Factoring numbers

Question

x^5+x^3-2x

I know how to get x(x^4+x^2-2), but past that I do not know.

Answer 1

Michelle,

As while factoring polynomials, we know that we start with breaking the largest exponent into halves.

So we know that we start out with (x² )(x² )

The next step is to recall how whenever we factor ax² + bx + c, for example, we know that we need to figure out two numbers that add up to b and multiply to c. Here we have x⁴ + x² - 2, so we know that we have to pick numbers that add up to 1 and multiply to -2. Those two numbers are -1 and 2, because -1 + 2 = 1, and -1 * 2 = -2. In conclusion, we factor this out to (x² -1)(x² + 2).

Hope this helps! :)

Answer 2

Hi Michelle,

X⁵+ X³-2x = x ( X⁴+ X²-x)

Substitute, Let U = X2, which also means square root of U also equals X.

squareroot(U)(U² + U - 2)

squareroot(U)(U-1)(U+2), Substitute back

X(X²-1)(X²+2), Please note that (a²+b²) = (a+b)(a-b), where a = x and b = 1.

X(x+1)(x-1)(x²+2)

Answer is X(x+1)(x-1)(x²+2)

Thanks,

Wesley

Answer 3