Factor: 30x^4 – 35x^3 -15x^2?

5 x ² (6 x ² - 7 x - 3)
5 x ² ( 3 x + 1 )( 2 x - 3 )

30x^4 - 35x^3 -15x^2=

5x^2(6x^2 - 7x - 3)=

5x^2[ (2x-3)(3x+1)]

Good luck with the rest of your homework!

30x^4 – 35x^3 -15x^2=
5x^2(6x^2-7x-3) =
5x^2(6x^2-9x+2x-3)=
5x^2[3x(2x-3)+(2x-3)]=
5x^2(2x-3)(3x+1)

First, take each piece of the equation and split it into all of its factors. So, for the first piece, you'd have:
30x^4 = 5 * 3 * x * x * x * x

Note that for the pieces that are subtracted (the 35x^3), you should also include a negative one.

When you have all of the factors for each piece, circle the factors that are the same in all three pieces. If there are factors that don't match in ALL of the pieces of the equation, leave them uncircled. When you've circled everything that matches, look at ONE of the pieces and multiply together the circled factors to get the common factor. Then for each piece, multiply the uncircled factors together to get the leftover pieces. Add the leftover pieces together, surround with parentheses, and multiply by the common factor. You may then have to factor the equation formed by the addition of the leftover pieces, which will require use of the theorems regarding multiplication of polynomials.

5x^2(3x+1)(2x-3)

5x^2(6x^2-7x-3)

the ( ) can then be factored.

30x^4 - 35x^3 - 15x^2
= 5x^2(6x^2 - 7x - 3)
= 5x^2(2x - 3)(3x + 1)

Factor: 30x^4 – 35x^3 -15x^2? Factor the GCF 1st, then factor by grouping.
= 5x²(6x² - 7x - 3)
= 5x²(6x² -9x + 2x - 3)
= 5x²[ 3x(2x - 3) + 1(2x - 3) ]
= 5x² (3x + 1)(2x - 3)