Midterm Review

Factoring

100

Factor 20x⁶-20x⁴-5x³-15x²

5x²(4x⁴-4x²-x-x)

200

Factor x²+7x+10

(x+2)(x+5) 

300

Factor r²+14r+33

(r+3)(r+11)

400

Factor 2b²+26b+24

2(b(b+1)12(b+1))

500

Factor 4p²+25p+25

(n+2)(3n-7)

Systems of Equations

100

Determine whether the ordered pair is the solution:

-x+y=2 (-1,1) 2x-y=-3

Yes, (-1,1) is a solution

200

Determine whether the ordered pair is the solution:

5x+3y=-1 (-2,3) x-y=1 

No, (-2,3) is not the solution

300

Solve with substitution:

X+(x+5)=-1

2x+5=-1

(-3,2)

400

Solve with elimination:

2x+3y=15

x-3y=3

(6,1)  

500

Solve with elimination:

6x-10y=-20

-6x+10y=30

No solution

Parents and Quadradic Equations

100

Find the vertex and axis of symmetry:

y=(x+3)²-4

Vertex: (-3,-4) AOS: -3

200

Find the vertex and axis of symmetry:

f(x)=x²+2x+3

Vertex: (-1,2) AOS: -1

300

Find the vertex and axis of symmetry:

f(x)=2(x-2)²+5

Vertex: (2,5) AOS: 2

400

Find the vertex and axis of symmetry:

f(x)=-(x-7)²+10

Vertex: (7,10) AOS: 7

500

Find the vertex and axis of symmetry:

y=x²+2x+1

Vertex: (0,-1) AOS: -1

Linear Equations

100

Solve the equation:

6x-19 = 3x – 10

x=3

200

Solve the equation:

5x+5=3x+7

x=1

300

Solve the equation:

4y+6=8y-8

y=7

400

Solve the equation:

3y+9=6y-1

y=5

500

Solve the equation:

7x+8=5-21x

x=-1