Question the-ex

2.4 Equivalent Expressions - Simplifying polynomials
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open parenthesis, one half x, plus three halves, close parenthesis, times, open parenthesis, three halves x, plus one half, close parenthesis

The expression above is equivalent to a, x squared, plus b x, plus c , where a, b, and c are constants. What is the value of b?

Enter your answer:

The expression above is equivalent to , where a , b , and c are constants.

Hard-difficulty · SAT Math · Equivalent Expressions — Simplifying polynomials. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

The correct answer is five halves. The expression open parenthesis, one half x, plus three halves, close parenthesis, times, open parenthesis, three halves x, plus one half, close parenthesis can be written in the form a, x squared, plus b x, plus c, where a, b, and c are constants, by multiplying out the expression using the distributive property of multipliion over addition. The result is one half x, times three halves x, plus, one half x, times one half, plus, three halves times three halves x, plus, three halves times one half. This expression can be rewritten by multiplying as indied to give three fourths x squared, plus, one fourth x, plus, nine fourths x, plus, three fourths, which can be simplified to three fourths x squared, plus, ten fourths x, plus, three fourths, or three fourths x squared, plus, five halves x, plus, three fourths. This is in the form a, x squared, plus b x, plus c, where the value of b is five halves. Note that 5/2 and 2.5 are examples of ways to enter a correct answer.