8/25 Review Unit 1 - Factoring (1 of 2)

Review Unit 1 - Factoring (1 of 2)

​Math Analysis Unit 1 Review

by Ms. Kunkel

​Factoring

You will need to know how to...

• ​Factor out the GCF

• ​Factor trinomials where a = 1

• ​​Factor by Grouping

• ​Factor trinomials where a > 1

• ​Factor the Difference of Squares

• ​Factor the Sum and Difference of Cubes

​Factoring out the GCF

​To factor out the GCF, look for the largest monomial that can be divided out of each term.

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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: 24x² - 6x

• 6x (x - 1)

• 6x(4x - 1)

• 4(6x - 1)

• 6x( 4x - x)

Multiple Choice

Factor 4b⁵+4b³+16b²

• 4b³(b⁴+b²+4b)

• 4b³(b⁴+4b+5)

• 4(b⁵+b³+4b²)

• 4b²(b³+b+4)

​Factor Trinomial when a = 1

​In the form

if the a value is 1 (you will not see the 1)

​

Find 2 numbers (factors) that

ADD to get b and MULTIPLY to get c.

​

​Pay attention to the signs!!

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Multiple Choice

Factor n² + 16n + 63

• (n-7)(n+4)

• (n+7)(n-9)

• (n-3)(n-10)

• (n+7)(n+9)

Multiple Choice

Factor r² -16r + 60

• (r - 15)(r + 4)

• (r - 6)(r + 10)

• (r - 6)(r - 10)

• (r +30)(r - 2)

Multiple Choice

Factor a² - a - 12

• (a - 4)(a + 3)

• (a + 6)(a - 4)

• (a - 6)(a + 4)

• (a + 4)(a - 3)

Multiple Choice

Factor x² - 4x - 32

• (x + 4)(x + 8)

• (x - 4)(x + 8)

• (x + 4)(x - 8)

• (x -2)(x + 3)

​Factor by Grouping

• ​Use this method when you have a polynomial with 4 terms

• ​Split in half (grouping the first two and last two terms)

• ​Factor out the GCF from both groups You should get a match

• ​Factor out the match

• ​The GCF's are the other factor

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Multiple Choice

Factor by grouping: 5n³-10n²+3n-6

• (5n²+3)(n-2)

• (5n²-3)(n-2)

• (5n³+3)(n-2)

• 10n(n²-6)

Multiple Choice

Factor by grouping:

20x³-25x²+4x-5

• (5x²-5)(4x+1)

• 5(x²-1)(4x+5)

• (5x²+1)(4x-5)

• (5x²+1)(4x-1)

​Factor Trinomials when a>1

• ​Multiply a times c

• ​Find factors of ac that add to b

• ​Split b up into two terms

• ​Write as a polynomial with 4 terms

• ​Factor by Grouping

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Multiple Choice

Factor 3v² - 4v - 7

• (3v-7)(v+1)

• 3(v-7)(v-1)

• (3v+1)(v-9)

• (3v+1)(v-10)

Multiple Choice

Factor 4n²-17n-15

• (n-10)(6n+1)

• (4n-5)(n-3)

• (n-5)(4n-3)

• (n-5)(4n+3)

Multiple Choice

Factor:

2x² + 3x - 9

• 2(x + 3)(x - 3)

• (2x - 3)²

• (x + 3)(2x - 3)

• (2x + 3)(x - 3)

​Factoring the Difference of Squares

• ​Make sure it is subtracting and not adding!

• ​There will be one + and one - in the parenthesis

• ​Find the square root of the first and last terms

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Multiple Choice

Factor completely.

121x² - 49

• ( 11x - 7 ) ²

• ( 11x - 7 ) ( 11x - 7 )

• ( 11x + 7 ) ( 11x - 7 )

• ( 12x + 7 ) ( 12x - 7 )

Multiple Choice

Factor completely.

64x² - 49y²

• ( 8x + 7 ) ( 8x - 7 )

• ( 8x - 7y ) ( 8x - 7y )

• ( 8x + 7y ) ( 8x - 7y )

• ( 8x - 7y )²

Multiple Choice

Factor completely.

a² - 16b²

• ( a + 4b ) ( a - 4b )

• ( a - 4b ) ²

• ( a - 4b ) ( a - 4b )

• ( a + 2b ) ( a - 8b )

Multiple Choice

Factor completely.

49x² + 16

• ( 7x + 4 ) ( 7x - 4 )

• ( 7x + 4 ) ( 7x + 4 )

• ( 7x - 4 ) ²

• does not factor (SUM of squares)

​Factoring the Sum and Difference of Cubes

• ​Identify a and b by finding the cube root of both terms...

  • ​Think what number would you times by itself 3 times to get that number.

  • ​Divide the exponent by 3

• ​Plug into the formula and simplify

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Multiple Choice

Factor 27x³-64

• (3x-4)(9x²+12x+16)

• (3x-4)(9x²-12x+16)

• (3x+4)(9x²-12x+16)

• (3x+4)(9x²+12x+16)

Multiple Choice

Factor: 8x³ - 1

• (2x - 1)(4x² + 2x + 1)

• (2x + 1)(4x² - 2x + 1)

• (2x - 1)(4x² - 2x - 1)

• (2x + 1)(4x² +2x + 1)

Multiple Choice

Factor this difference of cubes: x³ - 343

• (x + 7) (x² - 7x + 49)

• (x² + 1) (x - 343)

• (x - 7) (x² + 7x + 49)

• (x² - 343) (x + 1)

The End ​

Don't forget to review Part 2​ on Rational Expressions!