Question

find k if x + 3 is a factor x^3+ 3x^2-kx-3​

Answer 1

Let the given polynomial be f(x) = x³ + 3x² - Kx - 3.

Given that x + 3 is a factor of f(3).

In accordance with Factor Theorem,

f(3) = 0

$\longrightarrow$ 3³ + 3(3)² - 3K - 3 = 0

$\longrightarrow$ 27 + 3(9) - 3K - 3

$\longrightarrow$ 3K = 27 + 24

$\longrightarrow$ 3K = 51

$\longrightarrow$ K = 51/3

$\longrightarrow$ K = 17.

For K = 17, (x + 3) is a factor of the above polynomial.

Answer 2

$\sf{Answer}$

Step by step explanation:-

As they given x + 3 is a factor If we substuite that It should be equal to zero because It is a factor of x³+3x²-kx-3

So,

f(x) = x³+3x²-kx-3

f(3) = ?

f(x) = x³+3x²-kx-3

f(3) =0

x³+3x²-kx-3

(3)³ +3(3)²-k(3)-3 =0

27 +27 -3k -3 =0

54-3-3k =0

51 -3k =0

51 = 3k

k = 17

So, value of k is 17

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Know more about cubic polynomial:-

The polynomial whose degree is equal to 3 is called cubic polynomial

It has 3 factors

Its general form is ax³+bx²+cx+d

a is not equal to 0

Graph of cubic polynomial is cubic graph

Relation ship between zeroes &coefficients of cubic polynomial

Let α,ß, γ are roots of cubic polynomial

Sum of roots = -b/a

α, + ß, + γ = -b/a

Sum of product of roots two taken at a time = c/a

αß + ßγ + γα = c/a

Product of roots = -d/a

αßγ = -d/a

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