Factor. Write prime it the expression cannot be factored:?

Question

(1) 12w^2 + 10w - 8
(2) 20y^2 - 33y + 10
(3) 16e^2 - 4
(4) 49y^2 - 25

out of my 35 questions these are the only 4 i dont get. i appreciate your help

Answer 1

1. (2)(2w-1)(3w+4)
2. (5y-2)(4y-5)
3. (4)(2e-1)(2e+1)
4. (7y-5)(7y+5)

Answer 2

When you have trouble factoring, you can always rely on the quadratic equation. Since I cannot type a square root sign, you will have to accept the bracket [ ]^1/2 as meaning the square root of what is inside. If we start with a quadratic equation in the form of AX^2 + BX + C = 0, where A, B, and C are coefficients, the quadratic equation would be:
X = -B +/- [b^2 - 4AC]^1/2 with all this divided by 2A. That gives you two answers for the value of X. We then convert them into the factors of the equation. I know, your problems do not include an equal sign so we put one there and set the expression = 0 just to get the factors. Now lets get to work.

When I applied the quadratic equation to the first problem, I got W = -4/3 and W = 1/2. Lets convert that into the factors, starting with W = -4/3.

Multiply both sides by the fraction denominator to get:
3W = -4. Now move the -4 to the other side to get an equation that is equal to 0. That gives you:
3W + 4 = 0. (3W + 4) is one of the factors. Similarly, we get (2W -1) as the other. Now, if we multiply those two factors together, using the FOIL method, we get:
6W^2 + 5W -4. Oops, thats exactly half the required answer. However, you will note that the coefficients have a common factor of 2. We must now put the 2 back in and get:
2(3W + 4)(2W - 1) as the factoring.

Using similar methods, the second one is:
(4Y - 5)(5Y - 2)

Problems 3 and 4 can be solved the same way or we can take a shortcut. If you notice, both problems involve the difference between two squares. Therefore, we can use the factors of the difference of two squares directly:
A^2 - B^2 = (A+B)(A - B)

For problem 3, the square root of 16e^2 is 4e and the square root of "4" is "2" so the factors are:
(4e + 2)(4e - 2)

Similarly, the factors for problem 4 are:
(7Y + 5)(7Y - 5)

They all can be factored.

Answer 3

one way is to objective all of them and notice if one works (there's a finite quantity, so it may well be a risk) in any different case, the equation is a quadratic. 12w^2 + 10w - 8 w = [ -10 +/- SQRT( a hundred + 384 )]/24 w = [ -10 +/- 22 ] / 24 roots: w = -32/24 = -4/3 and w = +12/24 = a million/2 if w= -4/3 is a root, then 3w = -4 3w + 4 = 0 and (3w+4) is a ingredient do an analogous with the different w = a million/2 to discover the different ingredient. See in case you're able to desire to apply a linear ingredient (e.g., 2) to make confident that the multiplication comes out to the unique equation. this would experience like a protracted technique, yet while there is an answer (if the equation isn't best), then it continuously works to discover components.

Answer 4

(1) 2(6w^2 + 5w - 4) = 2(2w - 1)(3w + 4)
(2) (5y - 2)(4y - 5)
(3) 4(2e + 1)(2e - 1)
(4) (7y + 5)(7y - 5)

Answer 5

A tough Question ~