Question

Factor the polynomial 4x^4-20x^2-3x^2+15by grouping. Which is the resulting expression

Answer 1

Your answer appears to be $(x^2-5)(4x^2-3)$ and heres why:

$Steps\\ 4x^4-20x^2-3x^2+15 \\\\Step 1. Factor 4x^4-20\\\\4x^4-20x^2\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c\\x^4=x^2x^2\\=4x^2x^2-20x^2\\\\\mathrm{Rewrite\:as}\\=4x^2x^2-5\cdot \:4x^2\\\\\mathrm{Factor\:out\:common\:term\:}4x^2\\=4x^2\left(x^2-5\right)\\\\ Step 2. \mathrm{Factor}\:-3x^2+15:\quad 3\left(-x^2+5\right) \\-3x^2+15\\\\\mathrm{Rewrite\:as}\\=-3x^2+3\cdot \:5\\\\\mathrm{Factor\:out\:common\:term\:}3\\=3\left(-x^2+5\right)$

$Step\ 3.\\ =4x^2\left(x^2-5\right)+3\left(-x^2+5\right) \\\\\mathrm{Rewrite\:as}\\=4\left(x^2-5\right)x^2-3\left(x^2-5\right)\\\\\mathrm{Factor\:out\:common\:term\:}\left(x^2-5\right)\\=\left(x^2-5\right)\left(4x^2-3\right)$

Now, if you have anymore questions and would like to see more answers like this, please make sure to Like, Comment, and Rate! Also, make sure to send me a friend request. I'm always up for a challenge!

Thanks!

ps. could you please mark me as Brainlyest? I kinda need it to help maintain and to reach the next rank... thx

Answer 2

Answer:

$\boxed{\bold{\left(x^2-5\right)\left(4x^2-3\right)}}$

Step By Step Explanation:

Factor $\bold{4x^4-20x^2}$

$\bold{4x^2\left(x^2-5\right)}$

Factor $\bold{-3x^2+15}$

$\bold{3\left(-x^2+5\right)}$

Rewrite Equation

$\bold{4x^2\left(x^2-5\right)+3\left(-x^2+5\right)}$

Rewrite As...

$\bold{4\left(x^2-5\right)x^2-3\left(x^2-5\right)}$

Factor Out Common Term $\bold{\left(x^2-5\right)}$

$\bold{\left(x^2-5\right)\left(4x^2-3\right)}$

$\boxed{\bold{\black{Mordancy}}}$