Algebra 2 Study Guide for Polynomial Quiz 1 and answer key for practice problems
Classify polynomials:
 Classify by set of coefficients/constant as integral, rational, or real
 Classify by degree as constant, linear, quadratic, cubic, quartic, quintic, or degree n for
bigger than 5
 Classify by number of terms as monomial, binomial, trinomial or polynomial with n terms for
bigger than 3
Examples:
Integral, quadratic, trinomial
Rational, quartic, monomial
Real, quadratic, polynomial with 4 terms
5𝑥 2 − 2𝑥 + 3
−2
3
𝑦4
3𝑥𝑦 + 2𝑥 2 − .3𝑦 2 − √5
Practice problem answers
Pg 349 #91-93
91.
integral quartic polynomial with 4 terms, degree is 4, leading coefficient is 5
92.
integral quintic polynomial with 4 terms, degree is 5, leading coefficient is -2
93.
integral degree 7 polynomial with 4 terms, degree is 7, leading coefficient is -1
Note the following examples would not be polynomials in one variable
5xy+x 2 (too many variables) 2𝑥 2 +
3
𝑥
(no variables in denominator)
√𝑥 + 3 (no variable under a radical) 2𝑥 −3 + 4𝑦 .2 (variable’s exponents must be whole numbers)
Algebra 2 Study Guide for Polynomial Quiz 1 and answer key for practice problems
Pg 340 #1-9, 11-14
#11 is F, #12 is about 12.97 ft, #13 is D, #14 is 5.832 units.
Algebra 2 Study Guide for Polynomial Quiz 1 and answer key for practice problems
Pg 327 #51-54
51. 3[ (a - 4)3 - 2(a - 4)] + 3[4(a + 5)2 – 6(a + 5) + 8] then expand use Pascal for the cube,
I will include the Pascal step here
(𝑎 − 4)3 = 𝑎3 + 3𝑎2 (−4) + 3𝑎(−4)2 + (−4)3 = 𝑎3 − 12𝑎2 + 48𝑎 − 64
You should be able to foil the quadratic one (degree 2) then distribute all the coefficients and
collect like terms to get
3𝑎3 − 24𝑎2 + 240𝑎 + 66
52.
−2[4(2𝑎 + 3)2 − 6(2𝑎 + 3) + 8] − 4[(𝑎2 + 1)3 − 2(𝑎2 + 1)]
Pascal steps (𝑎2 + 1)3 = (𝑎2 )3 + 3(𝑎2 )2 + 3𝑎2 + 1 = 𝑎6 + 3𝑎4 + 3𝑎2 + 1
then foil or multiply out the quadratic one (2𝑎 + 3)2 = 4𝑎2 + 12𝑎 + 9
distribute all the coefficients and collect like terms to get
−4𝑎6 − 12𝑎4 − 36𝑎2 − 72𝑎 − 48
53.
5[(𝑎2 )3 − 2(𝑎2 )] − 8[4(6 − 3𝑎)2 − 6(6 − 3𝑎) + 8]
then simplify exponents, foil the quadratic, distribute coefficients and collect like terms to
get
5𝑎6 − 298𝑎2 + 1008𝑎 − 928
54.
−7[4(𝑎3 )2 − 6(𝑎3 ) + 8] + 6[(𝑎4 + 1)3 − 2(𝑎4 + 1)]
Simplify the exponents in the first part and distribute the coefficients then use Pascal
Pascal steps (𝑎4 + 1)3 = (𝑎4 )3 + 3(𝑎4 )2 + 3𝑎4 + 1 = 𝑎12 + 3𝑎8 + 𝑎4 + 1
then distribute the coefficients and collect like terms to get
6𝑎12 + 18𝑎8 − 28𝑎6 − 6𝑎4 + 42𝑎3 − 62