# How do you factor #x^4-61x^2+900#?

##### 4 Answers

#### Explanation:

#### Explanation:

Finding the correct factors for a quadratic trinomial which has a big value for (c) is not as daunting as it might appear at first:

There are a number of clues to look out for.

In

If

Also remember that an odd number can only come from

ODD + EVEN, so this immediately eliminates the situation of two even factors.

Therefore the required factors are not very far from

Consider factors less than

Ah,

so these are the factors we want.

A difference approach

#### Explanation:

Given:

Set

Set

compare to

where

Note about the minimums.

You must not assume that they are centrally located between the points where the plot crosses the x-axis. In fact if you differentiate and set it to 0 you will find that they are slightly off centre.

#### Explanation:

Call

Find 2 numbers knowing the sum

and the product (

To do so, compose factor pairs of

This last sum is

Therefore. the 2 numbers are:

Replace