5x 2 8x 5 0
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- factor quadratic ten^2-7x+12
- expand polynomial (x-three)(10^3+5x-2)
- GCD of 10^4+2x^3-9x^two+46x-xvi with x^4-8x^3+25x^2-46x+16
- quotient of x^3-8x^2+17x-6 with ten-3
- remainder of ten^3-2x^2+5x-7 divided by ten-three
- roots of x^ii-3x+2
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What is factoring?
A polynomial with rational coefficients can sometimes be written as a product of lower-degree polynomials that also have rational coefficients. In such cases, the polynomial is said to "factor over the rationals." Factoring is a useful way to discover rational roots (which correspond to linear factors) and simple roots involving square roots of integers (which correspond to quadratic factors).
Polynomials with rational coefficients e'er accept as many roots, in the complex plane, as their caste; all the same, these roots are ofttimes not rational numbers. In such cases, the polynomial will non factor into linear polynomials.
Rational functions are quotients of polynomials. Like polynomials, rational functions play a very important role in mathematics and the sciences. Just as with rational numbers, rational functions are usually expressed in "lowest terms." For a given numerator and denominator pair, this involves finding their greatest common divisor polynomial and removing it from both the numerator and denominator.
5x 2 8x 5 0,
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