Can someone please help me with this factoring? Thanks!
Factor 3x^2-7xy+2y^2
Factor 12x^2+8x-15
3x^2 -7xy +2y^2 = (3x -y)(x - 2y)
Now you try the other one.
Could you please tell me how you did the first one? I don't really want the answers. I just want help. :)
Of course, I can help you with the factoring.
To factor the expression 3x^2 - 7xy + 2y^2, we can look for two sets of parentheses that when multiplied together, give us the original expression.
First, let's look for factors of the coefficient of x^2 (which is 3). The factors of 3 are 1 and 3. Next, let's look for factors of the coefficient of y^2 (which is 2). The factors of 2 are 1 and 2.
Now, we need to find a combination of factors that, when multiplied together, give us the coefficient of xy, which is -7. The factors to consider are: 1 and 2, -1 and -2, 3 and 1, -3 and -1.
After examining the possible combinations, we find that -3 and 2 are the right combination because -3 times 2 equals -6, which is one less than -7 (the coefficient of xy).
Using these factors, we can write the factored form of the expression as:
(3x - 2y)(x - y)
Now, let's move on to the second expression: 12x^2 + 8x - 15.
First, let's look for factors of the coefficient of x^2 (which is 12). The factors of 12 are 1, 2, 3, 4, 6, and 12. Next, let's look for factors of the constant term (which is -15). The factors of -15 are -1, -3, -5, 1, 3, and 5.
Now, we need to find a combination of factors that, when multiplied together, give us the coefficient of x, which is 8. The combination that works is 6 and 2 because 6 times 2 equals 12, which is the coefficient of x^2, and 6 times 2 plus 6 times -5 equals 8, which is the coefficient of x.
Using these factors, we can write the factored form of the expression as:
(3x - 5)(4x + 3)
I hope this explanation helps!