# How do you simplify #(6t^3 + 5t^2 + 9) / (2t + 3)#?

##### 2 Answers

#### Explanation:

- 2t+3 on numerator and denomoniator cancel out.

ANSWER:

You have to factorise the top that

The are many ways of factorising

I would recommend polynomial division as its pretty straight forward to learn and rely on. Here is a link that will teach you all about it and you can practise with: http://www.purplemath.com/modules/polydiv2.htm

#### Explanation:

#"one way is to use the divisor as a factor in the numerator"#

#"consider the numerator"#

#color(red)(3t^2)(2t+3)color(magenta)(-9t^2)+5t^2+9#

#=color(red)(3t^2)(2t+3)color(red)(-2t)(2t+3)color(magenta)(+6t)+9#

#=color(red)(3t^2)(2t+3)color(red)(-2t)(2t+3)color(red)(+3)(2t+3)cancel(color(magenta)(-9))cancel(+9)#

#=color(red)(3t^2)(2t+3)color(red)(-2t)(2t+3)color(red)(+3)(2t+3)+0#

#rArr(cancel((2t+3))(3t^2-2t+3))/cancel((2t+3))=3t^2-2t+3#