4.3 Solve x2 + bx +c = 0 by Factoring

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Presentation transcript:

4.3 Solve x2 + bx +c = 0 by Factoring

Vocabulary: Monomial: one term (ex) x (ex) 4 (ex) 4x (ex) 4xy2 (ex) 3x3y2z Binomial: two terms (ex) x + 2 (ex) 3x – 2 (ex) 4x2 + 5 Trinomial: three terms (ex) x2 + 2x + 6 (ex) 4x4 + 3x2 – 16x

Factor the Expression form x2 + bx + c Factored form : (x + #) (x + #) Second sign of the trinomial identifies same (+) or different (-) signs have to be used in the binomials: First sign of the trinomial goes to both binomials if same is determined. First sign of the trinomial goes to the binomial with the largest number if different is determined. To identify the numbers in the binomials: the numbers must multiply to make “c” and add or subtract to create “b”.

Examples: (ex) x2 – 9x + 20 (ex) x2 + 3x - 12

Page 252 (1-3)

Special Pattern Difference of Squares: a2 - b2 = (a +b) (a – b) (ex) x2 – 4 = (x + 2) (x – 2) Perfect Trinomial: a2 + 2ab + b2 = (a+b)2 (ex) x2 + 6x + 9 = (x + 3)2 a2 - 2ab + b2 = (a - b)2 (ex) x2 – 4x + 4 = (x – 2)2

Factor with Special Patterns (ex) x2 – 49 (ex) 4x2 - 16 (ex) x2 + 25 (ex) 100x2 + 64

Factor with Special Pattern (ex) d2 + 12d + 36 (ex) z2 – 26z + 169

Practice Problems: Page 253 (4-7)

Solve a Quadratic Equation 1) Make sure the equation is in Standard Form 2) Factor the equation 3) Set the factored form equal to zero and solve for the variable. Solving an equation could be asked by the question: Find the zero’s of the function.

Practice Problems: (ex) x2 – 5x + 6 = 0 1) Standard Form (x – 3) (x – 2) 2) Factor x – 3 = 0 x – 2 = 0 3) Solve for x x = 3 x = 2 (ex) 8x – 16 = x2 Rewrite in Standard Form Factor and Solve