Factoring Polynomials
4x2 -25
(2x + 5) (2x-5)
State the vertex of y= (x -2)2 + 4
(2, 4)
When the discriminant is a negative, zero, or positive, the quadratic has __________, ____________, and _______ x- intercepts or solutions or roots.
0, 1, and 2
Simplify:
(x2 -3x -6) - (3x2 -2x +4)
-2x2 -x -10
x3 -13x2 -30x
x (x+2) (x-15)
Determine how long it takes the ball to reach its maximum height using the following equation where h is the height in feet and t is the time in seconds:
h(t)= -2t2 +8t +5
2 seconds
Use the quadratic formula to solve:
y= -2x2 - 2x +7
1 +/- square root of 15 over -2
Express in simplest form:
3x2 -5x3 -x (2x2 +4x)
-x2 -7x3
12v3 + 36v2 +16v +48
4 (3v2+ 4) (v+3)
Convert to vertex form:
y= x2 -6x +5
y = (x-3)2 -4
Complete the square to solve:
x2 -12x +11=0
(11,0) and (1,0)
or
x = 11 x = 1
Divide:
(m2 -7m -11) / (m -8)
m + 1 - 3/ m-8
6b2 -6b -180
6 (b-6) (b+5)
Convert to vertex form:
y= 2x2+36x +170
y= 2(x+9)2 +8
Solve the quadratic:
3x2 -5x +2 = 0
x = 2/3 x = 1
or
(2/3 ,0) and (1,0)
Divide:
(a2 -28) / (a-5)
a +5 - 3/a-5
4x2+ 2x - 42
2 (2x+7) (x-3)
State the vertex:
x -8 -6 -4 -2 0 2
y 3 0 -1 0 3 8
(-4, -1)
When solving x2 -10x -13 = 0 by completing the square, which equation is a step in the process?
A. (x -5)2 =38
B. (x -5)2 =12
C. (x -10)2 = 38
D. (x -10)2 =12
A. (x -5)2 =38
Is (x-4) a factor of x3+5x2 -32x -7?
No, because when we divide the quotient has a remainder of 9 not 0:
x2 + 9x +4 +9/x-4