&KDSWHU page 457 for exercise sets.Test-Taking Tips
- Reread the item.
- Use the Test-Prep strategy.
- Apply appropriate rules,
definitions, properties, or
strategies. - Analyze your answers.
JKL(^159)
not drawn to scale
x
Test Prep: Short-Answer Questions
Strategy: Show All Your Work
One way to show all your work when
answering short-answer questions is
to justify your steps. You should state
the rules and properties you used to
solve the problem.
Read the whole test item carefully.
- Reread the test item carefully.
- Show each step in the solution.
1.Use the Distributive Property.
2.Use properties of multiplication
and the Laws of Exponents to
simplify the terms.Solve the problem.
- Apply appropriate rules, properties,
and definitions.
2 x^3 (8x^2 x5) (–2x^3 • 8x^2 ) ( 2 x^3 • x) ( 2 x^3 • 5) Distributive Property
(2 • 8 • x^3 • x^2 ) (2 • x^3 • x) (2 • 5 • x^3 )
16 x^5 2 x^4 10 x^3
Answer: 16 x^5 2 x^4 10 x^3
To simplify the expression, first use the Distributive Property by multiplying
each term within the parentheses by the monomial 2x^3. To multiply, use the
Commutative Property of Multiplication, then apply the rules for signed
numbers and the Laws of Exponents.Multiply using rules for signed numbers
and the Laws of Exponents.Commutative Property
of MultiplicationSolve. Justify your steps.
1.Triangle JKLis a right triangle.
What is the length of side x?
Explain how you solved the problem.Check your work. Review your notes.
Make sure you have completed all parts of the item.
- Analyze your answers. Do they make sense?
Check by working backwards.
Find the GCF of the terms and factor the polynomial.
16 x^5 2 • 2 • 2 • 2 • x• x• x• x• x 2 x^4 2 • x• x• x• x 10 x^3 2 • 5 • x• x• x
GCF 2 • x• x• x 2 x^3
So 16 x^5 2 x^4 10 x^3 2 x^3 (8x^2 x5) ✓
Sample Test Item
Simplify the expression shown below.
2 x^3 (8x^2 x5)
Show all your work. Explain how you used properties
and rules to help you simplify the expression.