Sec. 8.6 HOMEWORK: Factoring by GCF

1- 15 : Factor each expression. (Reminder: if the first term is negative, the GCF must be negative)

1. 12x + 42y2. -4x4 + 24x33. 9x5 – x4 4. 4x2 – 4x

5. 18x2y – 42xy56. -6x3y – 18x2y4 7. 2x2 – 8x 8. 12x2 – 30x

9. -6x2 + 15x10. 4x2 – 2x11. -24y2 – 9x

12. 15x5 – 12x4 + 27x³ – 3x²13. 4m²n³ + 2m²n² + 6m²n

14. 12m2n5 + 3m6n8 + 6mn315. 14p10q2r – 4p6q2r3 + 10pq3r7

16: Use the provided cylinder. The surface area of a cylinder is given by the formula , where r is the radius and h is the height.

16. Factor a monomial (the GCF) from the formula.

17. What is the greatest common factor of the terms in the polynomial24x8+ 6x5+ 9x2?

  1. 3
  2. 3x2
  3. 6x
  4. 6x2

18-21:What is the GCF from each polynomial? ONLY GCF.

18. 15x4+ 20x3+ 35x=______19. 12m3− 8m2+ 16m+ 8 =______

20. 32y2+ 48y– 16 =______21. x5+x4+ 3x3+ 3x2 =______

22. Which of these polynomials cannot be factored because it doesn't have a GCF?

  1. 7x2+ 14x+ 21B. 49x3+ 21x2+x

C. x2+ 14x+ 7D. 35x3+ 28x2+ 7x

23. The figure shows the dimensions of a garden plot in the shape of a trapezoid. Write and simplify a polynomial for the perimeter of the plot. Then factor the polynomial completely.

24. The area of the rectangle shown below is6x2+ 9xsquare feet. The width of the rectangle is given in the figure. What is the length of the rectangle? Justify your answer.

25. Marcus saw the factorization shown below in his textbook, but part of the factorization was covered by a drop of ink. What expression was covered by the drop of ink?

-24x5- 16x3= -8x3( + 2)

26. James wrote that 4x5- 16x3+ 2 = 2x( 2x4-8x2+1). Do you agree? Explain how you can check James' answer to prove whether his answer is correct or incorrect.