905

→ -5k = 905

→ k = -905/5

→ k = -181

Hence the required value of k is (-181).

Answer 2

$\underline{\underline{\blue{\textbf{Step - By - Step - Explanation : -}}}}$

To Find :

• We need to find the value of k

Solution :

• x + 5 is a factor of given polynomial 4x³ - 16x² + kx - 5

x + 5 is a factor of given polynomial

x = -5

• Substracting of x in given polynomial

= 4x³ - 16x² + kx - 5

= 4 × (-5)³ - 16 × (-5)² + k × (-5) - 5

= 4 × (-125) - 16 × 25 - 5k - 5

= -500 - 400 - 5k - 5

= - 900 - 5 - 5k

= - 905 - 5k

- 905 - 5k = 0

- 5k = 905

k = 905/-5

k = -181

$\large\dag \large { \red{\underline{\bf{Hence }}}}$

• $\star\boxed{\underline{\pink{\textrm{Value of k = -181}}}}$

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