Factor as the product of two binomials. x^2-3x-10

Answer 1

There's also the ever-popular "ac" method.

For x² - 3x - 10 "a" is 1 and "c" is -10, so ac = 1 x (-10) = -10

What are the 2 factors of -10? They are 2, -5; -2, 5; 1, -10 and -1, 10.

Which one of these pairs adds to the "b" coefficient of -3?

Looks like 2 and -5 will work.

So the two binomial factors are (x + 2) and (x - 5).

Check using FOIL.

Answer 2

Hi Dannielle.

Factoring quadratics is most people's favorite solution method for solving quadratic equations.

With some practice, I'll bet you'll love it, too.

Factoring is like the opposite of FOILing.

(You're familiar with FOIL, "First, Outer, Inner, Last", yes?)

We're given a quadratic expression in the form x² + bx + c and asked to re-write it as an equivalent expression in the form (x - p)(x - q). In short, we're looking for two numbers p and q.

These number must multiply to c, and add (algebraically) to b.

NOTE: The binomials in the Factored Form are ALWAYS interpreted as SUBTRACTIONS!!

The appearance of a "+" is due to a double negative.

In the examples below the plus and minus symbols represent the APPEARENCE of the symbols in the final forms.

My advice is this, before you look at the numbers, check out the plus or minus symbols.

They'll tell you everything you need to know about the signs of p and q.

For instance, look closely at the following.

If c is positive, both p & q will have the same sign as b.

x² + bx + c, p & q are both positive (x + p) (x + q)

x² - bx + c, p & q are both negative (x - p) (x - q)

if c is negative, p & q will have opposite signs, and the sign b is assigned to the "bigger" number.

x² + bx - c, p & q will have opposite signs (x + p) (x - q) and the "bigger" number is positive.

x² - bx - c, p & q will have opposite signs (x - p) (x + q) and the "bigger" number is negative.

Let's use your problem as an example.

x2 - 3x - 10

The c is negative; therefore our number have opposite signs.

The b is negative; therefore the "bigger" number is negative.

Our answer is going to look like this (x - p) (x + q), where p is bigger than q (in the absolute value sense)

We're done thinking about the signs.

Now, we just focus on the numbers.

They multiply to 10

They have a difference of 3

The bigger number is negative.

2 and 5 multiply to 10 and have a difference of 3.

5 is bigger than 3, so 5 gets the minus sign.

Our answer: (x - 5) (x + 3)

Lastly, it's important that you ALWAYS check your answer.

To make sure your answer is correct, FOIL it.

If that does bring you back to where the problem began, oops, it's wrong.

I hope this helps.

Answer 3

x²-3x-10

What is needed is (x+a)(x+b) such that a+b = -3 and ab=-10. a and b will be factors of -10.

-10 = 1×(-10) or 2x(-5) or -1×10 or -2×5

You should be able to figure it out from here.