00:01
Okay, so we look at these problems here.
00:02
What is the reverse process of multiplying polynomials? that is called factoring, which of the following does not represent rational algebraic expressions.
00:11
The only one that's a rational algebraic expression would be d.
00:14
The rest of these are not rational expressions.
00:18
What is a simplified form of 2a minus 4 over a minus 2? so i'm going to start with factoring 2a minus 4 by taking out a common factor of 2.
00:28
Is going to be left with a minus two, and underneath is a minus two.
00:32
So now i have common factors here with the a minus two, a minus two, so my remaining is two.
00:37
What is the factor form of the difference of two squares? so difference of two squares, if these are perfect squares, it's going to be a plus and a minus in between them, so it would be x plus 6y, x minus 6y.
00:50
What is it called as a quotient of two algebraic expressions as p of q as long as q does not equal zero? that is a rational algebraic expression.
00:58
One of the factors of a trinomial is x plus 5 for this trinomial here, x squared plus 12x plus 35.
01:05
So what needs to be there to make it work out? if i focus on the 35 and the 12, 5 times 7 gives me 35, and then also 5 plus 7 gives me 12.
01:15
So this has got to be x plus 7.
01:19
Using grace common monomial factor, we want to factor out of this one.
01:23
The only thing that can come out is 4 because it comes out of both items, both terms.
01:28
So if i do that, there is no common x's so i can't take an x out.
01:33
So i can't do that, but we can take a four out of both of those.
01:36
So we have four times x a third plus six.
01:39
Simplified this, so i have difference of two squares in the numerator.
01:42
So as x plus y, oops, x minus y...