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Quadratic Equations

4x^{2 }– 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 **4x ^{2 }– 16** can be expressed as the multiplication of two factors

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 **4x ^{2 }**.

*The answer must be (A) 2, because 2x times 2x is the only value that multiplies to 4x^{2 }while 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^{2 }+ 20x -16

Notice how even though we got a 4x^{2}-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 ^{2 }– b^{2 }= (a+b)(a-b)**

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