Question

WILL GIVE BRAINLIEST, 5 STARS, THANKS!!!
Someone please factors these four problems all with step-by-step explanations!! I really don't understand how to do any of them, please help!!!
3x^2 + 10x+ 8

18x^2+39x-15

16x^2-25

6x^2-11x-10

PLEASEEEEE help me...!

Answer 1

Answer are in order:

$\left(3x+4\right)\left(x+2\right)$

$3\left(3x-1\right)\left(2x+5\right)$

$\left(4x+5\right)\left(4x-5\right)$

$\left(3x+2\right)\left(2x-5\right)$

Step-by-step explanation:

$3x^2 + 10x+ 8$

$\mathrm{Break\;the\;expression\;into \;groups}$

$=\left(3x^2+4x\right)+\left(6x+8\right)$

$\mathrm{Factor\;out\;x\;from\; 3x^2+4:}x(3x+4)$

$\mathrm{Factor\;out\;2\;from\;6x+8:2(3x+4)}$

$=x\left(3x+4\right)+2\left(3x+4\right)$

$=\left(3x+4\right)\left(x+2\right)$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$18x^2+39x-15$

$\mathrm{Factor\;out\;common\;term\;3:3(6x^2+13-5)}$

$18x^2+39x-15$

$\mathrm{Factor\;6x^2+13x-5:(3x-1)(2x+5)}$

$=3\left(3x-1\right)\left(2x+5\right)$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$16x^2-25$

$\mathrm{apply\;exponents\;rules}$

$=\left(4x\right)^2-5^2$

$\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}x^2-y^2=\left(x+y\right)\left(x-y\right)$

$\left(4x\right)^2-5^2=\left(4x+5\right)\left(4x-5\right)$

$=\left(4x+5\right)\left(4x-5\right)$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$6x^2-11x-10$

$\mathrm{Break\;the\;expression\;into\;groups}$

$=\left(6x^2+4x\right)+\left(-15x-10\right)$

$\mathrm{Factor\;out\;2x\;from\;6x^2+4x:2x(3x+2)}$

$\mathrm{Factor\;out\;-5\;from\;-15x-10:-5(3x+2)}$

$=2x\left(3x+2\right)-5\left(3x+2\right)$

$\mathrm{Factor\:out\:common\:term\:}3x+2$

$=\left(3x+2\right)\left(2x-5\right)$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~Learn with Lenvy~