How do you find the quotient of #(t^2+5t+4)div(t+4)#?

Question

Nathan Axel · Accepted Answer

You can factorize #t^2+5t+4=(t+1)(t+4)# So now we have: #=((t+1)(t+4))/(t+4)# We may now cancel the #(t+4)#'s provided #t!=-4# #=((t+1)cancel((t+4)))/cancel(t+4)=t+1#

Nathan Axel · Answer

First, rewrite this expression as:

#(t^2 + 5t + 4)/(t + 4)#

Next, factor the numerator:

#((t + 4)(t + 1))/(t + 4)#

Now, cancel the common terms in the numerator and denominator:

#(color(red)(cancel(color(black)((t + 4))))(t + 1))/(color(red)(cancel(color(black)(t + 4))# #= t + 1# where #t + 4 != 0# or #t != -4#

Abigail Allen · Answer

undefined To find the quotient of (t^2+5t+4) divided by (t+4), you can use long division or synthetic division.

Using long division:
- Divide the first term of the numerator (t^2) by the first term of the denominator (t). This gives t as the first term of the quotient.
- Multiply the entire denominator (t+4) by t, and subtract the result from the numerator (t^2+5t+4).
- Bring down the next term from the numerator (5t) and repeat the process.
- Continue this process until you have divided all terms of the numerator.
- The resulting quotient will be t+1.

Using synthetic division:
- Write the coefficients of the numerator (1, 5, 4) and the divisor (1, 4) in descending order.
- Bring down the first coefficient (1) and perform the synthetic division.
- The resulting quotient will be t+1.

Therefore, the quotient of (t^2+5t+4) divided by (t+4) is t+1.