The Basics
Determine if the following polynomial is constant, linear, quadratic, cubic, quartic, or quintic:
8y+7y^3
Cubic
Find the sum:
(2x+3y)+(4x+9y)
6x+12y
Simplify the expression:
f(f^2+2f+25)
f^3+2f^2+25f
Factor the following polynomial:
5z^2+10z
5z(z+2)
Find the product:
(10x-2)(10x+2)
100x^2-4
Put the following polynomial in standard form:
-9b^2 +10b-b^6
-b^6 -9b^2 +10b
Find the difference:
(2x+3x^2 )-(7-8x^2 )
11x^2 +2x-7
Simplify the expression:
2j^2(5j^3-15j^2+2j+2)
10j^5-30j^4+4j^3+4j^2
Factor the following polynomial by grouping:
24ty-18t+4y-3
(4y-3)(6t+1)
Find the product:
(8-10a)^2
64-160a+100a^2
Is the following expression a polynomial:
3x^-2 +7x-12
No because of the negative exponent
Find the sum:
(6k^2 +2k+9)+(4k^2 -5k)
10k^2 -3k+9
Use the Distributive Method to find the product:
(3b+4)(2b^2-b+4)
6b^3+5b^2+8b+16
Factor the following quadratic trinomial:
w^2-w-6
(w-3)(w+2)
Factor the special product:
q^2-121
(q+11)(q-11)
Give an example of a linear binomial.
Must include: 2 terms, highest degree of 1
Find the difference:
(-8xy+3x^2 -5y)-(4x^2-2y+6xy)
-14xy-x^2-3y
Use the Box Method to find the product:
(3c+1)(c-2)
3c^2-5c-2
Factor the following quadratic trinomial:
x^2+2x-8
(x+4)(x-2)
Factor the special product:
a^2+14a+49
(a+7)^2
Give an example of a quartic trinomial with leading coefficient of 4.
Must include: 3 terms, highest exponent of 4, L.C.=4
Find the sum/difference:
(5a^2-4)+(a^2-2a)-(4a^2-6a+8)
2a^2+4a-12
Use the F.O.I.L. Method to find the product:
(2m+2)(3m-3)
6m^2-6
Factor the following quadratic trinomial:
4x^2-13x+10
(4x-5)(x-2)
Factor the special product:
t^2-18t+81
(t-9)^2