Lesson 3 Practice Problems - Scottsdale Community College - Math ...
Lesson 3 Practice Problems - Scottsdale Community College - Math ...
Lesson 3 Practice Problems - Scottsdale Community College - Math ...
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Name: ________________________________<br />
Date: _____________<br />
1. Complete the table below.<br />
<strong>Lesson</strong> 3 <strong>Practice</strong> <strong>Problems</strong><br />
Skills <strong>Practice</strong><br />
Polynomial<br />
Name<br />
Leading<br />
Coefficient<br />
Constant<br />
Term<br />
Degree<br />
5n 8 ! n 5 +1<br />
x ! 5<br />
8r 2<br />
2. Simplify completely. Show all steps, and box your answers.<br />
( ) 0<br />
a. 3x 0 + 2x 0 b. 5 3n<br />
c. y 3 ! y 7 ! y d. 4 (!2x) 3 ! 4x (!2) 3<br />
e. 4 (!5w 8<br />
) 2 f. 10p 3 (!5p 7<br />
) 2<br />
<strong>Scottsdale</strong> <strong>Community</strong> <strong>College</strong> Page 55 Introductory Algebra
<strong>Lesson</strong> 3: Polynomials and Exponents, Part 1<br />
<strong>Practice</strong> <strong>Problems</strong><br />
g. 2a 3 b( 3ab 5<br />
) 2 h. ( 5x ! 7) 0<br />
i. (!4x) 2 + 4x 2 j. ( 3x 4<br />
) 3 ! ( 5x 6<br />
) 2<br />
3. Multiply and simplify completely. Show all steps, and box your answers.<br />
a. 4! ! (3! − 5) b. 4! ! (3! ! − 2! − 5)<br />
c. (p + 5)(p + 7) d. (! + 2)(! − 2)<br />
e. (2! − 4)(3! − 5) f. (5w – 8)(3w + 11)<br />
<strong>Scottsdale</strong> <strong>Community</strong> <strong>College</strong> Page 56 Introductory Algebra
<strong>Lesson</strong> 3: Polynomials and Exponents, Part 1<br />
<strong>Practice</strong> <strong>Problems</strong><br />
g. ( x + 2) 2 h. ( 2x ! 4) 2<br />
i. ( x ! 4) ( x 2 + x ! 5) j. 3( x + 2) ( x + 4)<br />
k. 4( x + 2) 2 l. ( q ! 2) 3<br />
4. Evaluate the algebraic expression x 2 given x = !7 . Show your work.<br />
5. Evaluate the algebraic expression 5x 3 given x = !2 . Show your work.<br />
<strong>Scottsdale</strong> <strong>Community</strong> <strong>College</strong> Page 57 Introductory Algebra
<strong>Lesson</strong> 3: Polynomials and Exponents, Part 1<br />
<strong>Practice</strong> <strong>Problems</strong><br />
6. Evaluate the algebraic expression ( 5x) 2 given x = !2 . Show your work.<br />
7. Evaluate the algebraic expression 5( 2x) 2 given x = !3. Show your work.<br />
Applications<br />
8. Write an expression that represents the total area of the figure shown below. Simplify<br />
completely.<br />
9. Write an expression that represents the area of the shaded region of the figure shown below.<br />
Simplify completely.<br />
<strong>Scottsdale</strong> <strong>Community</strong> <strong>College</strong> Page 58 Introductory Algebra
<strong>Lesson</strong> 3: Polynomials and Exponents, Part 1<br />
<strong>Practice</strong> <strong>Problems</strong><br />
10. Write an expression that represents the total area of the figure shown below. Simplify<br />
completely.<br />
a<br />
b a<br />
b a<br />
b<br />
11. Write an expression that represents the perimeter of the figure shown below. Simplify<br />
completely.<br />
a<br />
b a<br />
b a<br />
b<br />
12. Write a polynomial in simplest form that represents the volume of the figure shown below.<br />
<strong>Scottsdale</strong> <strong>Community</strong> <strong>College</strong> Page 59 Introductory Algebra
<strong>Lesson</strong> 3: Polynomials and Exponents, Part 1<br />
<strong>Practice</strong> <strong>Problems</strong><br />
Extension<br />
13. If possible, simplify each of the following by combining like terms or using properties of<br />
exponents.<br />
a. 2n 5 + 3n 5 = ______________ b. 2n 5 !3n 5 = ______________<br />
c. 3n 3 + 3n 5 = ______________ d. 3n 3 !3n 5 = ______________<br />
<strong>Scottsdale</strong> <strong>Community</strong> <strong>College</strong> Page 60 Introductory Algebra
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