Solving Polynomials by Factoring

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Presentation transcript:

Solving Polynomials by Factoring Solving polynomials means that there is an equal sign. Don’t add one. If there is no equal sign, the directions probably say “factor.” Steps: Factor completely. Set any part of the factored form that involves the variable equal to zero. 3. Solve. You may need to use the quadratic formula. 4. Check your answers by plugging back into original equation. - b ± √b2 – 4ac 2a This only works for quadratic (x2) equations. x =

Solving Polynomials by Factoring 1. 3x4 – 108 = 0 x = ± √6, x = ± √6 i 2. x4 + 6x3 = 9x2 + 54x x = 0, – 3, + 3, – 6

Solving Polynomials by Factoring 3. x3 = 1,331 x = 11, x = – 11/2 (1 ± √3 i) 4. 2x5 + 24x = 14x3 x = 0, x = ± 2, x = ± √3

Solving Polynomials by Factoring 5. 3(x – 1)2 = 4x + 2 x = 5/3 ± √22 6. 9x2 – 12x + 85 = 0 x = 2/3 ± 9 i

Solving Polynomials by Factoring 7. (x + 1)2 – 3(x – 1)2 = 6 x = 2 8. 4x2 – 28x + 49 = 0 x = 7/2

Solving Polynomials by Factoring 9. 12x4 + 54x2 – 30 = 0 x = ± √5 i, x = ± (√2/2) 10. x5 – 9x3 + 8x2 – 72 = 0 x = – 2, 3, – 3 and x = ± √3 i

Solving Polynomials by Factoring 11. 4x3 – 6x4 – 12x + 18x2 = 0 x = 0, 2/3 and x = ± √3