Sections: 4.1,4.2,4.3,4.4,4.5,4.6,4.7 1. Determine which of the following is a p

Question

Sections: 4.1,4.2,4.3,4.4,4.5,4.6,4.7 1. Determine which of the following is a polynomial and then find the degre of the polynomial. (a) fr47 2 (b) g(x)=2x+20.2 (c) h(x)-V2+6 2. Find the following produt:3y)y9) 3. Find the following product: (-x + 2y)(z2-3ry+2y2) 4. Find the following product: (2r+y)82 -4ry +5y) 5. Multiply: (2r +3)(82 + 3) 6. Perform the indicated operation: (812-4x + 4)-(-2t + 3-7) 7. Perform the indicated operation: (5x+3(- -1) 8. Perform the indicated operation:4+2ab-3ab) 9. If 325r+2 is subtracted from 7 2 + 2x-9, find the difference 10. Factor completely: 12ry-75ry 11. Factor completely:2-5s + 6 12. Factor completely: 4 - Sa2-1 13. Factor completely: 25m2 -20m +4 14. Factor completely: 4s 12s-8 15. Factor completely: 12r 10-12r 16. Factor completely: 42 100 17. Factor completely: 81s 18. Solve the equation: 2r 19. Solve the equation: 4x2 + 12x-0 20. Solve the equation: 2-2r2+-7 21. Solve the equation: 5 4x + 12-2x + 12 22. Solve the equation: 2-9-0 23. Solve the equation: 52 +2-42r2 + 2r +8 24. Solve the equation: 5z2 + 2-4-2r2 +2r + 8 10- 225t16

Explanation / Answer

(a) f(x) is a polynomial of degree 3.

(b) h (x) is not a polynomial.

2. (x+3y)(x2-3xy +9y2)= x3-3x2y+9xy2+3x2y-9xy2+27y3= x3-27y3 (we can also use the formula a3 – b3 = (a – b)(a2 + ab + b2), where a = x and b = 3y).

3. (-x+2y)(x2-3xy +2y2)= -x3 +3x2y-2xy2+2 x2y-6xy2+4y3= -x3 +5x2y-8xy2+4y3

6. (8x2-4x+4)-(-2x2+3x-7) = 8x2-4x+4 +2x2-3x +7 =10x2-7x+11.

8. –a2b3(–4a2b3+2ab2-3ab)= 4a4b6 -2a3b5+3a3b4 ( as mx *my = mx+y ).

10 12x3y- 75xy3 = 3xy(4x2-25y2)= 3xy[ (2x)2- (5y)2]= 3xy(2x+5y)(2x-5y). (as a2–b2 = (a+b)(a-b)) .

21. 5x2+4x +12 = 2x +12 so that 5x2+4x +12 - 2x -12= 0 or, 5x2+2x= 0 or, x(5x+2) = 0. Hence, either x = 0 or, 5x +2 = 0, in which case, x = -2/5.

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