Home > Algebra > Factoring Completely

How do you factor #x^2+3xy-10y^2#?

Answer 1

Kennedy Adams

We are looking for #a# and #b# such that #a+b = 3# and #axxb=-10#

A quick check of possible factors for #(-10)# gives us: #x^2+3xy-10y^2#

#=(x+5y)(x-2y)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Eli Assouline

To factor the expression (x^2 + 3xy - 10y^2), you can use the method of grouping.

First, find two numbers that multiply to give the product of the coefficient of (x^2) and the constant term, which is (1 \times (-10) = -10), and add up to the coefficient of the middle term, which is (3). The numbers are (5) and (-2).

Now, split the middle term using these two numbers: [x^2 + 5xy - 2xy - 10y^2]

Next, factor by grouping: [x(x + 5y) - 2y(x + 5y)]

Now, you can factor out the common factor (x + 5y): [(x - 2y)(x + 5y)]

So, (x^2 + 3xy - 10y^2) factors to ((x - 2y)(x + 5y)).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.