5 Chapter Test

Do you know HOW?

Write each polynomial function in standard form. Then classify it by degree and by number of terms and describe its end behavior.

1. y = 3 x 2 − 7 x 4 + 9 − x 4 y equals , 3 x squared , minus , 7 x to the fourth , plus 9 minus , x to the fourth
2. y = 2 x ( x 2 − 3 ) ( x 2 + 2 ) y equals 2 x open , x squared , minus 3 close open , x squared , plus 2 close
3. y = ( t − 2 ) ( t + 1 ) ( t + 1 ) y equals open t minus 2 close open t plus 1 close open t plus 1 close

Write a polynomial function for each set of zeros.

4. x = 1 , 2 , 3 5 x equals 1 comma 2 comma , 3 fifths
5. x = 2 , − i x equals square root of 2 , comma negative i
6. x = 3 + i , − 1 − 5 x equals 3 plus i comma negative 1 minus square root of 5

Find the quotient and remainder.

7. ( x 2 + 3 x − 4 ) ÷ ( x − 1 ) open , x squared , plus 3 x minus 4 close divides open x minus 1 close
8. ( x 3 + 7 x 2 − 5 x − 6 ) ÷ ( x + 2 ) open , x cubed , plus , 7 x squared , minus 5 x minus 6 close divides open x plus 2 close
9. ( 2 x 3 + 9 x 2 + 11 x + 3 ) ÷ ( 2 x + 3 ) open 2 , x cubed , plus , 9 x squared , plus 11 x plus 3 close divides open 2 x plus 3 close

For each equation, state the number of complex roots, the possible number of real roots, and the possible rational roots.

10. 3 x 4 + 5 x 3 − 2 x 2 + x − 9 = 0 3 x to the fourth , plus 5 , x cubed , minus , 2 x squared , plus x minus 9 equals 0
11. x 7 − 2 x 5 − 4 x 3 − 2 x − 1 = 0 x to the seventh , minus , 2 x to the fifth , minus , 4 x cubed , minus 2 x minus 1 equals 0

For each equation, find all the roots.

12. 3 x 4 − 11 x 3 + 15 x 2 − 9 x + 2 = 0 3 x to the fourth , minus , 11 x cubed , plus , 15 x squared , minus 9 x plus 2 equals 0
13. x 3 − x 2 − x − 2 = 0 x cubed , minus , x squared , minus x minus 2 equals 0
14. One x-intercept of the graph of the cubic function f ( x ) = x 3 − 2 x 2 − 111 x − 108 f open x close equals , x cubed , minus , 2 x squared , minus 111 x minus 108  is − 9 . negative 9 .  What are the other zeros?

Use synthetic division and the Remainder Theorem to find P ( a ) . p open eh close .

15. P ( x ) = 6 x 4 + 19 x 3 − 2 x 2 − 44 x − 24 ; a = − 2 3 p open x close equals , 6 x to the fourth , plus , 19 x cubed , minus , 2 x squared , minus 44 x minus 24 semicolon . eh equals negative , 2 thirds
16. P ( x ) = x 4 + 3 x 3 − 7 x 2 − 9 x + 12 ; a = 3 p open x close equals , x to the fourth , plus 3 , x cubed , minus , 7 x squared , minus 9 x plus 12 semicolon eh equals 3
17. P ( x ) = x 3 + 3 x 2 − 5 x − 4 ; a = − 1 p open x close equals , x cubed , plus 3 , x squared , minus 5 x minus 4 semicolon eh equals negative 1

Expand each binomial.

18. ( x + z ) 5 open x plus z close to the fifth
19. ( 1 − 2 t ) 2 open 1 minus 2 t close squared
20. Graph and write the equation of the cubic function that is obtained from the parent function y = x 3 y equals , x cubed  after this sequence of transformations: vertical stretch by a factor of 2, reflection across the x-axis, translation 3 units down and 4 units right.

Do you UNDERSTAND?

21. Physics You take measurements of the distance traveled by an object that is increasing its speed at a constant rate. The distance traveled as a function of time can be modeled by a quadratic function.

    1. Write a quadratic function that models distances of 10 ft at 1 sec, 30 ft at 2 sec, and 100 ft at 4 sec.
    2. Find the zeros of the function.
    3. Reasoning Describe what each zero represents for this real-world situation.
22. Writing For the polynomial x 6 − 64 , x to the sixth , minus 64 comma  could you apply the Difference of Cubes? Difference of Squares? Explain your answers.
23. The number of pairs of shoes Emily buys varies directly as the square of the area of the floor of her closet. If she can fit 12 pairs of shoes when her closet was 10 square feet, how many pairs of shoes will she fit when the area of her closet floor is 18 square feet?

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