5y^2-13y+6
If you wish to factor, the factors are:
(5y - 3)(y - 2)
Checking using FOIL (First, Outer, Inner, Last):
5y^2 - 10y - 3y + 6
Combining like terms:
5y^2 - 13y + 6
I hope this will help.
To factor the expression 5y^2 - 13y + 6, we need to find two binomials that multiply together to give us the original expression.
To begin factoring, we look at the coefficients of the terms. The coefficient of y^2 is 5, the coefficient of y is -13, and the constant term is 6.
We need to find two numbers that multiply together to give us the product of the coefficient of y^2 and the constant term, which is 5 * 6 = 30. Additionally, these two numbers need to add up to the coefficient of y, which is -13.
So we want to find two numbers that multiply to 30 and add up to -13.
After some trial and error, we find that -3 and -10 satisfy these conditions. (-3) * (-10) = 30, and (-3) + (-10) = -13.
Now that we have these two numbers, we can split the middle term -13y into two terms, using -3y and -10y.
The expression then becomes:
5y^2 - 3y - 10y + 6
We can now factor by grouping. We group the first two terms together and the last two terms together:
(5y^2 - 3y) - (10y - 6)
Now, we factor out the greatest common factor from each group:
y(5y - 3) - 2(5y - 3)
We see that we have a common binomial factor, (5y - 3), which we can factor out:
(5y - 3)(y - 2)
And there you have it! The factored form of the expression 5y^2 - 13y + 6 is (5y - 3)(y - 2).