新SAT官方Daily Practice每日一题数学(9.14）

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MathematicsStandard Multiple Choice

Read the following question and then select the best answer.

14q2+8pq-9p2+40pq-70q2+17p2

Which of the following is equivalent to the above expression?

A：-40p2q2+48pq

B：110p2q2+48pq

C: 8(p+7q)(p-q)

D: 8(p2+48pq-56q2)

Answer C

EXPLANATION

Choice C is correct. First, notice that some of the answer choices given

are polynomials in standard form and some are in factored form. Start by

combining like terms and then determine if the resulting polynomial can be

factored.

Like terms in a polynomial are terms that have the same variable part

raised to the same power. Combine the like terms in the above expression to

obtain the following polynomial.

14q2+8pq-9p2+40pq-70q2+17p2

=(14q2-70q2)+(8pq+40pq)+( -9p2+17p2)

=-56q2+8p2+48pq

Since this is not an answer choice, determine if the polynomial can be

factored.

=-56q2+8p2+48pq

=8(p2+6pq-7q2)

The equivalent expression is

=8(p+7q)(p-q)

难度系数：容易

你答对了吗?