Factoring Problem Solving

The new thing here is that the quadratic expression is part of an equation, and you're told to solve for the values of the variable that make the equation true.Here's how it works: of those things that we multiplied must also have been equal to zero.

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The product of the second and third of three consecutive integers is 2 more than 13 times the first integer. What are the domain and range of: f(x 5) and f(5) Find the equation of the line through (4,5) parallel to the y-axis Math Student's Civil Rights Oops I did it again!!

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And we have s squared minus 2s minus 35 is equal to 0. So when you do something by grouping, when you factor by grouping, you think about two numbers whose sum is going to be equal to negative 2. So, the fact that this number times that number is equal to zero tells us that either s plus 5 is equal to 0 or-- and maybe both of them-- s minus 7 is equal to 0. And so you have these two equations, and actually, we could say and/or.

Now if this is the first time that you've seen this type of what's essentially a quadratic equation, you might be tempted to try to solve for s using traditional algebraic means, but the best way to solve this, especially when it's explicitly equal to 0, is to factor the left-hand side, and then think about the fact that those binomials that you factor into, that they have to be equal to 0. So you think about two numbers whose sum, a plus b, is equal to negative 2 and whose product is going to be equal to negative 35. So if the product is a negative number, one has to be positive, one has to be negative. So you have s plus 5 times this s right here, right? It could be or/and, either way, and both of them could be equal to 0. Well, we can just subtract 5 from both sides of this equation right there.

Next Lesson: Quadratic Equations When you have a polynomial function of degree two, you have a quadratic function.

When a quadratic function is equated to zero, you have what is called a quadratic equation. How are they formed, how do you graph them, and how do you solve them? At Wyzant, connect with algebra tutors and math tutors nearby. Find online algebra tutors or online math tutors in a couple of clicks. Determine the two numbers if the sum of their reciprocals is 7/18 Suppose that f(x) has a domain of [5,12] and a range of [4,13].

Several previous lessons explain the techniques used to factor expressions.

This lesson focuses on an imporatant application of those techniques - solving equations.

So it will be-- or the product of the binomials, where those will be the a's and the b's. So that would've been a little bit of a shortcut, but factoring by grouping is a completely appropriate way to do it as well.

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