6.11: Proficiency Exam

Exercise $\PageIndex{1}$

The product is $27a^3+9a^2+9a$ and a factor is $3a$. Find the other factor.

Answer

$9a^2+3a+3$

Exercise $\PageIndex{2}$

The product is $15x^{n+5}y^{3n−2}$. Find the other factor.

Answer

$5x^ny^{2n−3}$

For the following problems, factor, if possible, the polynomials.

Exercise $\PageIndex{3}$

$−14x^2y^4b−28x^2y^3b−42x^2y^2$

Answer

$−14x^2y^2(y^2b+2yb+3)$

Exercise $\PageIndex{4}$

$(y+2)a+(y+2)c$

Answer

$(a+c)(y+2)$

Exercise $\PageIndex{5}$

$6x^2y^2z+5x^2y^3−12xyz−10xy^2$

Answer

$xy(xy−2)(6z+5y)$

Exercise $\PageIndex{6}$

$4a^2−16c^2$

Answer

$4(a+2c)(a−2c)$

Exercise $\PageIndex{7}$

$m^4−n^4$

Answer

$(m^2+n^2)(m+n)(m−n)$

Exercise $\PageIndex{8}$

$b^2+8b+16$

Answer

$(b+4)^2$

Exercise $\PageIndex{9}$

$9y^2−30y+25$

Answer

$(3y−5)^2$

Exercise $\PageIndex{10}$

$x^2+5x−15$

Answer

not factorable

Exercise $\PageIndex{11}$

$x^2−x−30$

Answer

$(x−6)(x+5)$

Exercise $\PageIndex{12}$

$4x^6−36x^4+80x^2$

Answer

$4x^2(x^2−5)(x+2)(x−2)$

Exercise $\PageIndex{13}$

$9x^2+25x−6$

Answer

$(9x−2)(x+3)$