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Section 4.4 – Factoring Quadratic Expressions

Section 4.4 – Factoring Quadratic Expressions. Factors of a given number are numbers that have a product equal to the given numbers. Factors of a given expression are expressions that have a product equal to the given expression.

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Section 4.4 – Factoring Quadratic Expressions

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  1. Section 4.4 – Factoring Quadratic Expressions Factors of a given number are numbers that have a product equal to the given numbers. Factors of a given expression are expressions that have a product equal to the given expression. Factoring is rewriting an expression as a product of its factors.

  2. Section 4.4 – Factoring Quadratic Expressions Essential Understanding: You can use the Distributive Property or the FOIL method to multiply two binomials. (x + 4)(x+2) = _____________

  3. Section 4.4 – Factoring Quadratic Expressions Essential Understanding: To factor x2 + 6x + 8, think FOIL in reverse. Find two binomials for which the first terms have the product of x2, the products of the outer and the inner have the sum of 6x, and the last terms have the product of 8. x2 + 6x + 8 = ___________________

  4. Section 4.4 – Factoring Quadratic Expressions Problem 1: What is the expression in factored form? x2 + 9x + 20

  5. Section 4.4 – Factoring Quadratic Expressions Problem 1: What is the expression in factored form? x2 + 14x – 72

  6. Section 4.4 – Factoring Quadratic Expressions Problem 1: What is the expression in factored form? -x2 + 13x – 12

  7. Section 4.4 – Factoring Quadratic Expressions Problem 1: What is the expression in factored form? x2 – 11x + 30

  8. Section 4.4 – Factoring Quadratic Expressions Problem 1: What is the expression in factored form? -x2 + 14x + 32

  9. Section 4.4 – Factoring Quadratic Expressions The greatest common factor (GCF) of an expression is a common factor of the terms in the expression. It is the common factor with the greatest coefficient and the greatest exponent.

  10. Section 4.4 – Factoring Quadratic Expressions Problem 2: What is the expression in factored form? 6n2 + 9n

  11. Section 4.4 – Factoring Quadratic Expressions Problem 2: What is the expression in factored form? 4x2 + 20x – 56

  12. Section 4.4 – Factoring Quadratic Expressions Problem 2: What is the expression in factored form? 7m2 – 21

  13. Section 4.4 – Factoring Quadratic Expressions Problem 2: What is the expression in factored form? 9x2 + 9x – 18

  14. Section 4.4 – Factoring Quadratic Expressions Problem 2: What is the expression in factored form? 4x2 + 8x + 12

  15. Section 4.4 – Factoring Quadratic Expressions Problem 3: What is the expression in factored form? 2x2 + 11x + 12

  16. Section 4.4 – Factoring Quadratic Expressions Problem 3: What is the expression in factored form? 4x2 – 4x – 3

  17. Section 4.4 – Factoring Quadratic Expressions Problem 3: What is the expression in factored form? 4x2 +7x + 3

  18. Section 4.4 – Factoring Quadratic Expressions Problem 3: What is the expression in factored form? 2x2 – 7x + 6

  19. Section 4.4 – Factoring Quadratic Expressions Problem 3: What is the expression in factored form? 2x2 +2x + 2

  20. Section 4.4 – Factoring Quadratic Expressions A perfect square trinomial is a trinomial that is the square of a binomial. For example, x2 + 10x + 25 = (x+5)2

  21. Section 4.4 – Factoring Quadratic Expressions If ax2 +bx +c is a perfect square trinomial, then ax2 and c are squares of the terms of the binomial and thus are both positive. bx is twice the product of the terms of the binomial.

  22. Section 4.4 – Factoring Quadratic Expressions

  23. Section 4.4 – Factoring Quadratic Expressions Problem 4: What is x2 – 6x + 9 in factored form

  24. Section 4.4 – Factoring Quadratic Expressions Problem 4: What is 64x2 +16x + 1 in factored form

  25. Section 4.4 – Factoring Quadratic Expressions Problem 4: What is 4x2 – 20x + 25 in factored form

  26. Section 4.4 – Factoring Quadratic Expressions The expression a2 – b2 is the difference of two squares. There is a pattern to its factors.

  27. Section 4.4 – Factoring Quadratic Expressions Problem 5: What is 25x2 – 49 in factored form?

  28. Section 4.4 – Factoring Quadratic Expressions Problem 5: What is 16x2 – 81 in factored form?

  29. Section 4.4 – Factoring Quadratic Expressions Problem 5: What is 81x2 + 49 in factored form?

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