91Ó°ÊÓ

Factoring polynomials involves breaking down a polynomial into simpler terms, or factors, that multiplied together give back the original polynomial. This is a crucial skill in algebra because it allows us to simplify expressions and solve equations easily.

Another way to think of this is like reversing the distributive property. Instead of multiplying out, we are finding what was multiplied. In the exercise, we broke down the polynomial \(x^2 - 13x + 36\) into factors \( (x - 9)(x - 4) \).

We need to find values that make this possible. By identifying the correct factors, we look for numbers that fulfill specific conditions based on the polynomial structure. Once the factors are found, we can rewrite the polynomial in its simplest form.

A quadratic equation is a second-degree polynomial in the form \( ax^2 + bx + c = 0 \). It is called 'quadratic' because 'quad' means 'square,' and the equation involves the variable raised to the power of two.

In the exercise, our quadratic equation was \(x^2 - 13x + 36\). Here:

• \(a = 1\) (coefficient of \(x^2\))
• \(b = -13\) (coefficient of \(x\))
• \(c = 36\) (constant term).

Quadratic equations can be solved by factoring (like in the exercise), using the quadratic formula \left( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \right)\, or completing the square. Understanding the components of a quadratic equation helps us apply different methods to solve it.

Coefficients are the numerical or constant parts of terms in expressions. In any polynomial, they are the numbers in front of the variables.

For instance, in our quadratic equation \(x^2 - 13x + 36\), we see:

• \