Question

How do you factor `k^ { 2} + 5k + 4`?

Answer 1

`k^2 +5k+4= (k+1)(k+4)`

Explanation:

This is a quadratic trinomial. There are three terms in the pattern,

`k^2 " "+- k^" "+-k^0`

A quadratic often come from multiplying two binomials:

`(k+- a)(k+-b)`

In `k^2+5k +4` , there are a lot of clues about the original factors.

The sign of `4` tells you two things:

• Find factors of 4 and ADD them to make 5.
• The signs in the brackets will be the SAME `(+xx+ =+) and (-xx- =+)`

The sign of the middle term (+5) , tells you they will be PLUS

`1xx4 = 4 and 1+4 = 5" "larr` 1 and 4 are the correct factors
`2xx2=4 and 2+2=4" "larr` 2 and 2 are incorrect factors

so we have: `k^2 +5k+4= (k+1)(k+4)`