Question

If x^3 -hx^2+kx-9 has a factor of x^2 +3, then what are the values of h and k?

Answer 1

Answer:

h= 3 and k= 3

Step-by-step explanation:

If x^3 -hx^2+kx-9 has a factor of x^2 +3, then what are the values of h and k?

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One of the factors is x^2+3, then the other factor will be ax+b

It is easy to find out that:

• a=1  (since x^2*ax=x^3 )

and

• b=-3 (since 3b=-9)

Then the factors are:

• x^2+3 and x-3

When multiplied we get:

• (x^2+3)(x-3)=x^3-3x^2+3x-9

Compare this with the given:

• x^3 -hx^2+kx-9=x^3-3x^2+3x-9

To get:

• h= 3 and k=3

Answer is h= 3 and k= 3