10.6 Introduction to factoring polynomials  (Page 4/6)

$120y^6+48y^4$

$144a^6+90a^3$

$4q^2+24q+28$

$10y^2+50y+40$

$15z^2-30z-90$

$12u^2-36u-108$

$3a^4-24a^3+18a^2$

$5p^4-20p^3-15p^2$

$11x^6+44x^5-121x^4$

$8c^5+40c^4-56c^3$

$\mathrm{-3}n-24$

$\mathrm{-7}p-84$

$\mathrm{-15}{a}^2-40a$

$\mathrm{-18}{b}^2-66b$

$\mathrm{-10}{y}^3+60y^2$

$\mathrm{-8}{a}^3+32a^2$

$\mathrm{-4}{u}^5+56u^3$

$\mathrm{-9}{b}^5+63b^3$

Revenue A manufacturer of microwave ovens has found that the revenue received from selling microwaves a cost of $p$ dollars each is given by the polynomial $\mathrm{-5}{p}^2+150p.$ Factor the greatest common factor from this polynomial.

Height of a baseball The height of a baseball hit with velocity $80$ feet/second at $4$ feet above ground level is $\mathrm{-16}{t}^2+80t+4,$ with $t=$ the number of seconds since it was hit. Factor the greatest common factor from this polynomial.

The greatest common factor of $36$ and $60$ is $12.$ Explain what this means.

What is the GCF of $y^4$ , $y^5$ , and $y^{10}$ ? Write a general rule that tells how to find the GCF of $y^{\text{a}}$ , $y^{\text{b}}$ , and $y^{\text{c}}$ .

$y^2+8y-20$

$\mathrm{-6}{a}^4$

$9x^3-1$

$n^3-3n^2+3n-1$

$16x^2-40x-25$

$5m+9$

$\mathrm{-15}$

$y^2+6y^3+9y^4$

$4p+11p$

$\mathrm{-8}{y}^3-5y^3$

Add $4n^5,\text{−}{n}^5,\mathrm{-6}{n}^5$

Subtract $10x^2$ from $3x^2$

$(4a^2+9a-11)+(6a^2-5a+10)$

$(8m^2+12m-5)-(2m^2-7m-1)$

$(y^2-3y+12)+(5y^2-9)$

$(5u^2+8u)-(4u-7)$

Find the sum of $8q^3-27$ and $q^2+6q-2$

Find the difference of $x^2+6x+8$ and $x^2-8x+15$

$200x-\frac{1}{5}{x}^2$ when $x=5$

$200x-\frac{1}{5}{x}^2$ when $x=0$

$200x-\frac{1}{5}{x}^2$ when $x=15$

$5+40x-\frac{1}{2}{x}^2$ when $x=10$

$5+40x-\frac{1}{2}{x}^2$ when $x=\mathrm{-4}$

$5+40x-\frac{1}{2}{x}^2$ when $x=0$

A pair of glasses is dropped off a bridge $640$ feet above a river. The polynomial $\mathrm{-16}{t}^2+640$ gives the height of the glasses $t$ seconds after they were dropped. Find the height of the glasses when $t=6.$

The fuel efficiency (in miles per gallon) of a bus going at a speed of $x$ miles per hour is given by the polynomial $-\frac{1}{160}{x}^2+\frac{1}{2}x.$ Find the fuel efficiency when $x=20$ mph.

$6^3$

${\left(\frac{1}{2}\right)}^4$

${(\mathrm{-0.5})}^2$

$-3^2$

$p^3·p^{10}$

$2·2^6$

$a·a^2·a^3$

$x·x^8$

${(y^4)}^3$

${(r^3)}^2$