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Objective

Objective. SWBAT review Chapter 9 concepts. Add Polynomials. Like Terms terms that have the same variable. (2x ³ – 5x² + x) +. (2x ² + x ³ – 1). You can add polynomials using the vertical or horizontal format. Vertical Format. Horizontal Format.

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Objective

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  1. Objective • SWBAT review Chapter 9 concepts

  2. Add Polynomials Like Terms terms that have the same variable (2x³ – 5x² + x) + (2x² + x³ – 1) You can add polynomials using the vertical or horizontal format. Vertical Format Horizontal Format (2x³+ x³) + (2x²– 5x²)+ x– 1 2x³ – 5x² + x x³ + 2x² – 1 3x³ – 3x² + x – 1 3x³ – 3x² + x – 1

  3. Subtract Polynomials Like Terms terms that have the same variable (4n² + 5) – (-2n² + 2n – 4) You can subtract polynomials using the vertical or horizontal format. Vertical Format Horizontal Format 4n² + 5 (4n²+ 2n²)– 2n + (5+ 4) – (-2n² +2n – 4) +(2n² -2n + 4) 6n² – 2n + 9 6n² – 2n + 9

  4. Section 9.2 “Multiply Polynomials” When multiplying polynomials use the distributive property. Distribute and multiply each term of the polynomials. Then simply. 2x³ (x³ + 3x² - 2x + 5)

  5. “Multiply Using FOIL” When multiplying a binomial and another polynomial use the method. FOIL First Outer Inner Last

  6. “Multiply Using FOIL” (3a + 4) (a – 2) combine like terms

  7. Section 9.4 “Solve Polynomial Equations in Factored Form” Zero-Product Property If ab = 0, then a = 0 or b = 0. The zero-product property is used to solve an equation when one side of the equation is ZERO and the other side is the product of polynomial factors. (x – 4)(x + 2) = 0 The solutions of such an equation are called ROOTS. x + 2 = 0 x – 4 = 0 x = -2 x = 4

  8. “Solving Equations By Factoring” 2x² + 8x = 0 When using the zero-product property, sometimes you may need to factor the polynomial, or write it as a product of other polynomials. Look for the greatest common factor (GCF) of the polynomial’s terms. GCF- the monomial that divides evenly into EACH term of the polynomial. Look for common terms GCF

  9. Solve Equations By Factoring 2x² + 8x = 0 Factor left side of equation 2x(x + 4) = 0 Zero product property x + 4 = 0 2x = 0 x = -4 x = 0 The solutions of the equation are 0 and -4.

  10. Section 9.5 “Factor x² + bx + c” Factoring x² + bx + c x² + bx + c = (x + p)(x + q) provided p + q = b and pq = c x² + 5x + 6 = (x + 3)(x + 2) Remember FOIL

  11. Factoring polynomials n² – 6n + 8 Find two ‘negative’ factors of 8 whose sum is -6. (n – 2)(n – 4)

  12. A shortcut…for factoring ax² + bx + c • (1) multiply ‘a’ and ‘c’ together. • (2) factor new polynomial normally. • (3) divide number terms of binomial by ‘a’. • (4) simplify fractions. • (5) move denominator of fractions in front of variable terms of binomials

  13. Section 9.6 “Factor ax² + bx + c” 2x² – 7x + 3 First look at the signs of b and c. (x – 3)(2x – 1)

  14. Section 9.7 “Factor Special Products” You can use the following special products patterns to help you factor certain polynomials. Perfect Square Trinomial Pattern (addition) a² + 2ab + b² (a + b)² (a + b)(a + b) Perfect Square Trinomial Pattern (subtraction) a² – 2ab + b² (a – b)² (a - b)(a - b) Difference of Two Squares Pattern a² – b² (a + b)(a – b)

  15. Factoring Polynomials Completely • (1) Factor out greatest common monomial factor. • (2) Look for difference of two squares or perfect square trinomial. • (3) Factor a trinomial of the form ax² + bx + c into binomial factors. • (4) Factor a polynomial with four terms by grouping. 3x² + 6x = 3x(x + 2) x² + 4x + 4 = (x + 2)(x + 2) 16x² – 49 = (4x + 7)(4x – 7) 3x² – 5x – 2 = (3x + 1)(x – 2) -4x² + x + x³ - 4 = (x² + 1)(x – 4)

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