A polynomial is a mathematical formula that involves the addition of powers in one or more variables, each multiplied by a specific coefficient. To ascertain if an expression falls into the category of a polynomial, ensure that it only encompasses constants, variables, positive integer exponents, alongside the operations of addition, subtraction, and multiplication. Expressions with division by a variable or those containing negative or decimal exponents are not deemed as polynomials.
| Topic | Problem | Solution |
|---|---|---|
| None | $x^{2}-13 x+12$ | Find the roots of the quadratic equation \(x^2 - 13x + 12 = 0\) using the quadratic formula: \(x = … |
| None | $6 x^{2}-5 x-6$ | Given the quadratic equation: \(6x^2 - 5x - 6 = 0\) |
| None | $2 x^{2}-5 x+3$ | This is a quadratic equation of the form \(ax^2 + bx + c\). |
| None | \( 15 x^{4}+12 x^{3}-18 x \) | \( \text{Factor out the greatest common factor }\)\( GCF(x, 15x^4, 12x^3, -18x) \) |
| None | \( 15 m^{4} n^{4}+6 m n^{3}+3 m^{2} n^{2} \) | \(\displaystyle \text{Factor out } m\cdot n^{2} \text{ from the expression:} \) |