﻿ Exercises - Polynomials - ALGEBRA - SAT SUBJECT TEST MATH LEVEL 1 ﻿

## CHAPTER 5 Polynomials

### Exercises

1. What is the value of  when a = –5.3 and b = 3.5?

(A) –8.8

(B) –1.8

(C) 1.8

(D) 4.4

(E) 8.8

2. If a2 + b2 = 4 and (a – b)2 = 2, what is the value of ab?

(A) 1

(B)

(C) 2

(D) 3

(E) 4

3. What is the result when (x + 3)(x – 5) is subtracted from (2x + 3)(2x – 5)?

(A) x(3x – 2)

(B) x(2 – 3x)

(C) 3x2

(D) 5x2 – 6x

(E) 5x2 – 6x – 30

4. If x > 10, then

(A)

(B) 6

(C)

(D)

(E)

5. If  what is the value of

(A) 10

(B) 98

(C) 100

(D) 102

(E) 110

 1. (B) 3. (A) 5. (B) 2. (A) 4. (B)

Solutions

Each of the problems in this set of exercises is typical of a question you could see on a Math 1 test. When you take the model tests in this book and, in particular, when you take the actual Math 1 test, if you get stuck on questions such as these, you do not have to leave them out—you can almost always answer them by using one or more of the strategies discussed in the “Tactics” chapter. The solutions given here do not depend on those strategies; they are the correct mathematical ones.

See Important Tactics for an explanation of the symbol ⇒, which is used in several answer explanations.

1.

Of course you could replace a by –5.3 and b by –1.8 in the original expression and evaluate it with your calculator.

2. (A) 2 = (a – b)2 = a2 – 2ab + b2 = 4 – 2ab  2ab = 2  ab = 1

3. (A) (2x + 3)(2x – 5) = 4x2 – 4x – 15 and (x + 3)(x – 5) = x2 – 2x – 15

(4x2 – 4x – 15) – (x2– 2x – 15) =
4x2 – 4x – 15 – x2 + 2x + 15 =
3x2 – 2x = x(3x – 2)

4. (B)

5. (B)

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