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Factoring quadratics Video transcript In this video I want to do a bunch of examples of factoring a second degree polynomial, which is often called a quadratic. Sometimes a quadratic polynomial, or just a quadratic itself, or quadratic expression, but all it means is a second degree polynomial.
So something that's going to have a variable raised to the second power. In this case, in all of the examples we'll do, it'll be x. So let's say I have the quadratic expression, x squared plus 10x, plus 9. And I want to factor it into the product of two binomials. How do we do that?
Well, let's just think about what happens if we were to take x plus a, and multiply that by x plus b. If we were to multiply these two things, what happens? Well, we have a little bit of experience doing this. This will be x times x, which is x squared, plus x times b, which is bx, plus a times x, plus a times b-- plus ab.
Or if we want to add these two in the middle right here, because they're both coefficients of x.
We could right this as x squared plus-- I can write it as b plus a, or a plus b, x, plus ab. So in general, if we assume that this is the product of two binomials, we see that this middle coefficient on the x term, or you could say the first degree coefficient there, that's going to be the sum of our a and b.
And then the constant term is going to be the product of our a and b. Notice, this would map to this, and this would map to this. And, of course, this is the same thing as this. So can we somehow pattern match this to that?
Is there some a and b where a plus b is equal to 10? And a times b is equal to 9? Well, let's just think about it a little bit. What are the factors of 9? What are the things that a and b could be equal to?
And we're assuming that everything is an integer. And normally when we're factoring, especially when we're beginning to factor, we're dealing with integer numbers.
So what are the factors of 9? They're 1, 3, and 9. Now, if it's a 3 and a 3, then you'll have 3 plus that doesn't equal So it does work. So a could be equal to 1, and b could be equal to 9.
So we could factor this as being x plus 1, times x plus 9.
And if you multiply these two out, using the skills we developed in the last few videos, you'll see that it is indeed x squared plus 10x, plus 9.
So when you see something like this, when the coefficient on the x squared term, or the leading coefficient on this quadratic is a 1, you can just say, all right, what two numbers add up to this coefficient right here?
And those same two numbers, when you take their product, have to be equal to 9. And of course, this has to be in standard form. Or if it's not in standard form, you should put it in that form, so that you can always say, OK, whatever's on the first degree coefficient, my a and b have to add to that.
Whatever's my constant term, my a times b, the product has to be that. Let's do several more examples. I think the more examples we do the more sense this'll make.
Let's say we had x squared plus 10x, plus-- well, I already did 10x, let's do a different number-- x squared plus 15x, plus And we want to factor this.
We have an x squared term. We have a first degree term. This right here should be the sum of two numbers. And then this term, the constant term right here, should be the product of two numbers.The tutorial shows a few ways to Vlookup multiple values in Excel based on one or more conditions and return multiple matches in a column, row or single cell.
When using Microsoft Excel for data analysis, you may often find yourself in situations when you need to get all matching values for a. Aug 20, · 1.y minus 12 leslutinsduphoenix.com product of 15 and c leslutinsduphoenix.com quiotient of 17 and k leslutinsduphoenix.com sum of v and 3 5a number t divided by 82 6the sum of 13 and twice a number h more than the product of 5 and n minutes the quotient of 3 and vStatus: Resolved.
In this video I want to do a bunch of examples of factoring a second degree polynomial, which is often called a quadratic. Sometimes a quadratic polynomial, or just a quadratic itself, or quadratic expression, but all it means is a second degree polynomial. Match each phrase with an expression.
The product of a number and 3 n ÷ 3 A number y minus 75 Section Writing Expressions 13 Write the phrase as an expression. Then evaluate when x = 5 and y = 3 less than the .
Write an algebraic expression for the word expression. 1./the sum of X and 9 2./6 more than the difference of B and 5 3./The sum of 15 and the product of 5 and V5/5(1). Click on Submit (the arrow to the right of the problem) and scroll down to “Find the Angle Between the Vectors” to solve this problem.
You can also type in more problems, or click on the 3 dots in the upper right hand corner to drill down for example problems.