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I forgot how to multiply polynomials and a problem that requires this skill showed up on my hw that it due tomorrow.

TheDeathlyHallows Feb 13, 2019

#1

#5**+1 **

Multiply 4x times each of the terms in the second factor...then multiply 17 times each of the terms in the second factor...

then collect like terms:

4x*3x + 4x * 2 + 17 * (3x) + 17 * 2

12x^2 + 59x + 34 Just be careful when there is a negative sign involved!

ElectricPavlov
Feb 13, 2019

#7**+2 **

I thought I was done and apparently, I have a division problem. (x^2-5x+6)/((2x-1)+(x/2)) is the problem.

TheDeathlyHallows
Feb 13, 2019

#8**+1 **

Hey, DeathlyHallows!

It looks like you want to simplify \(\frac{x^2-5x+6}{\textcolor{red}{2x-1+\frac{x}{2}}}\) . Let's transform all the terms in the denominator such that they all have common denominators; this way, we will be able to add them together.

\(\textcolor{red}{2x-1+\frac{x}{2}}\Rightarrow\textcolor{red}{\frac{4x}{2}-\frac{1}{2}+\frac{x}{2}}\)

Notice that I have not changed the value of the expression; I just created a common denominator. Now, combine like terms.

\(\textcolor{red}{\frac{4x}{2}-\frac{1}{2}+\frac{x}{2}\\ \frac{5x}{2}-\frac{1}{2}\\ \frac{5x-1}{2}}\)

Therefore, \(\frac{x^2-5x+6}{2x-1+\frac{x}{2}}=\frac{x^2-5x+6}{\frac{5x-1}{2}}\) . Now, it is time to simplify.

\(\frac{x^2-5x+6}{\frac{5x-1}{2}}*\frac{2}{2}\\ \frac{2(x^2-5x+6)}{5x-1}\\ \frac{2(x-2)(x-3)}{5x-1}\)

Even after I factored the numerator completely, I did not find any common factors present in both the numerator and the denominator, so this expression is already in simplest form.

TheXSquaredFactor
Feb 16, 2019