Please can someone help me with these?
factoring 2x^2+5x-3
and 3x^2-15x+12
Thanks in advance!!!
well rose. you nedd to distrubte the first one or find the gcf but there anit one, the second one do the same thing. for further questions just ask.
How can I do the same thing when you are saying there is nothing I can do for the first one?
On the first:
2x^2+5x-3
(2x-1)(x+3)
Does that help?
How do you know it is -1 and 3? I know -1 times 3 equals -3, but what does that have to do with 5? Is it because the 3 is half of 6 and 6 plus -1 equals 5?
simplify using identity
(a+b)3=a3+b3+3ab(a+b)
(5xy+6ab)3
2x^2+5x-3
OK, to start, split it up, like this:
( )( )
then, split up the 2x^2, like this:
(2x )(x )
The - sign in front of the 3 means you have to subtract to make 5.
Now, what are the factors of 3? 1 and 3, or 3 and 1... it doesn't matter. What you're trying to accomplish is to make 5. So far, the problem could look like this:
(2x 3)(x 1) or this: (2x 1)(x 3)
(we'll figure out the signs in a minute.)Now it's time to FOIL:
_____ _____ _____ ____
first outer inner last
Right now, we'll concentrate on the outer and inner. the first example would look like this:
+2x and the 2nd: +6x
+3x -1x
---- ----
+5x +5x
Can you see how the second one is right? +6x-1x=5x
The answer is (2x-1)(x+3)if you have any more questions, well, just ask!
To factor the expression 2x^2 + 5x - 3, you can follow these steps:
1. Start by splitting the middle term (5x) into two terms such that their coefficients multiply to give the product of the coefficient of the quadratic term (2) and the constant term (-3). In this case, you need to find two numbers whose product is -6 and whose sum is 5.
2. The numbers that satisfy this condition are 6 and -1. Knowing this, you can rewrite the expression as:
2x^2 + 6x - x - 3
3. Now, group the terms in pairs:
(2x^2 + 6x) + (-x - 3)
4. Factor out the greatest common factor (GCF) from each group:
2x(x + 3) - 1(x + 3)
5. Notice that both groups have a common factor of (x + 3). Factor this common factor out:
(x + 3)(2x - 1)
So, the factored form of 2x^2 + 5x - 3 is (x + 3)(2x - 1).
Similarly, to factor the expression 3x^2 - 15x + 12, you can follow these steps:
1. Split the middle term (-15x) into two terms such that their coefficients multiply to give the product of the coefficient of the quadratic term (3) and the constant term (12). In this case, you need to find two numbers whose product is 36 and whose sum is -15.
2. The numbers that satisfy this condition are -9 and -4. Rewrite the expression as follows:
3x^2 - 9x - 4x + 12
3. Group the terms in pairs:
(3x^2 - 9x) + (-4x + 12)
4. Factor out the GCF from each group:
3x(x - 3) - 4(x - 3)
5. Notice that both groups have a common factor of (x - 3). Factor this common factor out:
(x - 3)(3x - 4)
So, the factored form of 3x^2 - 15x + 12 is (x - 3)(3x - 4).