Solve. (3 x-2)(x+4)=12 x

Name: Problem 299, Chapter 6: Intermediate Algebra
Uploaded: 2022-09-24T14:44:27-08:00
Channel: Jill Stoner
Description: Solve. (3 x-2)(x+4)=12 x

Key Concepts

Expanding Binomials

This concept involves multiplying two binomials using the distributive property (also known as the FOIL method) to convert the product of expressions into a polynomial. It is a fundamental technique in algebra that helps in simplifying equations by eliminating parentheses.

Combining Like Terms

After expanding expressions, combining like terms is used to simplify the expression further by adding or subtracting coefficients of the same variable powers. This step is essential to reduce the expression to a simpler form, often preparing it for solving a standard equation.

Rearranging to Standard Quadratic Form

This involves moving all terms to one side of the equation so that the equation takes the form ax² + bx + c = 0. This standard form is crucial because it enables the use of systematic techniques such as factoring or applying the quadratic formula to find the roots of the quadratic equation.

Solving Quadratic Equations

Once the quadratic equation is in standard form, it can be solved by methods such as factoring, completing the square, or using the quadratic formula. This process is a core part of algebra and facilitates finding all possible solutions for the variable in the equation.

Transcript

00:01 The directions are to solve this equation by factoring.

00:04 So the first step is to get the equation into standard form, which means get all of the terms on one side of the equal sign and get a zero on the other side.

00:13 So the first step is going to be to multiply the left side out, multiply these two binomials.

00:18 The foil method is usually what we think of when we're doing that.

00:21 So we're going to multiply the first two terms within each group of parentheses first.

00:25 So we're going to take the 3x times x, which is 3x squared, and then we're going to multiply the outer and the inner terms together.

00:35 So the outer would be the 3x times the 4.

00:39 And then the inner terms, inside terms, would be the negative 2 and the x.

00:44 And then those will be like terms so we can combine them together.

00:47 So when we take this 12x and combine it with the negative 2x, we're actually going to end up with a positive 10x as a middle term.

00:56 And then when we multiply the last, the f -o -i -i, is done now we do the l so we're going to multiply the negative 2 and the positive 4 which results in a negative 8 so we get 3x squared plus 10x minus 8 when we use foil on the left side the 8 or the 12x is on the right side so we want to subtract that from both sides so that's going to be a negative 12x here and then a 0 on the right side we still have some like terms that we can combine this positive 10x and negative 12x can be combined into one term, so we're going to make that be a negative 2x.

01:36 So we really have this 3x squared, combining those x terms, we have a negative 2x, and then our constant term is a negative 8.

01:45 So now this is in standard form.

01:48 I'll put s f for standard form.

01:51 So now we're ready to factor the left side, and then we'll just set each of those factors equal to 0 once we have them.

01:57 So this is a trinomial.

02:00 So we're going to look for a greatest common factor.

02:03 There is no greatest common factor between those three terms.

02:07 So now we're going to look for a pair of binomial factors.

02:11 Remember what goes here and here has to multiply to give 3x squared.

02:15 So we're basically doing the reversal foil here.

02:17 So that would be a 3x and an x.

02:21 What goes here and here has to multiply to give this negative 8.