divide x4+2×2+1by x+1
Answers
Answer:
Since the remander is 0, the final answer is the quotient.
x2+0x+1
Step-by-step explanation:
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
x2 + 0x - 1 x4 + 0x3 + 0x2 + 0x - 1
Divide the highest order term in the dividend x4 by the highest order term in divisor x2.
x2
x2 + 0x - 1 x4 + 0x3 + 0x2 + 0x - 1
Multiply the new quotient term by the divisor.
x2
x2 + 0x - 1 x4 + 0x3 + 0x2 + 0x - 1
+ x4 + 0 - x2
The expression needs to be subtracted from the dividend, so change all the signs in x4+0-x2
x2
x2 + 0x - 1 x4 + 0x3 + 0x2 + 0x - 1
- x4 - 0 + x2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
x2
x2 + 0x - 1 x4 + 0x3 + 0x2 + 0x - 1
- x4 - 0 + x2
+ x2
Pull the next term from the original dividend down into the current dividend.
x2
x2 + 0x - 1 x4 + 0x3 + 0x2 + 0x - 1
- x4 - 0 + x2
+ x2 + 0x - 1
Divide the highest order term in the dividend x2 by the highest order term in divisor x2.
x2 + 0x + 1
x2 + 0x - 1 x4 + 0x3 + 0x2 + 0x - 1
- x4 - 0 + x2
+ x2 + 0x - 1
Multiply the new quotient term by the divisor.
x2 + 0x + 1
x2 + 0x - 1 x4 + 0x3 + 0x2 + 0x - 1
- x4 - 0 + x2
+ x2 + 0x - 1
+ x2 + 0 - 1
The expression needs to be subtracted from the dividend, so change all the signs in x2+0-1
x2 + 0x + 1
x2 + 0x - 1 x4 + 0x3 + 0x2 + 0x - 1
- x4 - 0 + x2
+ x2 + 0x - 1
- x2 - 0 + 1
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
x2 + 0x + 1
x2 + 0x - 1 x4 + 0x3 + 0x2 + 0x - 1
- x4 - 0 + x2
+ x2 + 0x - 1
- x2 - 0 + 1
0
Since the remander is 0, the final answer is the quotient.
x2+0x+1