Introduction to Factoring

Review of distribution and intro to factoring

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Hey there! Remember distribution?

• Distribution says if you have a value outside of some parentheses where other numbers are being added, you ccan multiply the outside value by each term inside.

• EX: 3x(5x+4) says multiply 3x by everything on the inside (5x+4)

• We learned two different methods of distributing: the traditional way and the box method

Multiple Choice

-4(8r + 3)

• -32r - 12

• 32r - 12

• -32r + 12

• 32r + 12

Multiple Choice

Multiply

Multiple Choice

Multiply

Multiple Choice

Multiply

Multiple Choice

Multiply

Multiple Choice

What is the simplified version of this expression? $$9\left(-5x+8\right)$$  

• $$45x-72$$  

• $$45x+72$$  

• $$-45x-72$$  

• $$-45x+72$$  

Factoring is a super simple idea! Factoring is the idea that we can undo the process of distribution . . . Even if we don't know what was ditributed in.

We do this by "pulling" the greatest common factors out of expressions and bringing them to the front.

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If you are strugglling to find which number factors out you need to get a better understanding of a greatest common factor

If you are having an easy time finding the numbers in common feel free to skip this slide

Multiple Choice

Factor:

p² - 14p

• p(1 - 14)

• 2p(p - 7)

• p²(1-14)

• p(p - 14)

Multiple Choice

Factor completely.

12x²y⁴ - 6xy

• 3xy (4xy³ - 2)

• 6xy (2xy³ - 1)

• 6xy (2x³y⁵ - x²y²)

• 6xy ( 2xy³)

Multiple Choice

Factor completely.

16xy - 24y

• 4y (4x - 6)

• 8y (2xy - 3y)

• 8y (2x - 3)

• 2xy (8 - 12y)

Multiple Choice

Factor using GCF or monomial factoring:

2n²-8n³

• 2n²(n-4n²)

• 2n²(1-4n)

• 2n³(10-8n²)

• 3n(1-4n)

Multiple Choice

Factor out the GCF

18x³ + 81x - 27

• 9x (2x² + 9x - 3)

• 3 (6x³ + 27x - 9)

• 9 (2x³ + 9x - 3)

• 9 (2x² + 9x - 3)

Multiple Choice

Factor out the GCF:

a³ + a² + a

• a²(a + a + 1)

• a³(1 + a + a)

• a(a² + a + 1)

• a(a² + a)

Multiple Choice

Factor out the GCF

3x³ + 9x

• 3x (x² + 3)

• 3x ( x³ + 9)

• x (3x² + 9)

• 3x (x³ + 3x)

Multiple Choice

Factor: -6r+6

• 6(r - 1)

• -6r(r + 1)

• -6(r - 1)

• -6(r + 1)

Let's try some harder ones!

Multiple Choice

Factor:

56a³ - 8a

• 8a²(56a³ - 8a)

• 8a(7a² - 1)

• 8a(7a³ - a)

• 8a²(35a² - a)

Multiple Choice

Factor: 12x²y⁴ - 6xy

• 3xy (4xy³ - 2)

• 6xy (2xy³ - 1)

• 6xy (2x³y⁵ - x²y²)

• 6xy ( 2xy³)

Multiple Choice

Factor completely:
16x² - 20xy

• 4 (4x² - 5xy)
• 4x (4x - 5y)
• 4x² (4 - 5y)
• 2(duck)