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 $f(x)=6 x^{3}+5 x^{2}-12 x+4$, answer the f… | Given that \(f(x)=6 x^{3}+5 x^{2}-12 x+4\) and \(\frac{1}{2}\) is a zero of \(f(x)\), we know that … |
| None | Given that 2 is a zero of the polynomial function… | Given that 2 is a zero of the polynomial function \(f(x) = x^{3} - 10x^{2} + 36x - 40\), we can fin… |
| 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 $\mathrm{f}$. Use the real… | The real zeros of a polynomial are the x-values for which the polynomial equals zero. These are als… |
| None | Factor $f(x)=3 x^{3}+7 x^{2}-155 x+225$ into line… | Given the polynomial function \(f(x)=3 x^{3}+7 x^{2}-155 x+225\) and -9 is a zero of \(f(x)\), it m… |
| 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 \(f(x)=4 x^{6}-64 x^{4}+x^{3}-15\), we are asked to find the remainde… |
| None | The polynomial of degree $3, P(x)$, has a root of… | 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 $4, P(x)$, has a root of… | 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 \(\alpha + \beta + \gamma = 2\), \(\alpha\beta + \alpha\gamma + \be… |