5.2.H: Homework

College Technical Math · LibreTexts

0%

Contents

    Text

    Size
    100%
    Theme
    Typeface
    Line length
    Spacing

    From LibreTexts, under CC BY 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    Practice Makes Perfect

    Find the Greatest Common Factor (GCF) of Two or More Expressions

    In the following exercises, find the greatest common factor.

    1. \(10p^3,12p\)

    Answer

    \(2p\)

    2. \(12m^2n^3,30m^5n^3\)

    Answer

    \(6m^2n^3\)

    Factor the Greatest Common Factor from a Polynomial

    In the following exercises, factor the greatest common factor from each polynomial.

    3. \(6m+9\)

    Answer

    \(3(2m+3)\)

    4. \(9n−63\)

    Answer

    \(9(n−7)\)

    5. \(3x^2+6x−9\)

    Answer

    \(3(x^2+2x−3)\)

    6. \(8y^3+16y^2\)

    Answer

    \(8y^2(y+2)\)

    7. \(5x^3−15x^2+20x\)

    Answer

    \(5x(x^2−3x+4)\)

    8. \(12xy^2+18x^2y^2−30y^3\)

    Answer

    \(6y^2(2x+3x^2−5y)\)

    9. \(20x^3y−4x^2y^2+12xy^3\)

    Answer

    \(4xy(5x^2−xy+3y^2)\))

    10. \(−2x−4\)

    Answer

    \(−2(x+4)\)

    11. \(−4p^3q−12p^2q^2+16pq^2\)

    Answer

    \(−4pq(p^2+3pq−4q)\)

    12. \(5x(x+1)+3(x+1)\)

    Answer

    \((x+1)(5x+3)\)

    Factor Differences of Squares

    In the following exercises, factor.

    Exercise 13

    \(x^2−16\)

    Answer

    \((x−4)(x+4)\)

    Exercise 14

    \(25v^2−1\)

    Answer

    \((5v−1)(5v+1)\)

    Exercise 15

    \(121x^2−144y^2\)

    Answer

    \((11x−12y)(11x+12y)\)

    Exercise 16

    \(169c^2−36d^2\)

    Answer

    \((13c−6d)(13c+6d)\)

    Exercise 17

    \(4−49x^2\)

    Answer

    \((2−7x)(2+7x)\)

    Exercise 18

    \(16z^4−1\)

    Answer

    \((2z−1)(2z+1)(4z^2+1)\)

    Exercise 19

    \(5q^2−45\)

    Answer

    \(5(q−3)(q+3)\)

    Exercise 20

    \(24p^2+54\)

    Answer

    \(6(4p^2+9)\)

    Applications

    Solve the following.

    Exercise 21

    The surface area of a right cylinder is given by the formula \(A=2\pi rh+2\pi r^2\) where \(r\) is the radius of the base and \(h\) is the height of the cylinder. Factor the right hand side of this equation.

    Answer

    \[A=2\pi r(h+r)\]

    Exercise 22

    In Einstein's theory of special relativity, the total energy of an object (\(E\)) considers both its momentum (\(p\)) and its rest-mass energy (\(mc^{2}\)). The relationship can be given by the formula

    \(E^2 − (pc)^2 = (mc^2)^2\)

    where \(c\) is the speed of light constant.

    Factor the left-hand side of this equation.

    Answer

    \((E+pc)(E−pc)\)

    This page titled 5.2.H: Homework was last modified on Mon, 06 Jul 2026 03:20:44 GMT and is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Kiersten Purves.