MAT221 W5D.docx - If your assigned number Factor if...

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If your assigned number Factor, if possible. If the Factor completely. If Factor using the AC 10 m 2 – 17m + 16 p. 346 #100 9t 2 + 5t – 4 Factor; GCF; Prime factors; Perfect square; Grouping To factor m 2 −17 m + 16, I need two integers that have a product of 16 and a sum of −17. Since the product is positive and the sum is negative, both integers must be negative and there is no prime number. m 2 -17m +16 = (m -16) (m-1) Only −1 and −16 have a product of 16 and a sum of −17. Now replace −17 m by −1 m + (−16) or −1 m 16 m and factor by grouping : m 2 -17 m + 16 = m 2 -16 m - 1 m + 16 Replace -17 m by -16 m- 1 m = m ( m -16) – 1( m -1) Factor out m and -16 =( m- 16) (m-1) Factor out m – 1 Check by FOIL: ( m -16) ( m -1) = m 2 -17 m + 16 Part 2. Factor completely. If polynomial is prime, say so. No

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