Day 1 Quiz

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Quadratic Equations

4x2 – 16 = (px + t)(px – t)

In the equation above, p and t are constants.  Which of the following could be the value of p?

A) 2
B) 4
C) 8
D) 9

[/vc_column_text][vc_text_separator title=”Day 1 Answer Explanation”][/vc_column][/vc_row][vc_row][vc_column][vc_column_text]The equation is saying that 4x2 – 16 can be expressed as the multiplication of two factors (px + t)(px – t).

Notice this is a difference of squares so  pxt + -pxt cancel out.

Since the equation is asking about the p term, not the t term, we can focus on what can be multiplied to give us 4x2 .

The answer must be (A) 2, because 2x times 2x is the only value that multiplies to 4xwhile preserving the difference of squares.

Why the other answers are wrong:

The equation tells us that p is one number, not two.  Therefore we can’t have 4 x 1 (ruling out B) or 8 x ½ (ruling out C).  These are also wrong because they would ruin the difference of squares and give you a middle x term.

For example: (4x+4)(x-4) = 4x+ 20x -16

Notice how even though we got a 4x2-16, we also popped out a 20x in the middle which the original equation doesn’t have.  This always happens when when have two different p terms.

(D) is wrong because 9 is not a factor of any of the terms.[/vc_column_text][/vc_column][/vc_row][vc_row][vc_column][vc_text_separator title=”Key Math Fact To Learn” css=”.vc_custom_1486133682139{padding-top: 20px !important;}”][/vc_column][/vc_row][vc_row][vc_column][vc_column_text]If you got this question wrong, create an index card with the problem on the front, the explanation on the back, and the following math fact:

What is the difference of squares?

a– b= (a+b)(a-b)