Question

If x+k is a factor of polynomial x3 + kx2-2x+k+5 then find the value of k

Answer 1

Value of k is -5/3.

Given:

• A polynomial ${x}^{3} + k {x}^{2} - 2x + k + 5$
• A factor (x+k) of given polynomial.

To find:

• Find the value of k.

Solution:

Theorem to be used:

Factor theorem: If x-a is a factor of polynomial p(x) degree of polynomial is greater or equal to 1, then p(a)=0.

Step 1:

Find value of x from factor.

$x + k = 0$

or

$\bf x = - k$

Step 2:

Put value of x in polynomial and apply factor theorem.

${( - k)}^{3} + k {( - k)}^{2} - 2( - k) + k + 5 = 0$

or

$- {k}^{3} + {k}^{3} + 2k + k + 5 = 0$

or

$3k + 5 = 0$

or

$3k = - 5$

or

$\bf k = \frac{ - 5}{3}$

Thus,

Value of k is -5/3.

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Learn more:

1) if x-3 and x-1/3 are both factors of ax 2+5x+b show that a=b

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2) For what value of ‘b’ is the polynomial x3 – 3x2 + bx – 6 divisible by x-3 ?

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Answer 2

Answer:-

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