5.1
What is a monomial?
A real number, a variable, or a product of a real number, and one or more variables.
True or false: (x-b) is a linear function
True.
How many techniques can be used for polynomial factoring?
6
Define synthetic division.
Simplifies the long division process for dividing a linear expression.
True or false: if a+bi is a root, then a-bi is a root.
True
What is a polynomial?
A monomial or the sum of monomials.
What is x^3-2x^2-15x in factored form?
x(x-5)(x+3)
Which technique would you use to solve x^2+10x+25?
Perfect square trinomials.
Solve using synthetic division: x^3-57x+56 divided by x-7
x^2+7x-8
True or false: if 3-2i and 5/2 are roots of P(x)=0, the other root is 4+3i.
False: the other root is 3+2i.
Name an example of a monomial
5, x^2, 3xy^2
Describe the factor theorem.
The expression x-a is a factor of a polynomial if and if the value of a is a zero of the related polynomial function.
What are the steps for solving polynomial equations using factoring?
First write the equation in form P(x)=0, then factor P(x) using zero product property to find the roots.
What is the remainder of x^3-14x^2+51x-54 divided by x+2?
-220
What are the positive real roots of x^3-x^2+1=0?
2,0
-4x^3+9x^2+3x is a cubic trinomial.
What is the polynomial function of zeros 3 and -3?
f(x)= X^2-9
Solve 6x^2+11x-10 using quadratic trinomials technique.
(2x+5)(3x-2)
What is the remainder theorem?
If you divide a polynomial P(x) by (x-a), then the remainder is P(a).
What cubic polynomial equation has roots of -4 and 2i?
P(x)= x^3+4x^2+4x+16
What is the end behavior of y=4x^3-3x and why?
Down and up because a is positive and n is odd.
What is the polynomial function in standard form with the given zeros? -2, -2, 2, and 3
f(x) = x^4-x^3-10x^2-14x+24
What are the real or imaginary solutions for x^3= 8x-2x^2?
x=0, x=-4, x=2
Evaluate: what is P(-4) if P(x)= x^5-3x^4-18x^3+5x+20?
P(-4)= -640
Find the positive and negative real roots of 2x^4-x^3+3x^2-1+0.
Negative real roots: 1