The Factor Theorem is a technique employed in the field of algebra to determine factors of a polynomial. If there exists a factor (x-k) for a polynomial f(x), then the equation f(k)=0 holds true. The process of identifying these factors involves substituting possible factors into the polynomial. If the outcome is zero, then this value is indeed a factor.
| Topic | Problem | Solution |
|---|---|---|
| None |
Given |
Given that |
| None | Given that 2 is a zero of the polynomial function… | Given that 2 is a zero of the polynomial function |
| None | For this exercise, consider the polynomial shown … | Find the factors of the constant term (12) and the leading coefficient (1): \(p_{\text{factors}} = … |
| None |
Find the real zeros of |
The real zeros of a polynomial are the x-values for which the polynomial equals zero. These are als… |
| None |
Factor |
Given the polynomial function |
| None | (a) Find the rational zeros and then the other ze… | Use the Rational Root Theorem to find the possible rational roots of the polynomial. The possible r… |
| None | Use the remainder theorem to find the remainder w… | Given the polynomial function |
| None |
The polynomial of degree |
The polynomial of degree 3 with a root of multiplicity 2 at x=3 and a root of multiplicity 1 at x=-… |
| None |
The polynomial of degree |
We are given a polynomial of degree 4, P(x), with a root of multiplicity 2 at x=2 and roots of mult… |
| None | b Describe the limiting behaviour of the polynomi… | Using Vieta's formulas, we have |