Sat 数学历年真题

3 term: (-2) × -2 = 4 4 term: (-2) × 4 = -8 5 term: (-2) × -8 = 16 6 term: (-2) × 16 = -32

E is the correct answer.

rdththth

Test 1 Section 3 Question 14

Factoring and exponents rear their ugly heads. Where to begin?

Let’s write our given: (2x-5)(2x+5) = 5

What are we looking for? The value of 4x.

We can’t factor because the equation = 5, not 0. Sometimes it’s best to just start working and manipulating the problem somehow. What if we foil* the left side of the equation?

(2x+5)(2x-5) = 5

4x + -10x + 10x + -25 = 5 -10x + 10x = 0. Get rid of those two terms. 4x + -25 = 5 4x = 30 Aren’t we looking for 4x? We fell into it! E is the correct answer.

Shortcut! Recognize the formula for the difference of perfect squares: (x-a)(x+a) = (x-a)

x term does not have to be by itself, it can be 2x, 5001x, or 42x, as long as

it is the SAME in both expressions. This also goes for the a term; it can be just a number or sometimes another variable (2y, 63z, or anything else), as long as it’s the SAME in both expressions.

x terms (2x) are the same, and so are the a terms (5).

It doesn’t matter that the 5 is subtracted in the second expression; it’s the same number 5.

(2x) - (5) = 5 4x - 25 = 5 2

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