Jasonbradley
Home

(x-3)(x-8)

2 min read Jun 17, 2024
(x-3)(x-8)

Factoring the Expression (x-3)(x-8)

The expression (x-3)(x-8) is already in its factored form. However, we can expand it to obtain a polynomial expression.

Expanding the Expression

To expand the expression, we use the distributive property (also known as FOIL - First, Outer, Inner, Last).

  1. First: Multiply the first terms of each binomial: x * x = x²
  2. Outer: Multiply the outer terms of the binomials: x * -8 = -8x
  3. Inner: Multiply the inner terms of the binomials: -3 * x = -3x
  4. Last: Multiply the last terms of each binomial: -3 * -8 = 24

Now we add all the terms together: x² - 8x - 3x + 24

Combining like terms, we get: x² - 11x + 24

The Factored Form vs. Expanded Form

  • Factored Form: (x-3)(x-8)
    • This form is useful for finding the roots or zeros of the expression. The roots are the values of x that make the expression equal to zero. In this case, the roots are x=3 and x=8.
  • Expanded Form: x² - 11x + 24
    • This form is useful for evaluating the expression for specific values of x or for graphing the function represented by the expression.

Conclusion

The expression (x-3)(x-8) is already in its factored form. Expanding it gives us the polynomial x² - 11x + 24. Both forms have their own uses, and understanding the relationship between them is important in algebra.

Related Post

Featured Posts