How would I do this problem step by step 16x^2-40x+25?

Question

How would I do this problem step by step 16x^2-40x+25?

Answer 1

What exactly are you supposed to do to the formula?  If you are trying to factor the polynomial, you'll have to do some guessing.

We know that any quadratic polynomial can be factored into (ax+b)(cx+d).  The logical starting place to guess is to factor 16x^2 into (4x)(4x).

So we have (4x + b) (4x + d).  Another logical guess for 25 would be to square root it as well, so we have:

(4x + 5) (4x + 5) = (4x + 5)^2

Check:

(4x + 5) (4x + 5) = 16x^2 + 20x + 20x + 25 = 16x^2 + 40x + 25.

We're off by a sign, so we change 5 to -5, which, because of the square, will not change any other term but 40x.  So the answer is:

(4x - 5)^2

Check for good measure:

(4x - 5) (4x - 5) = 16x^2 - 20x - 20x + 25 = 16x^2 - 40x + 25.

Answer 2

first recognize that 16 and 25 are square numbers

so that makes life easy

we are usign 4 and 5

(4x  )(4x   ) = creates the 16x^2

(4x  5)(4x  5 )  creates the 25

the signs must be the same to give us +25

lets try the negative 5

(4x - 5)(4x - 5 )

now we need to create the -40x

from inner and outer  we get = -20x-20x= -40x yay

(4x - 5)(4x - 5 )

Answer 3

factor and get

(4x-5)(4x-5) or (4x-5)^2

x=5/4