Question

Solve for the roots in the following equation. Hint: Factor both quadratic expressions.

(x^4 + 5x^2 - 36)(2x^2 + 9x - 5) = 0

Answer 1

Do we factor both expressions separately or do we simplify the expression and then factor? Which one do they want

Answer 2

2x * x = 2x^2

Answer 3

did that help?

Answer 4

factor x^4+5x^2-36

and

then factor 2x^ 2+9x-5

I like to find two numbers that multiply to be a*c and add up to b
then factor by grouping (of course you can do short cut way if a=1)

Answer 5

You have (x^4 + 5x^2 - 36)(2x^2 + 9x - 5) = 0, and are to find the roots.
Factor the polynomial within each set of parentheses: Factor (x^4 + 5x^2 - 36) as far as possible, and then factor (2x^2 + 9x - 5) as far as possible. Then, set each of your factors = to 0 and find the solution(s). List all of the solutions as your final answer.

Answer 6

Hint:

1. When there are only even powers in a polynomial to be factored, replace \(x^{2n}\) by \(y^n\) and proceed to factor the reduced polynomial.
Example:
Factor \(a^4-b^2\)
substitute y=a^2, then
\(a^4-b^2=y^2-b^2=(y+b)(y-b)=(a^2+b)(a^2-b)\)

2. Use the usual rules to factorize each quadratic. Do not multiply out.
For great examples, read through all simple, hard and weird cases at the following link:
http://www.purplemath.com/modules/factquad.htm