# How do you factor completely t^2-4t+3?

Jun 12, 2016

$\left(x - 3\right) \left(x - 1\right)$

#### Explanation:

Find factors of 3 which add up to 4.
THe signs in the brackets will be the same (because of the +) they are both negative. (because of -4)

$\left(x - 3\right) \left(x - 1\right)$

Jun 12, 2016

${t}^{2} - 4 t + 3 = \left(t - 1\right) \left(t - 3\right)$

#### Explanation:

To factorize ${t}^{2} - 4 t + 3$, we should split the middle term $- 4$ in two parts whose product is product of coefficients of other two terms i.e $1 \times 3 = 3$. These are $- 3$ and $- 1$. Hence,

${t}^{2} - 4 t + 3$

= ${t}^{2} - 3 t - t + 3$

= $t \left(t - 3\right) - 1 \left(t - 3\right)$

= $\left(t - 1\right) \left(t - 3\right)$