Abeka grade 9 Algebra 1 Test 9 (2023/2024)

6x²-7xy+2y²

(2x-y)(3x-2y) 6x²-7xy+2y².............................ac=(6)(2)=12 =6x²-3xy-4xy+2y²...................12=(-3)(-4) =(6x²-3xy)+(-4xy+2y²)............b=-7=-3-4 =3x(2x-y)-2y(2x-y) =(2x-y)(3x-2y)

9x²+12x+4

(3x+2)²

2x³+2x²+x+1

(x+1)(2x²+1) 2x³+2x²+x+1 =(2x³+2x²)+(x+1) =2x²(x+1)+1(x+1) =(x+1)(2x²+1)

2x²+6x-8

2(x-1)(x+4) 2x²+6x-8 =2(x²+3x-4) =2(x-1)(x+4)

Short Answer I: Factor each polynomial. Show all work. 8a²b²+10ab³c

2ab²(4a+5bc)

Identify the zeros for the equation y=x²+6x-27.

a. (0,3) and (0,-9) b. (0,-3) and (0,9) c. (3,0) and (-9,0) d. (-3,0) and (9,0) x²+6x-27=0 (x-3) (x+9)=0 x-3=0 or x+9=0 x=3 or x=-9 (3,0) and (-9,0)

Identify the vertex for the equation y=(x-1)²-5.

a. (1,5) b. (1,-5) c. (-1,5) d. (-1,-5) y=(x-h)²+k y=(x-1)²+(-5) (h,k)=(1,-5)

Identify the vertex for the equation y=x²+4x+3.

a. (2,-1) b. (-2,-1) c. (2,15) d. (-2,15) x=-b/2a=-4/2(1)=-4/2=-2 y=x²+4x+3 =(-2)²+4(-2)+3 =4-8+3 =-1

-³√-8

a. -2 b. 2 c. -2³√-2 d. none of these -³√-8=-(-2)=2

Multiple Choice I: Write the letter of the correct choice in the blank. Show all work. Without solving, determine how many real solutions 9x²-3x+1=0 has.

a. 0 b. 1 c. 2 d. infinitely many b²-4ac=(-3)²-4(9)(1) =9-36 =-27

Screen size is usually considered to be the diagonal distance from one corner to the opposite corner. If a screen 18 inches wide has a screen size of 20 inches, how tall is it to the nearest whole inch?

a. 10 inches b. 11 inches c. 12 inches d. none of these c²=a²+b² 20²=18²+b² b²=400-324=76 b=√76=8.71...∼9

Multiple Choice II: Simplify each expression. Write the letter of the correct choice in the blank. Show all work. √12x⁵

a. 2x√3x² b. 4x√3x² c. 2x²√3x d. 4x²√3x √12x⁵=√4*3*x⁴*x =√4*√x⁴*√3x =2x²√3x√

4y / √2y

a. 2y b. 2√2y c. 1 / 2y d. none of these 4y / √2y * √2y / √2y = 4y√2y / 2y = 2√2y

Find the distance between (1,3) and (4,-1).

a. 5 b. 25 c. √13 d. none of these d=√(x₂-x₁)²+(y₂-y₁)² =√(4-1)²+(-1-3)² =√3²+(-4)² = √9+16 = √25 =5

5 / √7-1

a. 5√7+5 / 6 b. 5√7-5 / 6 c. 5√7+5 / 48 d. 5√7-5 / 48 5/√7-1*√7+1/√7+1=5√7+5/7-1 =5√7+5 / 6

(√a+2)(√a+3)

a. 6a b.a+6 c. a-6√a+6 d. none of these (√a+2)(√a+3) =(√a)²+3√a+2√a+(2)(3) =a+5√a+6

√x²-4x+13=x+7

x= -2 (√x²-4x+13)²=(x+7)² x²-4x+13=x²+14x+49 -4x+13=14x+49 -18x=36 x=-2 Verify: √x²-4x+13 = x+7 ...................=(-2)+7 ...................=5

x²-x=6

x=-2 or x=3 x²-x=6 x²-x-6=0 (x+2)(x-3)=0 x+2=0 or x-3=0 x= -2 or x=3

x²-2x-2=0

x=1 ± √3 x²-2x-2=0 x²-2x=2 x²-2x+1=2+1 (x-1)²=3 √(x-1)²= ±√3 x-1=±√3 x=1±√3

2x²+5x-3=0

x=1/2 or x=-3 x=-b±√b²-4ac / 2a ; a=2, b=5, c=-3 x=-5±√(5)²-4(2)(-3) / 2(2) x=-5±√25+24 / 4 = -5±√49 / 4 = -5±7 / 4 x= 2/4 or x=-12/4 x=1/2 or x=-3

Short Answer II: Solve each equation. Write the answer in the blank. Show all work. 5x²-3=17

x=±2 5x²-3=17 5x²=20 x²=4 √x²=±√4 x=±2