How do you use the remainder theorem to find the remainder for the division #(3t^3-10t^2+t-5)div(t-4)#?

3 Answers
Jul 28, 2018

The remainder is 31.

Explanation:

Remainder Theorem :
When we divide a polynomial #f(x)# by #(x−c)# the remainder is # f(c) #
So to find the remainder after dividing by #(x-c)# we don't need to do any division: Just calculate #f(c).#

In this case,
#f(4) = 3(4)^3 - 10(4)^2 + 4 - 5#
#f(4) = 31#

Jul 28, 2018

The remainder is 31.

Explanation:

Note that the dividend is equal to the divisor times the quotient plus the remainder.

Let Q equal the quotient and R the remainder.

#3t^3-10t^2+t-5=Q(t-4)+R#

Notice that when #t=4#, the divisor #t-4# becomes zero, meaning that anything multiplied to it will still result in zero.

Let's try #t=4#

#=>3(4)^3-10(4)^2+(4)-5=Q(4-4)+R#

#=>192-160+4-5=R#

#=>31=R#

That is the answer!

Jul 28, 2018

#31#

Explanation:

#"the remainder when "f(x)" is divided by "(x-a)" is "f(a)#

#3(4)^3-10(4)^2+4-5=31larrcolor(blue)"remainder"#