Question

solve it for 100 points
x+7/x3 + 3x² + 3x​

Answer 1

Answer:

Step-by-step explanation:

you can solve the problem using long divison just like regular numbers.

x+1 | x^3+3X^2-2x+7

you start on the left to see what you can divide x+1 into. You start off with x^3. You can make x^3 if you multiply x+1 by x^2. That gives you (x+1)*x^2 = x^3 + x^2. You subtract that from the larger expression, and get rid of the x^3. You are left with: 2x^2 - 2x + 7.

Repeat. What do you multiply x+1 with so that you can get rid of 2x^2? (x+1) * 2x = 2x^2 + 2x. Subtract that from 2x^2-2x+7 and you get: -4x+7.

Repeat again. This time you have (x+1) * -4 = -4x-4. Subtract that from -4x+7 and you have 11.

Thus, x^3 + 3x^2 - 2x + 7 divided by x + 1 is x^2 + 2x - 4 + 11/(x+1)

Answer 2

☯ GiveN :

( x³ + 3x² + 3x + 1) is devided by (x + 7)

$\rule{200}{2}$

☯ To Find :

We have to find the remainder and quotient when polynomial ( x³ + 3x² + 3x + 1) is devided by (x + 7)

$\rule{200}{2}$

☯ Solution :

We can do this question by two methods.

★ First Method ⤵⤵⤵

$\sf{x + 7 = 0} \\ \\ \sf{x = -7} \\ \\ \bf{Putting \:value \: of \: x \: in \: polynomial.} \\ \\ \sf{\dashrightarrow (-7)^3 + 3(-7)^2 + 3(-7) + 1} \\ \\ \sf{\dashrightarrow -343 + 3(49) - 21 + 1} \\ \\ \sf{\dashrightarrow -364 + 148} \\ \\ \sf{\dashrightarrow -216}$

$\Large{\implies{\boxed{\boxed{\sf{Remainder : - 216}}}}}$

$\rule{200}{2}$

★ Second Method ⤵⤵⤵

$\Large{\implies{\boxed{\boxed{\sf{Quotient : x^2 - 4x + 31}}}}}$

$\Large{\implies{\boxed{\boxed{\sf{Remainder : - 216}}}}}$