Question

Which of the following equations shows the correct form of the equation x 2 + 10x + 25 = 16 if the zero product property is to be used? (x + 5)(x + 5) = 16 (x + 1)(x + 9) = 0 (x - 1)(x - 9) = 0

Answer 1

(x-1)(x-9)=0

Explanation:

Solve the equation step by step.

Step 1: Subtract 16 from both sides.

x2+10x+25−16=16−16

x2+10x+9=0

Step 2: Factor left side of equation.

(x+1)(x+9)=0

Step 3: Set factors equal to 0.

x+1=0 or x+9=0

x=−1 or x=−9

Answer 2

(x + 1)(x + 9) = 0

Explanation:

After you subtract 16 from both sides, you get ...

x² +10x +9 = 0

When you factor this equation, it becomes ...

(x +1)(x +9) = 0

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For the zero product property to be of any use, the form of the equation must be a product that equals zero.

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Comment on the other answer choice

(x -1)(x -9) = 0 = x² -10x +9 . . . . . the x term is different from that in the given equation. It has the wrong sign.