# MAT221 Week 5 Discussion 1 - #80 For this problem I have to...

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#80 For this problem I have to factor this polynomial: w2 + 30w +81 W 2 + 30w +81 The GCF for this polynomial is w. The Prime Factor of this problem is 81. Now I have to find two numbers that add up to 30 but will multiply to 81. The Prime Factor of 81 is 3 and 27 because 3 X 27 = 81 Answer is (w + 3)(w +27) I can check this by multiplying back together: w 2 +3w + 27w +81 = w 2 +30w +81 #106 I have to factor this polynomial ac + xc + aw 2 + xw 2 The four terms means start with grouping . ac + xc and aw 2 + xw 2 I have to factor out the common term for both the groups. c(a + x) c is the GCF of the first group and it factored out like this c(a + x) w 2 (a + x) For the second group the GCF is w 2 which factored out to w 2 (a + x) Now I have to write it as an equation which would look like this c(a + x) + w 2 (a + x) or (c(a + x) + w 2 (a + x) Now I have to factor (a + x) which equals (a+x)(c + w 2 ) So the answer is (a+x)(c + w 2 ) If you multiply it back together it is: ac + xc + aw 2 + xw 2 #68 I will factor the following 10a