Question

Factor completely.9 - 25.22Show CalculatorStuck? Watch a video or use hint

Answer 1

Given the expression:

`9-25x^2`

9 is the exact square of 3

25 is the exact square of 5

So you can rewrite this expression as:

`(3^2)-(5x)^2`

Now considering the formula for the difference of squares:

`a^2-b^2=(a+b)(a-b)`

If we consider a=3 and b=5x, we can say that

`(3+5x)(3-5x)`

So we have that the steps to factor the given expression are:

`9-25x^2=(3)^2-(5x)^2=(3+5x)(3-5x)`

*-*-*-*-*-

`3x^2+0x-174`

In this case, none of the terms is a perfect square, so you have to use another method.

I'll ignore the 0x term, since its irrelevant, the expression is then:

`3x^2-147`

Both 3 and 147 are divisible by 3, so the first step will be to divide the expression by three to simplify it:

`\begin{gathered} (3x^2)/(3)-(147)/(3) \\ x^2-49 \end{gathered}`

Now the terms of the equation are expressed as exact squares.

x²= x*x

and

49=7²=7*7

We reached the lowest simplification, now we can determine the diference of squares using a=x and b=7

`\begin{gathered} (a+b)(a-b) \\ (x+7)(x-7) \end{gathered}`

Finally multiply the factoring by 3 → at the begining we divided it by 3 to simplify the expression but if you dont multiply the final factoring by 3 again the result won't be equivalent to the original equation.

So the factoring of 3x²+0x-147 is 3(x+7)(x-7)