Praxis Mathematics - Content Knowledge (5161) Chapter 23 - Polynomials Quiz Questions

28. Factor the quadratic x^2-4. (x+2)(x+2) (x+2)(x-2) (x+4)(x-4) (x-1)(x+4) (x-2)(x-2)

(x+2)(x-2)

25. Factor x^2+4x-5. (x-1)(x+5) (x+1)(x-5) (x-1)(x-5) Not enough information. (x+1)(x+5)

(x-1)(x+5)

16. Subtract: (x^2 + 3x + 4) - (7x^2 - 5x + 2) -6x^2 + 8x + 2 -6x^2 - 8x - 2 6x^2 + 8x + 2 -6x^2 - 8x + 2

-6x^2 + 8x + 2

8. What does z equal when x = 1 and y = 2? x + y + z = 3 -3 2 -1 0 1

0

1. Which of the following equals (x^2)/(x^3*x^n)? x^{n - 1} x^{n + 1} x^n x^{1 - n} 1/(x^{n + 1})

1/(x^{n + 1})

2. Find a * b if a = 2^6 and b = 2^8. 2^{48} 2^6 2^{14} 2^{-2} 2^2

2^{14}

21. Divide the following polynomials: (6x^3-7x^2+2)/(3x+1) 2x^2-3x-1-(1/(3x+1)) 2x^2-3x+1+(3/(3x+1)) 2x^2-3x-1+(1/(3x+1)) 2x^2-3x+1+(1/(3x+1))

2x^2-3x+1+(1/(3x+1))

24. Divide the following polynomials: (2x^3-5x^2-28x+15)/(x-2) 2x^2-x-30+(-45/(x-2)) 2x^2-x-30+(45/(x-2)) 2x^2-x+30+(-45/(x-2)) 2x^2+x-30+(-45/(x-2))

2x^2-x-30+(-45/(x-2))

20. Use the Remainder Theorem to find the remainder when f(x) = x^4 + 4x^3 - x^2 - 16x -12 is divided by x - 4. -92 36 420 548

420

7. What does x equal when y = 3? x + y = 8 5 8 4 3 6

5

29. What does a^b equal if a = 4 and b = 3? 3 36 72 12 64

64

4. Which one of the following equals 2 * 2 * 2 * 2? I) 2^4 II) 2^2 * 2^2 III) 2^6/2^4 III only I, II, and III I and II I only II only

I and II

26. Which of the following are polynomials? I) f(x) = x^4+x II) f(x) = x^2+x*sin(x) III) f(x) = x+2*sin(2) I only I and III I and II III only II only

I only

14. What is the procedure for subtracting polynomials: Multiply the second expression by +1 and add the two expressions together. Multiply the second expression by -1 and subtract the two expressions. Multiply the second expression by +1 and subtract the two expressions. Multiply the second expression by -1 and add the two expressions together.

Multiply the second expression by -1 and add the two expressions together.

18. Which of the following should be evaluated in order to determine if x - 2 is a factor of x^3 + 3x - 4? f(2) f(-2) f(4) f(x - 2)

f(2)

17. Which example correctly illustrates the Factor Theorem? f(x) = x^3 - x^2 + x - 1; f(1) = 0, so x + 1 is a factor of f(x) f(x) = x^3 - x^2 + x - 1; x - 1 is a factor of f(x), so f(-1) = 0 f(x) = x^3 - x^2 + x - 1; f(2) = 5, so x - 2 is a factor of f(x) f(x) = x^3 - x^2 + x - 1; f(1) = 0, so x - 1 is a factor of f(x)

f(x) = x^3 - x^2 + x - 1; f(1) = 0, so x - 1 is a factor of f(x)

19. Which example correctly illustrates the Remainder Theorem? f(x) = x^5 - 5; if f(x) is divided by x - 1, then the remainder equals f(-1) f(x) = x^5 - 5; if x - 1 is a factor of f(x), then f(1) equals 0 f(x) = x^5 - 5; if f(1) equals 0, then x - 1 is a factor of f(x) f(x) = x^5 - 5; if f(x) is divided by x - 1, then the remainder equals f(1)

f(x) = x^5 - 5; if f(x) is divided by x - 1, then the remainder equals f(1)

5. Solve for t. 2s + 2t = 4 t = 2 + s t = 4 - 2s t = 2 - s t = 4 + s t = 4 - s

t = 2 - s

27. Use factoring to find a solution of the following equation: 2x^2+8x = x^2+2x-8. (Remember that if one side of the equation equals zero, and the other side of the equation is a product, then at least one of the parts of the product must equal zero. For example, if 0 = x(3-x), then x must be 0 or (3-x) must be 0.) x = 2 x = -2 x = 0 x = 4 x = 8

x = -2

3. Find x if 4x = 2^4. x = 0 x = 8 x = 2 x = -2 x = 4

x = 4

30. Solve for x. x + 2x = y x = 2y y = 3x y = 2x x = y/2 x = y/3

x = y/3

11. Divide using long division. (x^2+3x-18)/(x-3) x^2+6 x+6 x-6+(2/(x-3)) x-6 x^2+6x

x+6

13. Multiply: (x + 1)(x + 6) 2x + 7 x^2 + 6x + 5 x^2 + 7x + 6 2x + 6

x^2 + 7x + 6

12. Divide using long division. (x^3+12x^2+47x+60)/(x-9) x^2+12x+60+(49/(x-9)) x^2+21x+236+(2184/(x-9)) x^2+21x+236-(2184/(x-9)) x^2+21x+236+(21/(x-9)) x^2+21x+236+(-2184/(x+9))

x^2+21x+236+(2184/(x-9))

9. Divide using long division. (x^3+6x^2-x-30)/(x-2) x^2-8x+15 x^2+8x-15 x^2+8x+12+(3/(x-2)) x^2+8x+15 x^2+8x-12+(2/(x-2))

x^2+8x+15

10. Divide using long division. (x^3+7x^2-6x-72)/(x+6) x^2+x+12 x^2+x-12 x^2+4x+3 x^2-6x-9 x^2-x+12

x^2+x-12

23. Divide the following polynomials: (x^4+81)/(x^2+1) x^2-1+(82(x^2+1)) x^2-1+(-82(x^2+1)) x-81 x^2-81

x^2-1+(82(x^2+1))

22. Divide the following polynomials: (2x^3-13x^2+17x+12)/(2x+1) x^2-7x+12 x^2+x+11+(1/(2x+1)) x^2-x-11+(1/(2x+1)) 2x^2+x-30+(-45/(x-2))

x^2-7x+12

15. Subtract: (x^3 + x^3 + 6) - (x^3 - 2x + 1). x^3 + 2x + 5 x^3 + 2x - 5 3x^3 + 2x - 5 x^2 + 2x - 5

x^3 + 2x + 5

6. Solve for z. x + z = 2 z = z + x x = 2 - z x = z + 2 z = 2 - x z = 2 + x

z = 2 - x