Answer:
[tex](x-7)(x-7)[/tex]
Step-by-step explanation:
We begin with the given quadratic expression:
[tex]49-14x+x^2[/tex]
Just for my own ease, I will rewrite this in descending order of powers
[tex]x^2-14x+49[/tex]
In order to factor this expression, we need to look for two numbers that meet the following criteria.
When they are added together, you get [tex]-14[/tex]
When they are multiplied together, you get [tex]49[/tex]
A simple way to find our answer is to begin with the product of multiplication and list each of the numbers that can be multiplied together to get us our given result
To get 49, we could multiply
1 and 49
-1 and -49
7 and 7
-7 and -7
Now, we can just add both of these terms together to see while one gives us our desired result
[tex]1+49=50\\-1-49=-50\\7+7=14\\-7-7=-14[/tex]
As you can see, -7 and -7 were the two values that gave us -14.
This means that they are the terms within our factor.
Therefore, our factored form would be [tex](x-7)(x-7)[/tex]
Answer:
(7 - x) (7 - x)
Step-by-step explanation:
First, I'm multiplying 49 by the co-efficient of x(1) to get 49. Then I'm going to see what factors of 49 add up to -14. Those are -7 and -7.
Next, I'm going to rewrite this polynomial:
49 - 7x - 7x + x^2
Then, I group them into two groups:
49 - 7x
&
-7x + x^2
Then, I factor them out:
49 - 7x = 7 (7 - x)
-7x + x^2 = -x (7 - x)
After that, I take the outer coefficients and put them in parenthesis:
7 (7 - x)
&
-x (7 - x)
= (7 - x)
Finally, I put both of our grouped parenthesis together:
(7 - x) (7 - x)
