Combine factoring methods in a full chapter dedicated to strategy and method diagnosis.
Common CoreA-SSE.B.3
5 lessons18 short videos4 key concepts, out loud
13.1
Factoring ax^2 + bx + c (a > 1)
Factor when the leading number isn't 1
A-SSE.B.3
Key idea
To factor a quadratic trinomial where the leading coefficient is greater than 1, find two numbers that multiply to ac and add to b, then rewrite the middle term to factor the expression by grouping.
Learn how to factor quadratic trinomials with a leading coefficient greater than 1 by rewriting the middle term and factoring by grouping.
Key concept · Lesson 13.1
Multiply the ends, split the middle
Listen0:00 / 0:22
Transcript. Multiply the two ends: two times three is six. Now find a pair that multiplies to six and adds to seven, the middle number. Six and one. Use them to split seven x, then factor each pair. Both leave the same bracket, and that twin with the two outside pieces gives your factors.
13.2
Factoring Perfect-Square Trinomials
Recognize and factor the square pattern
A-SSE.A.2A-SSE.B.3
Key idea
To factor a perfect-square trinomial, recognize the pattern a^2 + 2ab + b^2 or a^2 - 2ab + b^2 and rewrite it directly as (a + b)^2 or (a - b)^2 after verifying that the middle term is exactly twice the product of the square roots of the first and last terms.
Learn how to spot the special perfect-square trinomial pattern and use a shortcut to factor it instantly into a squared binomial.
Key concept · Lesson 13.2
Check the middle before you shortcut
Listen0:00 / 0:17
Transcript. Both ends being perfect squares is not enough. Take the square root of the first term and of the last, multiply them, then double it. Only if that matches the middle term can you write the two roots in one bracket and square the whole bracket.
13.3
Multi-Step Factoring (GCF First!)
Combine techniques in the right order
A-SSE.B.3
Key idea
To factor a polynomial completely, always look for and extract the greatest common factor (GCF) first, then apply trinomial factoring or special product patterns to the remaining expression.
Learn how to simplify and completely factor complex polynomials by extracting the greatest common factor before applying other factoring methods.
Key concept · Lesson 13.3
Park the GCF outside, then finish
Listen0:00 / 0:18
Transcript. Always take the greatest common factor out first. Park it in front, then keep factoring whatever is left inside the brackets. The most common mistake is doing that inner work perfectly and then dropping the factor you pulled out, so write it into your final answer.
13.4
Choosing a Factoring Strategy
Diagnose which method a polynomial needs
Key idea
To factor any polynomial completely, always check for a greatest common factor (GCF) first, then count the remaining terms to select the correct method: difference of squares for binomials, trinomial methods for three terms, or grouping for four terms.
Learn how to analyze any polynomial by counting its terms to choose the right factoring method and ensure it is factored completely.
Key concept · Lesson 13.4
Count the terms, pick the method
Listen0:00 / 0:24
Transcript. Start every problem the same way: pull out any common factor. Then count the terms that are left. Two terms suggest a difference of squares, but check that it really is one; three terms point to a trinomial method and four terms to grouping. Finish by checking whether any factor still breaks down further.
13.5
Review & Assessment
Complete factoring, mixed
Review, practice, quiz and test
Key idea
Review complete factoring with targeted practice, a practice test, and a chapter test.
This is one chapter of the climb.
Algebra 1 spans 16 chapters, every lesson taught on video with a key concept you can hear, and Vector on hand to answer questions out loud.
