# Factoring quadratics

11 videos

8 skills

Just saying the word "quadratic" will make you feel smart and powerful. Try it. Imagine how smart and powerful you would actually be if you know what a quadratic is. Even better, imagine being able to completely dominate these "quadratics" with new found powers of factorization. Well, dream no longer.
This tutorial will be super fun. Just bring to it your equation solving skills, your ability to multiply binomials and a non-linear way of thinking!

### More examples of factoring quadratics with a leading coefficient of 1

VIDEO
16:30 minutes

Can't get enough of Sal factoring simple quadratics? Here's a handful of examples just for you!

### Example 1: Factoring quadratics with a leading coefficient of 1

VIDEO
4:20 minutes

Factor x^2-14x+40 as (x-4)(x-1) and x^2-x-12 as (x+3)(x-4).

### Factoring quadratics with a leading coefficient of 1

PRACTICE PROBLEMS

Use the "sum-product" form to factor quadratics of the form x^2+bx+c.

### Solving a quadratic equation by factoring

VIDEO
6:22 minutes

U09_L2_T2_we1 Solving Quadratic Equations by Factoring.avi

### Recognizing a perfect square quadratic

VIDEO
3:19 minutes

U09_L2_T2_we2 Solving Quadratic Equations by Factoring 2.avi

### Solving quadratics by factoring

PRACTICE PROBLEMS

Factor quadratics to find the x-intercepts. Solve a polynomial by factoring.

### Example 1: Factoring trinomials with a common factor

VIDEO
5:01 minutes

Factoring trinomials with a common factor

### Factoring polynomials using quadratic methods

PRACTICE PROBLEMS

Factor polynomials that can be factored as the product of a monomial and a quadratic expression, then further factor the quadratic expression.

### Solving quadratics by factoring 2

PRACTICE PROBLEMS

Solve quadratics by factoring, where the leading coefficient is not 1

### Example 1: Factoring a difference of squares with two variables

VIDEO
1:49 minutes

Factor x^2-49y^2 as (x+7y)(x-7y).

### Factoring simple special products

PRACTICE PROBLEMS

Factor quadratic expressions into the special products of the general forms (x+a)^2, (x-a)^2, and (x+a)(x-a).

### Example 6: Factoring a difference of squares with two variables

VIDEO
2:30 minutes

Factor 49x^2-49y^2 as (7x+7y)(7x-7y) or as 49(x+y)(x-y).

### Factoring differences of squares

PRACTICE PROBLEMS

Factor quadratic expressions of the general difference of squares form: (ax)^2-b^2. The factored expressions have the general form (ax+b)(ax-b).

### Example 2: Factoring a difference of squares with leading coefficient other than 1

VIDEO
2:23 minutes

Factor 45x^2-125 as 5(3x+5)(3x-5).

### Making use of structure 2 - Factoring polynomials with special product forms

PRACTICE PROBLEMS

Factor "advanced" polynomials (i.e. polynomials of various degrees and or with two variables) using special product factorization methods.

### Example 3: Factoring quadratics by taking a common factor and grouping

VIDEO
4:46 minutes

Factor 35k^2+100k-15 as 5(k+3)(7k-1)

### Example 4: Factoring quadratics by taking a negative common factor and grouping

VIDEO
5:17 minutes

Factor -12f^2-38f+22 as -2(2f-1)(3f+11).

### Factoring quadratics with a leading coefficient other than 1

PRACTICE PROBLEMS

Use the grouping method to factor quadratics of the form ax^2+bx+c.