Practice Makes Perfect
Recognize and Use the Appropriate Method to Factor a Polynomial Completely
In the following exercises, factor completely.
Exercise \(\PageIndex{31}\)
\(10x^4+35x^3\)
- Answer
-
\(5x^{3}(2x+7)\)
Exercise \(\PageIndex{32}\)
\(18p^6+24p^3\)
Exercise \(\PageIndex{33}\)
\(y^2+10y−39\)
- Answer
-
\((y−3)(y+13)\)
Exercise \(\PageIndex{34}\)
\(b^2−17b+60\)
Exercise \(\PageIndex{35}\)
\(2n^2+13n−7\)
- Answer
-
\((2n−1)(n+7)\)
Exercise \(\PageIndex{36}\)
\(8x^2−9x−3\)
Exercise \(\PageIndex{37}\)
\(a^5+9a^3\)
- Answer
-
\(a^{3}(a^2+9)\)
Exercise \(\PageIndex{38}\)
\(75m^3+12m\)
Exercise \(\PageIndex{39}\)
\(121r^2−s^2\)
- Answer
-
\((11r−s)(11r+s)\)
Exercise \(\PageIndex{40}\)
\(49b^2−36a^2\)
Exercise \(\PageIndex{41}\)
\(8m^2−32\)
- Answer
-
\(8(m−2)(m+2)\)
Exercise \(\PageIndex{42}\)
\(36q^2−100\)
Exercise \(\PageIndex{43}\)
\(25w^2−60w+36\)
- Answer
-
\((5w−6)^2\)
Exercise \(\PageIndex{44}\)
\(49b^2−112b+64\)
Exercise \(\PageIndex{45}\)
\(m^2+14mn+49n^2\)
- Answer
-
\((m+7n)^2\)
Exercise \(\PageIndex{46}\)
\(64x^2+16xy+y^2\)
Exercise \(\PageIndex{47}\)
\(7b^2+7b−42\)
- Answer
-
\(7(b+3)(b−2)\)
Exercise \(\PageIndex{48}\)
\(3n^2+30n+72\)
Exercise \(\PageIndex{49}\)
\(3x^3−81\)
- Answer
-
\(3(x−3)(x^2+3x+9)\)
Exercise \(\PageIndex{50}\)
\(5t^3−40\)
Exercise \(\PageIndex{51}\)
\(k^4−16\)
- Answer
-
\((k−2)(k+2)(k^2+4)\)
Exercise \(\PageIndex{52}\)
\(m^4−81\)
Exercise \(\PageIndex{53}\)
\(15pq−15p+12q−12\)
- Answer
-
\(3(5p+4)(q−1)\)
Exercise \(\PageIndex{54}\)
\(12ab−6a+10b−5\)
Exercise \(\PageIndex{55}\)
\(4x^2+40x+84\)
- Answer
-
\(4(x+3)(x+7)\)
Exercise \(\PageIndex{56}\)
\(5q^2−15q−90\)
Exercise \(\PageIndex{57}\)
\(u^5+u^2\)
- Answer
-
\(u^{2}(u+1)(u^2−u+1)\)
Exercise \(\PageIndex{58}\)
\(5n^3+320\)
Exercise \(\PageIndex{59}\)
\(4c^2+20cd+81d^2\)
- Answer
-
prime
Exercise \(\PageIndex{60}\)
\(25x^2+35xy+49y^2\)
Exercise \(\PageIndex{61}\)
\(10m^4−6250\)
- Answer
-
\(10(m−5)(m+5)(m^2+25)\)
Exercise \(\PageIndex{62}\)
\(3v^4−768\)
Self Check
a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
b. Overall, after looking at the checklist, do you think you are well-prepared for the next section? Why or why not?