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At this point, you have extensively studied quadratics, which are really polynomials of degree 2 (in the same way a square is also a rectangle). You've learned the quadratic formula,
for the roots of a quadratic, and you've seen how there are no real roots if b2−4ac<0. We also learned that these roots were related to factors. If a quadratic has roots α and β, then we can write it in the factored form
The roots are obvious in this form, as substituting x=α or x=β makes the whole expression 0.
I'm giving you this brief refresher because polynomials work in much the same way. All polynomials have roots and corresponding factors, but the methods for finding them are far harder than for quadratics. However, many of the patterns we've learned about quadratics generalize in useful ways for higher order polynomials.
At this point, you have extensively studied quadratics, which are really polynomials of degree 2 (in the same way a square is also a rectangle). You've learned the quadratic formula,
for the roots of a quadratic, and you've seen how there are no real roots if b2−4ac<0. We also learned that these roots were related to factors. If a quadratic has roots α and β, then we can write it in the factored form
The roots are obvious in this form, as substituting x=α or x=β makes the whole expression 0.
I'm giving you this brief refresher because polynomials work in much the same way. All polynomials have roots and corresponding factors, but the methods for finding them are far harder than for quadratics. However, many of the patterns we've learned about quadratics generalize in useful ways for higher order polynomials.