Introduce factoring as reverse distribution to build confidence.
Common CoreA-SSE.B.3A-APR.B.3
6 lessons21 short videos5 key concepts, out loud
12.1
Factoring the GCF
Reverse the distributive property
A-SSE.B.3
Key idea
To factor a polynomial by its greatest common factor (GCF), identify the largest integer and the lowest power of any shared variables that divide all terms, then rewrite the expression as the GCF multiplied by the remaining quotient.
Learn how to find the greatest common factor of a polynomial and rewrite the expression as a product, reversing the distributive property.
Key concept · Lesson 12.1
Divide every term by the GCF
Listen0:00 / 0:23
Transcript. Factoring undoes the distributive property. Take the largest number and the lowest power of every shared variable, write that outside the parentheses, then divide each original term by it to fill the inside. When a term is exactly the greatest common factor, it leaves a one behind, never nothing.
12.2
Factoring Trinomials (x^2 + bx + c)
Find two numbers that multiply and add right
A-SSE.B.3
Key idea
To factor a trinomial of the form x^2 + bx + c, find two numbers that multiply to the constant term c and add to the coefficient b, then write the factored expression as (x + p)(x + q).
Learn how to factor trinomials into two binomials by finding a pair of numbers that multiply to the constant term and add to the middle term's coefficient.
Key concept · Lesson 12.2
Multiply to c, add to b
Listen0:00 / 0:19
Transcript. One pair of numbers has to pass two tests at once. They must multiply to the constant term and add to the middle coefficient. A pair that only adds correctly will fail the product test, so settle the signs from the product first, then drop the numbers into the brackets.
12.3
The Diamond / Box Method
An organizer that makes factoring reliable
A-SSE.B.3
Key idea
The Diamond/Box method uses a visual diamond to find two numbers that multiply to the constant term c and add to the linear coefficient b, then places them in a 2x2 grid to systematically factor quadratic trinomials.
Learn how to use a visual diamond and box organizer to break down trinomials and factor them quickly and reliably.
Key concept · Lesson 12.3
Find the pair, then fill the box
Listen0:00 / 0:20
Transcript. The diamond finds the pair, and the box places it. Park x squared in one corner and the constant in the opposite corner, then split the middle term across the other two. Pull a common factor out of every row and column, sign included, and read the brackets off the edges.
12.4
Factoring by Grouping
Factor four-term polynomials in pairs
A-SSE.B.3
Key idea
To factor a four-term polynomial by grouping, split the expression into two pairs, factor out the greatest common factor (GCF) from each pair, and then factor out the resulting common binomial factor.
Learn how to group a four-term polynomial into pairs to find and extract a shared binomial factor.
Key concept · Lesson 12.4
Split in pairs, match the brackets
Listen0:00 / 0:18
Transcript. With four terms, draw a line down the middle and factor each pair on its own. The two brackets that appear must be identical, and that shared bracket then comes out front. If the third term is negative, pull out a negative factor so the second bracket matches.
12.5
Factoring Difference of Squares
a^2 - b^2 = (a + b)(a - b)
A-SSE.A.2A-SSE.B.3
Key idea
To factor a difference of squares, recognize binomials in the form a^2 - b^2 and rewrite them as the product of two binomials with alternating signs, (a + b)(a - b), where the middle terms cancel out.
Learn how to recognize binomials made of two perfect squares separated by a minus sign and factor them instantly using a special algebraic shortcut.
Key concept · Lesson 12.5
Two squares, one minus sign
Listen0:00 / 0:21
Transcript. Two terms, both perfect squares, separated by a minus sign. Take the square root of each term, the number in front included, then write one bracket with a plus and one with a minus. A sum of two squares, like x squared plus nine, cannot be factored at all.
12.6
Review & Assessment
Basic factoring, mixed
Review, practice, quiz and test
Key idea
Review basic 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.
