Question

if x + 3 is a factor of x³ + kx + 6 , then find the value of k.​

Answer 1

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Answer 2

Answer:

K = -7

Step-by-step explanation:

Given :-

$\implies \sf p(x) = x^3 +kx +6$

$\implies \sf f(x) = x + 3$

To find:-

Value of variable 'k'.

Procedure:-

Finding zero of x + 3.

$\implies \sf x + 3 = 0$

$\implies \sf x = - 3$

Since p(x) = 0,

$\implies \sf (-3)^3 + k(-3) + 6 = 0$

$\implies \sf -27 -3k + 6 = 0$

Combine Like Terms:-

$\implies \sf (-3k) + (-27+6)=0$

$\implies \sf -3k -21 = 0$

Add 21 to both sides:-

$\implies \sf -3k -21 +21 = 0+21$

$\implies \sf -3k = 21$

$\implies \sf -3k = 21$

Divide both sides by -3:-

$\sf \implies \dfrac{-3k}{-3}= \dfrac{21}{-3}$

$\bf{\boxed{\bf{k = -7}}}$

NotE:-

• Polynomial : A variable bases language in maths. or A string of variables and numbers put together.

• Degree of polynomial : Highest power of a polynomial is called degree of polynomial.

• Coefficient : A number by which a variable is multiplied.

• Constant : It's a numerical term holding no variable.