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Review - 3 x 3-3 x 2-11 x-6 2 x 4 13 x 3 28 x 2 23 x 6 13...

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Review 1. Solve for x : 4 4 x = 16 8 x 2. Rationalise and simplify 1 ( x + 3)( x - 4) . 3. For what value of x does log 4 (2 3 x 5 ) = log 8 (4 x 3 )? 4. How many digits are there in 5 200 ? 5. Factor f ( x ) = 2 x 3 + 7 x 2 + 7 x + 2 6. A child’s age increased by 10 years gives a number which has a square root (whole number). Decreased by 10 years, the child’s age gives that square root. How old is the child? 7. Divide using long division with remainder: x 5 + x 4 - 2 x 3 + 2 x 2 + 4 x + 1 by x 3 + x - 1. 8. Divide using Synthetic division with remainder: x 6 - x 5 + x 4 + x 3 + x 2 - x - 1 by x 2 + 2 x - 2. 9. What polynomial has roots which are reciprocals of: x 4 - x 3 + x 2 - x +1. 10. What polynomial has roots which two times those of 2 x 4 +2 x 3 - x 2 +4 x - 1. 11. Find GCD(512,1424). 12. Find GCD( x 4 + 3
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Unformatted text preview: + 3 x 3-3 x 2-11 x-6 , 2 x 4 + 13 x 3 + 28 x 2 + 23 x + 6). 13. For any n ≥ 1 1 + 7 + 19 + ... + (3( n-1)( n-2) + 1) + (3 n ( n-1) + 1) = n 3 14. a For any n ≥ 1, prove that 2 n +2 does divide 3 2 n-1. (only one of (x-1),(x+1) can be divisible by four at the same time, if one is even both are even) 14. b For any n ≥ 1, prove that 2 n +3 does not divide 3 2 n-1. (Easy ±rst case, use the last problem to build up to this one.) 15. Expand the ±rst 3 terms of (2 x + 3) 15 . 16. How many ways are there to pick 8 books from 10 and put them in order on the bookshelf?...
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