Combining Polynomials
The result of adding (5p2−3) to (2p2−3p3)
−3p3+7p2−3
The quotient of (m2−7m−11)÷(m−8)
m+1
Is the binomial (k−2) a factor of (k3−k2−k−2)?
Yes
List all possible rational roots for f(x)=3x2+2x−1.
±1, ±1/3
For f(x)=x3−4x2+7, what is the degree of the function? Is this function even or odd?
Degree: 3
Odd
The product of (2x) and (−2x−3)
−4x2−6x
The quotient of (n2−3n−21)÷ (n−7)
n+4
What is the remainder when (p4+5p3−11p2−25p+29) is divided by (p+6)?
−1
List all possible rational roots of f(x)=x2+8x+10
±1, ±2, ±5, ±10
For the function f(x)=x4−4x3+5x+1, what is the degree of the function? Is the function even or odd?
Degree: 4
Even
The difference of (12a5−6a−10a3) and (10a−2a5−14a4)
14a5+14a4−10a3−16a
The quotient of (x3+7x2+14x+3)÷(x+2)
x2+5x+4
What is the remainder when (r5+6r4−13r3−5r2−8r+14) is divided by (r−2)?
List all possible rational roots of f(x)=x6−64.
±1, ±2, ±4, ±8, ±16, ±32, ±64
Fill in the blanks for the function f(x)=x3−4x2+4:
as x→−∞, f(x)→ ______
as x→+∞, f(x)→ ______
as x→−∞, f(x)→−∞
as x→+∞, f(x)→+∞
The product of (8p−2) and (6p+2)
48p2+4p−4
The quoteint of (50k3+10k2−35k−7)÷(5k−4)
10k2+10k+1
Given f(x)=3x2+kx−12, and the remainder when f(x) is divided by x+4 is 40, what is the value of k?
k=−1
State the possible rational roots for f(x)=x3+x2−5x+3. Then find all rational roots.
Possible Rational Roots: ±1, ±3
Rational Roots: x=−3, 1
Fill in the blanks for the function f(x)=−x4+3x3−2−5x:
as x→−∞, f(x)→ ______
as x→+∞, f(x)→ ______
as x→−∞, f(x)→−∞
as x→+∞, f(x)→−∞
The product of (n2+6n−4) and (2n−4)
2n3+8n2−32n+16
The quotient of (−5x2+x3+8x+4)÷(−1+x)
x2−4x+4
Given f(x)=6x3+20x2−15x+k, and the remainder when f(x) is divided by x+4 is 5, what is the remainder when f(x) is divided by (x−3)?
306
State the possible rational roots for f(x)=3x3+11x2+5x−3. Then, find all rational roots.
Possible Rational Roots: ±1, ±3, ±1/3
Rational Roots: x=1/3, −1, −3
Fill in the blanks for the function f(x)=−x5+4x3−x+1:
as x→−∞, f(x)→ ______
as x→+∞, f(x)→ ______
as x→−∞, f(x)→+∞
as x→+∞, f(x)→−∞