Find all values of k such that f(x) = kx^3 + x^2 + k^2x + 3k2 + 11 is completely divisible by polynomial p(x) = x + 2
I have no idea on how to solve this.
Well, mwok. Let's try synthetic division on this one.
. Since is a factor, then .
Now then, we know the remainder should be 0, so....Code:-2 | k 1 k^2 3k^2 +11 -2k 4k-2 -2k^2-8k+4 ------------------------------------ k -2k+1 k^2+4k-2 k^2-8k+15
Solve for the two possible values of k and you're done.
There are only 3 terms with an x in them. In those 3 terms, whatever has been multiplied by x is a coefficient. Any other terms (without x) would constitute the constant.
a is the coefficient of the quadratic term.
b is the coefficient of the linear term.
c is the constant.
It just so happens that the c in your function is , but a constant none the less.
Not so. Your attachment is incorrect. Review Synthetic Division
Hello, mwok
We are expected to know this theorem:Find all values of such that is divisible by
. . If , then is a factor of .
For this problem, if , then is a factor of
We have: .
. . which simplifies to: .
. . which factors: .
. . and has roots: .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
If you dare, you can try Long Division . . .
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If the division "comes out even", then the remainder is zero.
So we have: .