This document provides practice problems involving polynomials. Students are asked to write polynomials in standard form, classify polynomials by degree and number of terms, and perform addition and subtraction of polynomials using both vertical and horizontal formats. They are also given word problems involving finding the area of shapes described by polynomial expressions.

1. LESSON
10.1
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 576–582
Write the polynomial in standard form.
4x 2 2. 5x2 7x3
1. 3x 5 4 3x 2
3. x
4x2 5. 5x2 4x3 7x4 5x3
4. 8 2x 2x 4x 1
6.
2 2 3
7. 3x 7 2x 8. 7x 2 2x 2
x x
9.
Identify the leading coefficient, and classify the polynomial by
degree and by number of terms.
Lesson 10.1
3x2
10. 14 11. 2x 3 6x 2
12.
13. x3 x4 15. x2 x4 3x3
5 14. 1 4x 8
2 2 3 2
16. 2x 5x 1 17. 2 3x 9
x 18. x x
Use a vertical format to add or subtract.
19. x2 4x2 20. 5x2 2x2
2x 7 3 2x 4 3x 1
x
5n2 6n2 5n2
2n 3 2 4n 6 2
n n
21. 22.
23. 2a3 4a2 2a2 24. 4n2 8n2
7 3 6n 5 3
a n
Use a horizontal format to add or subtract.
25. x2 26. 3m2 2m2
2x 1 3 2m 1 4m
x
x2 28. 5x2 3x2
27. 7x 1 3x 5 9 5x 9
7x3 8x2 9x2 n2 5n2
4 5x 2 2n 3n 1
29. 30.
Use a vertical format or a horizontal format to add or subtract.
31. 2x3 7x2 2x2 5x2
5x 2 7x 3 3x 7
x 32.
x3 x2 x2
33. 3 7x 13x 4 1 1
x x
34.
35. 2x2 3x2 36. x2 3x2
3 6x 4 3 5x 2
x x
37. Photograph Mat A mat in a frame has an 38. Floor Plan The first floor of a home has the
opening for a photograph (see figure). Find floor plan shown below. Find an expression in
an expression for the area of the mat. (Area standard form for the area of the first floor.
of opening: A ab ).
2x
x
b 3x 2 3x
a 4
6
x
2
x 5
x
x
2
15
Algebra 1
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