Question

Please do 41 and 46. Please show your work and explain how you did it. Thank you!

Answer 1

$\bf 41)\\\\ 8x^4-24x^3+18x^2\implies 2x^2(\stackrel{2,2}{4}x^2\stackrel{(2\cdot -3)+(2\cdot -3)}{-12}x+\stackrel{3,3}{9}) \\\\\\ 2x^2(2x-3)(2x-3)\\\\ -------------------------------\\\\ 46)\\\\ x^2(x-1)-25(x-1)\implies \stackrel{\stackrel{common}{factor}}{(x-1)}(x^2-25) \\\\\\ (x-1)\stackrel{\textit{difference of squares}}{(x^2-5^2)}\implies (x-1)(x-5)(x+5)$

Answer 2

$8x^4-24x^3+18x^2=2x^2(4x^2-12x+9)=2x^2(4x^2-6x-6x+9)\\\\=2x^2[2x(2x-3)-3(2x-3)]=2x^2(2x-3)(2x-3)$

$x^2(x-1)-25(x-1)=(x-1)(x^2-25)\\\\=(x-1)(x^2-5^2)=(x-1)(x-5)(x+5)\\\\Used:\ a^2-b^2=(a-b)(a+b)$