新SAT官方Daily Practice每日一题数学(9.14）

2017年09月14日14:50 来源：小站整理

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Mathematics>Standard 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?