Question

can someone clarify if i did this right

Answer 1

Chase wants to factor x2 + 10x + 25 by grouping; however, Paige says it is a special product and can factor a different way. Using complete sentences, explain and demonstrate how both methods will result in the same factors.

Answer 2

so far this is all i got... is it right?

First you would group the equation x^2 + 5x + 5x +25 giving us (x+5) (x+5).

^2 + 5x) + (5x + 25)
x(x+5)+ 5(x+5)
(x+5)(x+5)

Next knowing that the polynomial is a perfect square, it can be derived by simply multiplying (x + 5) two times.

Answer 3

The factoring by grouping is correct.

Now you need to show that it can be factored by noticing that it is the square of a binomial.

You need to show that the given trinomial follows the pattern of the square of a binomial.

\(a^2 + 2ab + b^2 = (a + b)^2\)

Answer 4

"Next knowing that the polynomial is a perfect square, it can be derived by simply "

\(\large \begin{array}{cccllll}
x^2 + &10x + &25\\
\uparrow &\uparrow &\uparrow \\
\sqrt{x^2}&2\cdot \sqrt{x^2}\cdot \sqrt{25}&\sqrt{25}\\
\downarrow &\downarrow &\downarrow \\
x&2\cdot 5\cdot x&5
\end{array}\)

Answer 5

so u just simplified it basically?

Answer 6

simplify it using the TEMPLATE for a perfect square trinomial, yes
if it's one, the TEMPLATE will show so

Answer 7

alright i got it now, ill probably be able to take it from here Thsnk you!

Answer 8

yw

Answer 9

To determine if a trinomial is a perfect square trinomial, follow these steps:
1. Is the first term a perfect square?
If no, stop. It's not the square of a binomial.
If yes, what is it the square of? Let's call it x.
2. Is the third term a perfect square?
If no, stop. It's not the square of a binomial.
If yes, what is it the square of? Let's call it y.
3. Is the middle term of the trinomial the product of 2 and the two roots you found in
steps 1 and 2 (that we called x and y)?
If no, stop. It's not the square of a binomial.
If yes, it is the square of binomial (x + y).

Answer 10

Now let's do it with your example.
Is x^2 a perfect square? Yes, it's the square of x.
Is 25 a perfect square? Yes, it's the square of 5 or of -5.
Is 10x equal to 2 * x * 5 or is 10x equal to 2 * x * (-5)?
Yes, 10x is equal to 2 * x * 5.
That means this trinomial is the square of the binomial (x + 5).
In other words, \(x^2 + 10x + 25 = (x + 5)^2\)