Question

$find \: the \: value \: of \: k \: if \: the \: division \: of \: kx ^{3} + 9x ^{2} + 4x - 10 \: by \: x + 3 \: leaves \: a \: remainder \: - 22$
Answer is k = 3 , but I want solution

Most satisfying answer will mark as brainliest.

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Answer 1

Given

$k {x}^{3} + 9 {x}^{2} + 4x - 10$

is divided by

$(x + 3)$

leaves the remainder -22

To find:

Value of k

Explanation:

let f(x)=kx³+9x²+4x-10

$x + 3 = 0 \\ = > x = - 3$

When x=-3 is substituted f(x)=-22

Substituting x=-3 in f(x)

$\underline {\sf f(-3)=-22}$

$= > k {( - 3)}^{3} + 9 {( - 3)}^{2} + 4( - 3) - 10 = - 22$

$= > - 27k + 9(9) + 4( - 3) - 10 = - 22$

$= > - 27k + 81 - 12 - 10 = - 22$

$= > - 27k + 59 = - 22$

$= > - 27k = - 22 - 59 = - 71$

$= > k = 3$

Therefore

$\huge \underline{\sf k=3}$

Some more information:

↔What is a polynomial?

➡️A polynomial is an expression consisting of variables and coefficients

➡Types of polynomials are monomial,binomial,and etc

Answer 2

ANSWER:-

Given:

kx³ + 9x² +4x-10 by x+3 is a Factor.

Remainder: -22

To find:

The value of k.

Solution:

Let p(x)= kx³ +9x² +4x-10

According to the question:

p(x) leaves the remainder is -22 when divided by (x+3).

=) x+3 =0

=) x= -3

Therefore,

➨p(-3)=k(-3)³ + 9(-3)² + 4(-3)- 10= -22

➨p(-3)=k(-27) + 9(9) + (-12) - 10= -22

➨p(-3)= -27k + 81 - 12 - 10= -22

➨p(-3)= -27k +81 -22= -22

➨p(-3)= -27k + 59= -22

➨p(-3)= -27k = -22 - 59

➨p(-3)= -27k= -81

➨p(-3)= k= -81/-27

Therefore,

➨k= 3

Thus,

The value of k is 3.

Hope it helps ☺️