Function Given Zeros
Write a polynomial function with the given zeros.
x=-1,-1,6
f(x)=x^3-4x^2-11x-6
Find the real of imaginary solutions of each equation by factoring.
x^2-11x=-24
3,8
Divide using long division.
(x^3+7x^2+15x+9)÷ (x+1)
x^2+6x+9
Find the rational roots of P(x).
P(x)=2x^3-4x^2-10x+12
3,-2,1
Use the Binomial Theorem to expand each binomial.
(x+9)^3
x^3+27x^2+243x+729
Write a polynomial function with the given zeros.
x=-1,0,2
f(x)=x^3-x^2-2x
Find the real of imaginary solutions of each equation by factoring.
4x^2=-4x-1
-1/2
Divide using long division.
(2x^3-7x^2-7x+13) ÷ (x-4)
2x^2+x-3, R1
Find the rational roots of P(x).
P(x)=x^3+2x^2+4x+21
-3
Use the Binomial Theorem to expand each binomial.
(3a+1)^3
27a^3+27a^2+9a+1
Write a polynomial function with the given zeros.
x=1,2,3
f(x)=x^3-6x^2+11x-6
Find the real of imaginary solutions of each equation by factoring.
3x^3+3x^2=27x
0,(-1+-sqrt37)/2
Divide using synthetic division.
(x^3+5x^2-x-5) ÷ (x+5)
x^2-1
Find the rational roots of P(x).
P(x)=x^3+5x^2+x+5
-5
Use the Binomial Theorem to expand each binomial.
(x-2y)^3
x^3-6x^2y+12xy^2-8y^3
Write a polynomial function with the given zeros.
x=-2,1,4
f(x)=x^3-3x^2-6x+8
Find the real of imaginary solutions of each equation by factoring.
2x^2+3=4x
(2+-isqrt2)/2
Divide using synthetic division.
(2x^3+14x^2-58x) ÷ (x+10)
2x^2-6x+2, R-20
Find the rational roots of P(x).
P(x)=2x^3+7x^2-5x-4
1,-4,-1/2
Use the Binomial Theorem to expand each binomial.
(3a+4b)^5
243a^5+1620a^4b+4320a^3b^2+5760a^2b^3+3840ab^4+1024b^5
Find the zeros of each function. State the multiplicity of any multiple zeros.
y=x^4-8x^2+16
2(multiplicity 2), -2(multiplicity 2)
Find the real of imaginary solutions of each equation by factoring.
x^3+4x^2=12x
0,2,-6
Divide using synthetic division.
(5x^3+8x^2-60) ÷ (x-2)
5x^2+18x+36, R12
Find the rational roots of P(x).
P(x) =3x^4+2x^3-9x^2+4
1,-2,-2/3
Use the Binomial Theorem to expand each binomial.
(2x-1)^6
64x^6-192x^5+240x^4-160x^3+60x^2-12x+1