Polynomials
Why is this not a polynomial?
5x^2-4/(x^x+x)+x^5
There is a variable in the denominator
What type of problems are these, and what steps to solve each?
A) f(x)+g(x)
B) (f-g)(x)
C) f(x)*g(x)
f(x)/g(x)
A) Adding - combine like terms
B) Subtracting - Distribute Negative sign, then CLT
C) Multiply - Double Distribute
D) Divide - Just set it up and check for excluded value
What do you do to the exponents in the following rules
A) Product Rule
B) Power Rule
C) Quotient Rule
D) Negative Rule
A) Add exponents
B) Multiply exponents
C) Subtract exponents
D) Move and make positive
Simplify the radical:
sqrt(32
4sqrt(2
Identify the real part and the imaginary part:
-7-6i
Real: -7
Imaginary: -6i
Simplify and write as a complex number:
(4+8i)-(-6+7i)
10+i
Rewrite this polynomial in Standard Form
-8k+6k^4-2k^5+k^2
-2k^5+6k^4+k^2-8k
Evaluate the following function
f(2)=x^2-8x+5
f(2)=-7
Finish each exponent rule
a^m*a^n=
(a^m)^n=
a^m/a^n=
a^-m=
a^0=
a^(m+n)
a^(m*n)
a^(m-n)
1/a^m
1
Simplify:
3sqrt(48a^3)
12asqrt(3a)
Simplify:
sqrt(-200)
10isqrt2
Write in radical form:
(3x)^(4/5)
root(5)((3x))^4
In the following polynomial, what are the coefficients and what is the constant?
-6r^3+10r^2-8r+1
Coefficients: -6, 10, and -8
Constant: 1
Perform the indicated operation:
f(x)=3x+2
g(x)=3x-3
(f-g)(x)
5
Simplify:
4b*2b^4*2b^3
16b^8
Simplify:
2sqrt(54)+2sqrt(24)
10sqrt(6)
Simplify the power of i:
i^39
-i
Simplify:
(3x-4)^2
9x^2-24x+16
Give the full name of the polynomial:
-3k^4+4k^2-k
Find the excluded value:
(2x+3)/(4x-12)
x!=3
Simplify:
(2x^2)/(4x^3)
1/(2x)
Simplify:
-3sqrt3*sqrt4
-6sqrt(3)
Multiply and write as a complex number:
(8-5i)(-2-i)
-21+2i
Simplify:
root(3)(27x^3)
3x
Write a 6th degree binomial with -2 as a coefficient and 3 as a constant
-2x^6+3
Peform the operation:
f(x)=x-4
g(x)=3x+2
(f*g)(x)
3x^2-10x-8
Simplify:
x^3/(3x*2x^-3)
x^5/6
Simplify:
sqrt(10)(2+5sqrt(2))
2sqrt(10)+10sqrt(5)
Rationalize the denominator:
sqrt3/(sqrt2
sqrt6/2
Simplify the Fraction:
1/2div3/2
1/3