please factor this one?

Question

x squared - 14x +49

Answer 1

(x + a)(x + b) = x^2 + ax + bx + ab

or

x^2 + (a+b)x + ab


for this problem:
x^2 - 14x + 49

you have to think of sums (a+b) for -14 and factors (ab) for + 49.

what + whatever = -14
and
what * whatever = +49

not a lot of stuff multiplied together = +49 and the first thing to notice is that +49 is a square of 7.... and -7.

Then you notice that -14 would work out really nicely with -7 + -7 cause that's -14

so you try that... (there is some trial and error in factoring)

(x - 7)(x - 7)
that's
x^2 - 7x - 7x + 49

or

x^2 -14x + 49

which is it.

and to make the teacher happy that you can show things in the simplest forms:
Answer: (x - 7)^2

Answer 2

since x^2 and 49 are the squares of x and -7 and since -14 x is double and the product of x and -7, X^2-14x+49 is a trinomial square

then x^2 - 14x +49 = (x-7)^2

hope i helped you

Answer 3

x² - 14x + 49

x² - 7x - 7x + 49

= x (x-7) - 7 (x-7)

= (x - 7) (x - 7)

Answer 4

It's a perfect square: (x-7)(x-7) or (x-7)^2

that's it!

Answer 5

it is a perfect sq
(x-7)^2

Answer 6

(x-7)(x-7)

Answer 7

(x-7)(x-7)