8/10 Algebra - Polynomials Practice
Subtract, then put into standard form (2x-7)-(3x²-2x-8)
-3x²+4x+1
Subtract, then put into standard form (x²+5x+4)-(4x²+9)
-3x²+5x-5
Subtract, then put into standard form (6x+3)-(3x²+2)
-3x²+6x+1
(16y⁴-24y³)÷(-8y³)
-3y+3
(15y³-20y²-10y)÷(-5y)
-3y²+4y+2
(15t⁴-21t³)÷(-3t²)
-5t²+7t
Subtract, then put into standard form (2x+7)-(3x-5)
-x+12
(14x⁴-42x³+56x²)÷(-14x²)
-x²+3x-4
Subtract, then put into standard form (2x²-3x+5)-(3x²-8x+1)
-x²+5x+4
Subtract, then put into standard form (3x-2)-(x²+2x-1)
-x²+x-1
(-48x⁴+36x³)÷(-4x²)
12x²-9x
(2b²-7b+3)÷(b-3)
2b-1
(6x²+13x+6)÷(3x+2)
2x+3
Add, then put into standard form. (3x²-2x-5)+(-x²+5)
2x²-2x
(8x⁴-12x³)÷(4x²)
2x²-3x
(6x⁴-2x³+9x²)÷3x
2x³-⅔x²+3x
(9x²-42x+45)÷(3x-8)
3x-6 r-3
Subtract, then put into standard form (5x²+3x)-(2x²-7)
3x²+3x+7
Add, then put into standard form. (x²+2x-3)+(2x²-3x+8)
3x²-x+5
(28x²+84x)÷7x
4x+12
Add, then put into standard form. (6x+3)+(4x²+6)
4x²+6x+9
Add, then put into standard form. (4x³+2x)+(9x²+2)
4x³+9x²+2x+2
Add, then put into standard form. (2x²-3x-1)+(3x²+2x)
5x²-x-1
Subtract, then put into standard form (6x²-3)-(3x+4)
6x²-3x-7
Add, then put into standard form. (4x²-3x-9)+(2x²-6x-3)
6x²-9x-12
Subtract, then put into standard form (9x²-2x-3)-(2x²-7x+2)
7x²+5x-5
(7y²-3y-4)÷(y-1)
7y+4
rel. mins:-5 ; rel. maxs:-1
Give the relative mins and maxs for y=-x³-3x²-1.
rel. mins:1 ; rel. maxs:5
Give the relative mins and maxs for y=x³-6x²+9x+1.
rel. mins:2 ; rel. maxs:3
Give the relative mins and maxs for y=x⁴-2x²+3.
rel. mins:-1 ; rel. maxs:1
Give the relative mins and maxs.
rel. mins:-3 and -1 ; rel. maxs:2 and 1
Give the relative mins and maxs.
rel. mins:-4 and 0 ; rel. maxs:6 and 10
Give the relative mins and maxs.
rel. mins:0 ; rel. maxs:4
Give the relative mins and maxs.
rel. mins:0 ; rel. maxs:none
Give the relative mins and maxs.
rel. mins:0; rel. maxs:2
Give the relative mins and maxs.
rel. mins:1 ; rel. maxs:4
Give the relative mins and maxs.
rel. mins:1 ; rel. maxs:5
Give the relative mins and maxs.
rel. mins:approx. -1.5 ; rel. maxs:approx. 10
Give the relative mins and maxs.
Factor Theorem
If (x-a) is a factor of p(x), then remainder equals 0
(-9a⁴+27a³-81a²)÷(-9a²)
a²-3a+9
(b²-3b-28)÷(b+4)
b-7
Only use synthetic when...
dividing by linear binomial
Remainder Theorem
p(x) is divided by x-a, then p(a)=r
(8x+24)÷8
x+3
(x²+10x+24)÷(x+4)
x+6
(x²+11x+30)÷(x+5)
x+6
(x²-15x+56)÷(x-8)
x-7
Add, then put into standard form. (x+3)+(x²+9x-4)
x²+10x-1
(x⁴-2x²+1)÷(x²-2x+1)
x²+2x+1
Add, then put into standard form. (x²-3x-7)+(5x-2)
x²+2x-9
Subtract, then put into standard form (6x²-2x+8)-(5x²-3x-9)
x²+x+17
Put into standard form. y=9-2x
y=-2x+9
Put into standard form. y=8x-2x³+3x²
y=-2x³+3x²+8x
Put into standard form. y=8-4x²+7x
y=-4x²+7x+8
Put into standard form. y=5-x⁴
y=-x⁴+5
Put into standard form. y=-3x+2x²-4
y=2x²-3x-4
Put into standard form. y=9x⁴-4x²+3x⁵
y=3x⁵+9x⁴-4x²
Put into standard form. y=4x-5x²+6x³
y=6x³-5x²+4x
Put into standard form. y=7+3x+x⁵
y=x⁵+3x+7
