加拿大数学10年级练习第三部分.doc

1. Write y = (x 6)(x 4)(x + 2) in standard form. y = x3 + 48 y = x3 8x2 + 4x + 48 y = x3 2x2 + 4x 8 y = x3 8x2 8x + 24 2. Factor x4 8x2 + 15. (x 3)2(x 5)2 (x 3)(x + 3)(x 5)(x + 5) (x )(x + )(x )(x + ) (x )2(x )2 3. Solve x3 + 5x2 9x 45 = 0 by graphing. 5, 3 5, 3, 3 3, 5, 3 5, 9 4. Evaluate . 60,480 504 84 5. Find the roots of x3 + 4x2 + 3x + 12 = 0. x = 4, i x = 4, x = 4, 3i x = 4, i 6. Classify 2x3 2x by degree and by number of terms. cubic monomial quadratic binomial cubic binomial cubic trinomial 7. Divide (5x3 6 5x) (10 + 5x) using synthetic division. x2 2x + 3, R 24 x2 3x, R 44 x2 2x + 3, R 36 x2 3x, R 56 8. Use a graphing calculator to find a polynomial function to model the data. f(x) = 4.68x3 + 8.87x2 + 4.25x + 6.32 f(x) = 4.68x2 + 8.87x + 6.32 f(x) = 4.68x3 8.87x2 4.25x 6.32 f(x) = 0.4468x3 + 8.87x2 + 4.25x + 6.32 9. Factor 3q3 81. 3(q 3)(q2 + 3q + 9) (q + 3)(q2 + 3q + 9) 3(q 3)(q2 + 3q + 9) (q 3)(q2 + 3q + 9) 10. The table shows the number of hybrid cottonwood trees planted in tree farms in Oregon since 1987. Find a cubic function to model the data and use it to estimate the number of cottonwoods planted in 1998. T(x) = 0.3x3 + 0.3x + 0.4; 167.2 thousand trees T(x) = 0.3x3 + 0.3x2 + 0.1x + 0.1; 167.2 thousand trees T(x) = 0.1x3 + 0.3x2 + 0.3x + 0.1; 172.8 thousand trees T(x) = 0.1x3 + 0.1x + 0.4; 172.8 thousand trees 11. Solve x4 17x2 + 16 = 0. x = 1, 2i x = 1, 4 x = 1, 4i x = 1, 2 12. If no digit appears more than once, how many 3-digit numbers can be formed from the digits 2, 4, 5, 7, and 9? 60 numbers 10 numbers 5 numbers 25 numbers 13. Evaluate . 14,190 4 8555 14. Evaluate . 99 110 55 77 15. Assume red and green are equally likely occurrences. What is the probability that you will get zero green lights in a row of five lights?16. Write a polynomial in standard form with zeros 3, 6, and 1. x3 + 10x2 + 27x + 18 = 0 x3 10x2 27x 18 = 0 x3 2x2 + 21x + 18 = 0 x3 4x2 + 9x + 18 = 0 17. Divide (x4 11x3 49x2 + 899x 2506) (x 8). x3 3x2 24x 584, R 14 x3 3x2 + 73x + 315, R 1483 x3 + 8x2 24x 584, R 1483 x3 3x2 73x + 315, R 14 18. A fifth-degree polynomial equation with rational coefficients has the roots 2, 7i, and 7 + i. Find the remaining roots. 7i, 7 + i 2, 7i, 7 i 7