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Do Now: Factor the polynomial.

Do Now: Factor the polynomial. 1.) 2x 2 – 3x – 20 2.) x 2 – 36 3.) x 2 + x – 20. Algebra II. 4 .4: Factoring Polynomials. Chapter 3. We learned how to factor the following. Factoring Polynomials.

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Do Now: Factor the polynomial.

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  1. Do Now: Factor the polynomial. 1.) 2x2 – 3x – 20 2.) x2 – 36 3.) x2 + x – 20

  2. Algebra II 4.4: Factoring Polynomials

  3. Chapter 3 • We learned how to factor the following

  4. Factoring Polynomials • We can also factor polynomials with degree greater than 2. Some can be factored completely using techniques we already know. • A factorable polynomial with integer coefficients is factored completely if it is written as a product of unfactorable polynomials with integer coefficients.

  5. Factoring Polynomials • 2(x+1)(x – 4) is factored completely • 3x(x2 – 4) is not factored completely because x2 – 4 = (x + 2)(x – 2)

  6. Factor: Find Common Monomial • x3 – 4x2 – 5x • 3y5 – 48y3 • 5z4 + 30z3 + 16z2

  7. Factoring Cubes In the second part of the last slide, the special factoring pattern for the difference of two squares was used to factor the expression completely. There are also factoring patterns that we can use to factor cubes.

  8. Factoring Cubes • Sum of Two Cubes a3 + b3 = (a + b)(a2 – ab + b2) • Difference of Two Cubes a3 – b3 = (a – b)(a2 + ab + b2)

  9. Factor the sum or difference of cubes 1.) x3 – 125 2.) 16s5 + 54s2

  10. Factoring by grouping. For some polynomials, you can factor by grouping pairs of terms that have a common monomial factor. This is very similar to our strategy for factoring quadratics of the form ax2 + bx + c when |a| > 1.

  11. Factor by grouping 1) z3 + 5z2 – 4z – 20

  12. Factoring polynomials in quadratic form An expression of the form au2 + bu + c, where u is an algebraic expression, is said to be in quadratic form. The factoring techniques we have studied can sometimes be used to factor such expressions.

  13. Factor Polynomials in Quadratic Form • 16x4 – 81 • 3p8 + 15p5 + 18p2

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