Review of Factoring

Definition: Difference of Squares

• A² - B² = (A + B)(A - B)

• A² + B² = (A + B)(A - B)

• A² - B² = (A - B)(A - B)

• A² + B² = (A + B)(A + B)

Definition: Binomial

• A polynomial with two terms.

• A polynomial with three terms.

• A polynomial with one term.

• A polynomial with four terms.

Factor: x² + 7x - 30

• (x + 10)(x - 3)

• (x + 5)(x + 6)

• (x - 10)(x + 3)

• (x + 15)(x - 2)

Which of the following is a factor of 3x² - 7x + 2?

• x - 2

• 3x + 1

• x + 2

• x - 1

Example: Factor 2x² + 8x

• 2x(x + 4) - Factor out the greatest common factor.

• 2(x + 4)(x) - Incorrect factorization.

• x(2x + 8) - Incorrect grouping.

• 4(2x + 2x) - Incorrect common factor.

Definition: Factoring

• The process of breaking down an expression into a product of simpler factors.

• A method of solving equations by finding the roots.

• The technique of simplifying fractions to their lowest terms.

• A way to combine like terms in an algebraic expression.

Example: Factor x² + 5x + 6

• (x + 2)(x + 3) - This is a perfect square trinomial.

• (x + 1)(x + 6) - This is a perfect square trinomial.

• (x + 3)(x + 2) - This is a difference of squares.

• (x + 4)(x + 1) - This is a perfect square trinomial.

Definition: Roots of a Polynomial

• Values of x that make the polynomial equal to zero.

• The coefficients of the polynomial.

• The degree of the polynomial.

• The factors of the polynomial.

Definition: Perfect Square Trinomial

• An expression that can be factored into the square of a binomial, e.g., (a + b)² = a² + 2ab + b².

• A polynomial that has no real roots.

• An expression that can be factored into the product of two linear factors.

• A trinomial that is always positive for all values of its variables.

Factor: x² + 11x + 24

• (x + 8)(x + 3)

• (x + 6)(x + 4)

• (x + 12)(x + 2)

• (x + 10)(x + 1)