Hello, I have this multinominal and I also have the expanded version of it.
The problem is I cannot understand how the expanded version was achieved.
Can someone please explain it to me. Thanks kindly for any help.
2x^3 + 9x^2 +12x +4
expands to:
(2x+1) (x^2 + 4x +4)
but what is the method ?
Hello, fran1942!
Your language is incorrect and confusing . . .
I have this multinominal and I also have the expanded version of it.
The problem is I cannot understand how the expanded version was achieved.
Can someone please explain it to me. Thanks kindly for any help.
. This is the expanded version!
. .
. This is the factored form!
You are asking how the polynomial was factored, right?
Apply the Rational Roots Theorem and the Remainder Theorem.
If this could be factored as " " then the leading coefficient would be ac and the constant term would be bd. That is, a must be a factor of the leading coefficient, 2, and b must be a factor of the constant term, 4. Further, if is a factor, then (so that ax+ b= 0) would be a zero of the polynomial.
The only possible factors of 2, the only possible values for a, are 2 and 1. The only possible factors of 4, the only possible values of b, are 4, 2, and 1. So the only possible values for are 4/2= 2, 2/2= 1, 1/2. Further, since a sum of positive numbers cannot be 0, any possible rational zero of the polynomial must be one of -2, -1, -1/2 and -4.
For
x= -2, the polynomial is .
So we get an immediate zero, x= -2, and a factor: x-(-2)= x+ 2.
Now, divide by x+ 2:
x+ 2 divides into exactly so we must have
. Repeating that argument on the last factor, or because it is quadratic, using the quadratic formula to find integer zeros, we find that it cannot be factored further in terms of integer coefficients.
(The quadratic formula gives the roots of as so that we can factor into linear terms as .