Name:_______________________________________________________ Date:____________________________ Chapter 5 Test Review Formulas you need to MEMORIZE: Formula you will be given: 3
3
2
2
Difference of cubes: a – b = (a – b)(a + ab + b ) Quadratic formula: 3
3
2
2
Sum of cubes: a + b = (a + b)(a – ab + b ) !b ± b 2 ! 4ac
x
=
2
2
Difference of squares: a – b = (a + b)(a-­‐b) 2a
#1-­‐5: Matching. From the list at the right, choose the 2 words that correctly describe each of the polynomials. You may use some of the words more than once, and some might not be used at all.
______ ______ 1. 3x – 4x2 A.
B.
C.
D.
E.
F.
G.
______ ______ 2. 2x4 ______ ______ 3. 2x + 1 ______ ______ 4. 5x2 – 2x + 3x3 ______ ______ 5. 8x2 – x4 – 9 Monomial Binomial Trinomial Linear Quadratic Cubic Quartic
6. Write the end behavior for the following graph. The pick which of the following equations would have to be the equation of the graph. End behavior: A. y= x4 + 2x3 + 2x2 – 4 B. y= -­‐x4 + 2x3 + 2x2 – 4 C. y= x3 + 2x2 + 2x – 4 D. y= -­‐x3 + 2x2 + 2x – 4 7. Write the end behavior for the following graph. The pick which of the following equations would have to be the equation of the graph. A. y= -­‐x2 – 3x + 1 End behavior: B. y= -­‐x3 – 3x + 1 C. y= x2 – 3x + 1 D. y= x3 – 3x + 1 Name:_______________________________________________________ Date:____________________________ 8. If m, n, p, q, and r represent integers (which means they could be positive or negative), which equation could match with each graph? *Hint think about our end behavior rules* Equations: Matching graph: _______ i). y = x4 + mx3 + nx2 + px + r A B C _______ ii). y = -­‐x4 + mx3 + nx2 + px + r _______ iii). y = -­‐x3 + mx2 + nx + p D E F _______ iv). y = x2 + mx + n _______ v). y = x5 + mx4 + nx3 + px2 + qx + r G H _______ vi). y = x3 + mx2 + nx + p _______ vii). y = -­‐x2 + mx + n _______ viii). y = -­‐x5 + mx4 + nx3 + px2 + qx + r 9. What does "the multiplicity of a zero" mean?
10. Write a quadratic function in standard form with a multiplicity of 2 for the zero at 5. 11. Write a polynomial function in factored form with zeros -­‐4, 0, and 3. 12. Write a polynomial function in factored form with the following zeros: x = 9 with multiplicity 2 x = -­‐11 with multiplicity 3 x = 6 Name:_______________________________________________________ Date:____________________________ 13. Find the zeros of each function. State the multiplicity of multiple zeros. a) y = (x + 1)(x − 8)(x − 9) b) y = x2(x + 1) c) y = (x − 3)(x − 4)2 14. Write a polynomial function in factored form for each graph. a). b). Equation: ________________________ d). Equation: _______________________ c). 4 Equation: _____________________ Equation: ________________________ 15. Factor the following expressions completely: a) 4x + 8y b) 3x 2 !18x + 24 c) x 3 + 64 d) 2x 2 ! 200 f) x 3 ! 4x 2 ! 7x g) 343x 3 !1000 h) 2x 4 ! 5x 3 ! 3x 2 j) 4x 2 ! 81 k) 6x 2 +11x !10 l) 3x 3 +12x 2 ! 3x !12 n) 2x 3 ! 54 o) 2x 3 + 250 p) x 4 !12x 2 ! 64 e) x 3 + 2x 2 + 5x +10 i) x 2 !10x + 9 m) 3x 2 !18x Name:_______________________________________________________ Date:____________________________ 16. Find all real and imaginary solutions of the equation: x3 – 125 = 0 17. Find all real and imaginary roots of the equation: 27x3 + 8 = 0 18. Divide using long division. ( x 3 +11x 2 + 25x ! 21 ) ÷ ( x + 7 ) 19. Divide using synthetic division. a) (x3 − 3x2 + 2) ÷ (x − 1) b) (x5 – 2x2 + 3x – 1) ÷ (x + 2) 20. For the following polynomial x 5 ! 8x 3 ! 9x a) State the degree: _____________ b) Classify by the number of terms: _____________________________ c) Predict the number of zeros: ______________________ d) Find all roots of the polynomial: ______________________________ ����������������������������������������� ��������� �
22. Find a function of best fit for the following data:�
21. Find the roots.
a)
b)