Question

What value, in the place of the question mark, makes the polynomial factor a perfect square?

x^2 + 12x + ?

Answer 1

Please post the question as your question. It's significantly more respectful of the people who are going to give you help.

Answer 2

Do you know how completing the square works?

Answer 3

@shadowfiend as you see there was a attatchment SORRY.

Answer 4

and no i dont may you explain :)?

Answer 5

I did see. As you see, I edited your question so that the question in the attachment is visible here more easily for helpers ;)

Answer 6

Two seconds, let me brush up on my square completing mission ;)

Answer 7

AW THANKS :)

Answer 8

Hm. Actually, completing the square may not be the way to go here. So we have:

\(x^2 + 12x + ?\)

Answer 9

To factor this, we want:

\((x + y)(x + z)\)

Because of the way this multiplies out, the above will give us:

\(x^2 + yx + zx + yz\)

Answer 10

Well a perfect square is a number mulitplyed by itsself.

Answer 11

That means:

\(x^2 + (y + z)x + yz\)

And we want \(y + z = 12\). Then \(yz\) is the value of our ? from above.

Answer 12

But! Notice they said they want a *perfect* square.

Answer 13

A perfect square means the same thing multiplied by itself, or:

\((x + y)(x + y) = (x + y)^2\)

In the equations we wrote above, that means \(y = z\).

Answer 14

Above, we said \(y + z = 12\). Since y = z, that means \(2y = 12\), which means \(y = 6\).

Answer 15

So we have \((x + 6)^2\). We can multiply this out now:

\[x^2 + 6x + 6x + 6\cdot 6\\
x^2 + 12x + 36\]

And that's our ? :)

Answer 16

ANSWER!
THANKS SO MUCH <3

Answer 17

No problems. Medals away ;)

Answer 18

OFCOURSE!

Answer 19

are you sure it is not -36 i'll check