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## Polynomials

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**GCF**Greatest Common Factor**GCF with Variables**Note: With variables, the GCF will always be the smallest exponent of a common variable Examples: 12x3, 16x2 45a5, 50a7 GCF = 4x2 GCF = 5a5**Factor out the GCF**Put the GCF outside of (parenthesis). Divide each term by the GCF. You will always have the same numbers of terms you start with**16x2 – 8x**8x(2x – 1)**10x – 10y**10(x – y)**8r2 – 24r**8r(r – 3)**6n2 + 15n**3n(2n + 5)**6x3 – 9x2 + 3x**3x(2x2 – 3x + 1)**2a3 – 6a**2a(a2 – 3)**8y3 – 20y2 + 12y**4y(2y2 – 5y + 3)**7x3 – 28x2**7x2(x – 4)**4m3 – 20m**4m(m2 – 5)**3x(x + 2) – 2(x + 2)**(x + 2)(3x – 2)**5z(z – 6) + 4(z – 6)**(z – 6)(5z + 4)**1. Group the 1st two terms and the 2nd two terms**Steps to Factor by Grouping 4 terms 2. Factor out the GCF of each group 3. Write down the common parenthesis 4. In another parenthesis, write the GCFs 5. Check to see if the parenthesis can factor again**x3 + 12x2 – 3x – 36**x2(x + 12) – 3(x + 12) (x + 12)(x2 – 3)**y3 – 14y2 + y – 14** (y3 – 14y2) + (y – 14) y2(y – 14) + 1(y – 14) (y – 14)(y2 + 1)**m3 – 6m2 + 2m – 12**(m3 – 6m2) + (2m – 12) m2(m – 6) + 2(m – 6) (m – 6)(m2 + 2)**p3 + 9p2 + 4p + 36**(p3 + 9p2) + (4p + 36) p2(p + 9) + 4(p + 9) (p + 9)(p2 + 4)**x3 + x2 + 5x + 5**(x3 + x2) + (5x + 5) x2(x + 1) + 5(x + 1) (x + 1)(x2 + 5)**x3 – 3x2 – 5x + 15** (x3 – 3x2) + (-5x + 15) x2(x – 3) – 5(x – 3) (x – 3)(x2 – 5)**3x3 – 3x2 + x – 1** (3x3 – 3x2) + (x – 1) 3x2(x – 1) + 1(x – 1) (x – 1)(3x2 + 1)**t2 + 2t + 3kt + 6k**(t + 2)(t + 3k)**x2 + 3x + xk + 3k**(x + 3)(x + k)**ad + 3a – d2 – 3d**(d + 3)(a – d)**2ab + 14a + b + 7**(b + 7)(2a + 1)**CW/HW - Textbook**p. 95 #1 – 18