Algebra 2 Semester 1 Review

Factoring Review

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Factoring when a=1

x²+9x+20

Multiple Choice

Factor

d² - 10d + 25

• (d + 5) (d - 5)

• (d - 15) (d + 10)

• (d + 5) (d - 20)

• (d - 5) (d - 5)

Multiple Choice

Factor

r² -16r + 60

• (r - 15)(r + 4)

• (r - 6)(r + 10)

• (r - 6)(r - 10)

• (r +30)(r - 2)

Factoring a Difference of Perfect Squares

9x²-100

Multiple Choice

x² - 9

• (x + 3)²

• (x + 3) (x - 3)

• (x - 3)²

• x + 3(x - 3)

Multiple Choice

4x² - 25

• (2x + 5) (2x - 5)

• (2x - 5)²

• (2x + 5)²

• 2x + 5(2x - 5)

Multiple Choice

We can't factor using difference of two square this

49x² + 4y². Why?

• Because 4 is not a perfect cubed number.

• Because 4 is not a perfect squared number.

• Because 49 is not a perfect squared number.

• Because we can't factor using difference of two squares if it is addition sign.

Factoring a GCF out

30a³-10a

Multiple Choice

Factor:

56a³-8a

• 8a²(56a³-8a)

• 8a(7a²-1)

• 8a(7a³-a)

• 8a²(35a²-a)

Multiple Choice

Factor:

2n²-8n³

• 2n²(n-4n²)

• -2n²(4n-1)

• 2n³(10-8n²)

• 3n(1-4n)

Multiple Choice

Factor:

80x⁵-70x²-60x⁷

• 2x²(80x³-70-60x⁶)

• 10x²(80x⁴-70x-60x⁶)

• 10x²(8x³-7-6x⁶)

• 3x²(80x³-40-60x⁵)

• Guess-and-Check

• AC Method

Guess-and-Check Method

12x²-29x+15

AC Method

12x²-29x+15

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

5x²-28x+32

• (3x-10)(x+6)

• (x-8)(5x-4)

• (5x-8)(x-4)

• (5x-8)(x+7)

Multiple Choice

Factor Completely: 14p²-24p-8

• (5p+3)(p-4)

• (3p-2)(p+10)

• 2(7p-2)(p+2)

• 2(7p+2)(p-2)

Factor by Grouping

xy-5y-2x+10

Factor by Grouping (again)

x³-3x²+5x-15

Multiple Choice

What is the factored form of x³+7x²-2x-14

• (x²-2)(x-7)

• (x²+2)(x-7)

• (x²+2)(x+7)

• (x²-2)(x+7)

Multiple Choice

Decide if (x-3) is a factor of 3x³+10x²-3x-10

• Yes, it is a factor

• No, it is not a factor

Multiple Choice

Factor p³ - 3p² - 16p + 48

• p² ( p - 3) (p - 3)

• (p² - 16) (p - 3)

• (p + 4) (p - 4) (p - 3)

Multiple Choice

30x³+15x²-18x-9

• (5x²-3)(6x+1)

• (5x²-3)(6x+3)

• 3(5x²+3)(2x-1)

• 3(5x²-3)(2x+1)

​Let us fully understand the process of solving quadratic equations.

Multiple Choice

Use quadratic formula to solve: $$x^2+4x+3=0$$  

• $$\left\{1,3\right\}$$  

• $$\left\{-1,-3\right\}$$  

• $$\left\{4,-3\right\}$$  

• $$i\sqrt{3}$$  

Multiple Choice

Use quadratic formula to solve: $$8x^2-4x-18=0$$  

• $$\left\{\frac{1\pm\sqrt{37}}{4}\right\}$$  

• $$\left\{8,4,18\right\}$$  

• $$\left\{\frac{38}{4},-\frac{38}{4}\right\}$$  

• $$i\sqrt{37}$$  

Poll

What are we feeling least confident with?

• Factoring when

  $$a=1$$

• Factoring when $$a\ne1$$ (guess and check or ac method)

• Factoring a GCF

• Difference of Perfect Squares

• Factoring by Grouping