Need Help Please... 3 problems I am having trouble with...?

Question

1. Factor: 12x^4y^3 + 16x^3y^3 – 20x^3y^4

2. Factor by grouping: x^3 – 3x^2 + 4x – 12

3. Label a, b, and c. 9x – 3x^2 – 10

Answer 1

2. Factor by grouping: x^3 – 3x^2 + 4x – 12

seperate the first 2 terms from the last
(x^3 – 3x^2) + (4x – 12)

then take out a common factor
x^2(x - 3) + 4(x - 3)

since the term in parenthesis are the same than you can combine the outside terms like this
(x^2 + 4)(x - 3)

then check if you can factor the new formed factors, and in this case you can't so you are done

3. Label a, b, and c. 9x – 3x^2 – 10

put it in decending order of degrees
-3x^2 + 9x - 10

the a,b,c are the cooficients, not the degrees so the are
a = -3
b = 9
c = -10

Answer 2

1. Factor: 12x^4y^3 + 16x^3y^3 – 20x^3y^4
let's start with the variables: the highest exponential for the x is 3, the highest exponential for y is 3, so let's take those out first
12x^4y^3 + 16x^3y^3 – 20x^3y^4
xˆ3(12xyˆ3) + xˆ3 (16yˆ3) -xˆ3 (20yˆ4)
(xˆ3yˆ3)(12x) + (xˆ3yˆ3)(16) - (xˆ3yˆ3)(20y)
then find the highest common denominator between 12, 16 and 20: that's 4. so pull out 4.
(4xˆ3yˆ3)(3x) + (4xˆ3yˆ3)(4) - (4xˆ3yˆ3)(5y)
now you see that three different times, the factor 4xˆ3yˆ3 multiplies something else. you can bunch them together -- and watch that minus sign
(4xˆ3yˆ3)(3x+4+5y) = (4xˆ3yˆ3)(3x +5y +4)

2. Factor by grouping: x^3 – 3x^2 + 4x – 12
let's group the first two together, and the last two together.
so what factor(s) do the first two have in common? xˆ2 and the second two have the highest common denominator of 4 and 12 in common, which is 4. so let's take those out:
xˆ2(x-3) + 4(x-3)
now you can see that both sets have the common factor of (x-3) so you can bunch them:
(xˆ2+4)(x-3)

3. Label a, b, and c. 9x – 3x^2 – 10
watch for the little trap here. you want to organize the equation so that it's in order of xˆ2, then x, then a number. also keep an eye out for minus signs. so reorganized equation becomes:
-3xˆ2+9x-10
the quadratic equation is:
axˆ2+bx+c
so
a=-3
b=9
c=-10

good luck!

Answer 3

1. Factor: 12x^4y^3 + 16x^3y^3 – 20x^3y^4
=4x^3y^3(3x +4- 5y)

2. Factor by grouping: x^3 – 3x^2 + 4x – 12
=x^2(x-3) +4(x-3)
= (x-3)(x^2+4)

3. Label a, b, and c. 9x – 3x^2 – 10
a = 9, b=-3, c = -10

Answer 4

1. Factor: 12x^4y^3 + 16x^3y^3 – 20x^3y^4
4x^3y^3( 3x+4-5y)

2. Factor by grouping: x^3 – 3x^2 + 4x – 12
x^2(x-3) +4(x-3)
(x^2+4)(x-3)

3. a=9
b= -3
c = -10

Answer 5

1. 4*x^3*y^3*(3x+4-5y)
2. can't really factor this.... don't know what you mean by grouping...
3. a=-3, b=9, c=-10
When they say to label a, b,c, then a is the number in front of x^2, b is in front of x and c is the number with no x's