Assistance on zero product property???

I have a few problems here. I just wanted to know what to do if I can't factor the equation such as (4x^2) -9=0. That up thing is to indicate what power the number is by so its 4x squared. I have MANY. one good explanation will just help me a lot. heres a few more. (7x^2)=18x-11 (10u^3)-(5u^2)=0 (8y^2)-9y+1=0

(p^2)-p-6=0 2x(x-20)=0

Thanks so much

Re: Assistance on zero product property???

$\displaystyle 4x^2 - 9 = 0$

does not need polynomial factoring. You can use reverse order of operations to solve for x directly.

$\displaystyle 7x^2 = 18x-11$

can be re-written as

$\displaystyle 7x^2 - 18x + 11 = 0$

which can be solved using polynomial factoring. Here you can consider how you can factor in terms of (7x + ?)(x + ?) since the only way to multiply to give 7 is 7*1 since 7 is prime. Alternatively you can factor out 7 to get

$\displaystyle 7 (x^2 - (18/7)x + 11/7) = 0$

and then factor the polynomial in the brackets with the coefficient of x^2, which is 1, and use other methods.

For $\displaystyle 10u^3 - 5u^2 = 0$,

you can consider methods of substitution or to look for common factors with each of your terms, and then factor out. In this case, we can identify 5u^2 as a common factor between 10u^3 and -5u^2 and hence the equation can be rewritten as

$\displaystyle 5u^2 (2u-1)=0$

$\displaystyle 8y^2 - 9y + 1$

similar method as mentioned above.

$\displaystyle p^2 - p - 6$

What two numbers, a and b, add to give you -1, and multiply to give you -6? Think about what happens if you were to foil (p+a)(p+b) if the two conditions were satisfied.

$\displaystyle 2x(x-20)=0$

is already factored.