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If (x+2) is a factor of x^3-6x^2+kx+10, k=

Sagot :

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If a polynomial is divisible by [tex]x-a[/tex], then [tex]a[/tex] is a root of this polynomial.
Here (x-a) is equal to x+2:

[tex]x-a=x+2 \\ -a=2 \\ a=-2[/tex]

So -2 is a root of the polynomial. That means x³-6x²+kx+10=0 for x=-2. Now substitute -2 for x in the equation and solve for k:

[tex](-2)^3-6 \times (-2)^2+ k \times (-2)+10=0 \\ -8-6 \times 4-2k+10=0 \\ -8-24-2k+10=0 \\ -2k-22=0 \\ -2k=22 \\ \boxed{k=-11}[/tex]
skydreammer50923

Answer:

k=-11

Step-by-step explanation:

For plato

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