How do you simplify (6t^3 + 5t^2 + 9) / (2t + 3)6t3+5t2+92t+3?

2 Answers
May 10, 2018

3t^2 - 2t^2 + 3 3t22t2+3

Explanation:

(6t^3 + 5t^2 + 9) / (2t+3)6t3+5t2+92t+3

(2t+3(3t^2-2t+3)) / (2t+3)2t+3(3t22t+3)2t+3

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

ANSWER: 3t^2 - 2t^2 + 3 3t22t2+3

You have to factorise the top that 2t + 32t+3 directly factorises 6t^3 + 5t^2 + 96t3+5t2+9 so that it cancels the denominator giving you a value of 3t^2 - 2t^2 + 33t22t2+3.

The are many ways of factorising 6t^3 + 5t^2 + 96t3+5t2+9, polynomial division, rational root theorem.

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

May 10, 2018

3t^2-2t+33t22t+3

Explanation:

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

"consider the numerator"consider the numerator

color(red)(3t^2)(2t+3)color(magenta)(-9t^2)+5t^2+93t2(2t+3)9t2+5t2+9

=color(red)(3t^2)(2t+3)color(red)(-2t)(2t+3)color(magenta)(+6t)+9=3t2(2t+3)2t(2t+3)+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