math help-factoring polynomials?

Question

How would you factor:
100+4x^2-16y-40x
Include steps and explanations?

Answer 1

You have
100 +4X^2 -16y -40x

First let's factor out a 4, since 4 is a factor of each term, that gives

4*(x^2 -10X +25) -16Y

Of course I rearranged the terms so the highest powers of X are
on the left. I didn't factor 4 out of -16Y because I want the
quadratic (X^2-10X+25), which I know I can factor.

since (X^2-10X+25) = (X-5)*(X-5) = (X-5)^2, we have

4*(X-5)^2 -16Y

The secret is being able to recognize that
(x^2 -10X +25) = (X-5)^2

Answer 2

The best way to do is to do it the old fashioned way... so that you will learn how it's exactly done (and propbably get a good ACT score) When adding and subtracting polynomials, remember that you can only add or subtract like terms. the exponents do not change. to add or subtract the coefficients -

( 2y 2 + 5y - 15 ) + (3y 2 - 5 )

We are adding two polynomials so all we do is to collect like terms. It's a good idea to put the answer in descending order as we go.

Adding like terms the answer will be: 5y 2 + 5y - 20

subtracting two polynomials: you need to "add the opposite" in the second polynomial. add like terms, beginning with the highest exponent so that your answer will be in descending order

( 6x 2 -7y 2 + 8xy ) - ( 5xy + 4x 2 + 2y 2 ) will be: ( 6x 2 -7y 2 + 8xy ) + ( - 5xy - 4x 2 - 2y 2 ) the answer will be -2x 2 - 3xy - 5y 2

Answer 3

Most probably the expression would be 100+4x^2-16y^2-40x.If not.follow the hints given above .And if I am correct,do it in the following way
given exp= 4(25+x^2-4y^2-10x
=4{(5)^2+(x)^2-2*5*x)-(2y)^2}
=4{(5-x)^2-(2y)^2}
=4(5-x+2y)(5-x-2y)

Answer 4

This is a tough one because it makes you want to factor it further than it can actually go. If it were +40x then you could factor that out as well, but because it is minus, you can't. All you can do is factor out 4 from each term:

4 (x^2 - 10x - 4y +25)

Answer 5

enable y=x^2 So y^2-3y-4=0 that would nicely be honestly factored to (y-4)(y+a million) y = x^2, so (y - 4)(y + a million) = (x^2 - 4)(x^2 + a million) and when you consider that x^2 - 4 is the version of two squares, the expression would nicely be factored to: (x+2)(x-2)(x^2+a million) The roots are 2 and -2.

Answer 6

(2x-10)(2x-10) - 16y

Step 1 factor
Step 2 check answer

Answer 7

i think you are missing something in question. check it again.