Math Question Need Help!! Need Help Thank You?

Question

i have a question on factoring how owuld you factor lets say these X(2x-1)+2(2x-1) and (x+3)^2-3(x+3) and 8x^4-31x^2-4 Im having trouble factoring those Help would be appreciated thank you!!

Answer 1

(x + 2)(2x - 1);

(x + 3)(x + 3 - 3)
x(x + 3);

The last one is more intuitive...You have to try to think of numbers that when combined will come to 31 and then play around with them...In this case 8 times 4 is 32 less one is 31...so playing around with those numbers I tried
(8x^2 +4)(x^2 -1)...the 8x^4 works and the -4 works but instead of -31x^2 we would get 4x^2...so try flipping the 1 and the 4 gives us:
(8x^2 +1)(x^2 - 4)

Works out perfectly!

Answer 2

To factor the first one, you would factor out a (2x-1), which would make it (2x-1)(X+2)

The second one, you pull out a (x+3), which would make it (x+3)(x)