8/10 Algebra - Polynomials Practice

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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


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