Let a(x)=x^5+2x^4-x^3+2a(x)=x
5
+2x
4
−x
3
+2a, left parenthesis, x, right parenthesis, equals, x, start superscript, 5, end superscript, plus, 2, x, start superscript, 4, end superscript, minus, x, cubed, plus, 2, and b(x)=x^3+3b(x)=x
3
+3b, left parenthesis, x, right parenthesis, equals, x, cubed, plus, 3.
When dividing aaa by bbb, we can find the unique quotient polynomial qqq and remainder polynomial rrr that satisfy the following equation:
\dfrac{a(x)}{b(x)}=q(x) + \dfrac{r(x)}{b(x)}
b(x)
a(x)
=q(x)+
b(x)
r(x)
start fraction, a, left parenthesis, x, right parenthesis, divided by, b, left parenthesis, x, right parenthesis, end fraction, equals, q, left parenthesis, x, right parenthesis, plus, start fraction, r, left parenthesis, x, right parenthesis, divided by, b, left parenthesis, x, right parenthesis, end fraction,
where the degree of r(x)r(x)r, left parenthesis, x, right parenthesis is less than the degree of b(x)b(x)b, left parenthesis, x, right parenthesis.
What is the quotient, q(x)q(x)q, left parenthesis, x, right parenthesis?
q(x)=q(x)=q, left parenthesis, x, right parenthesis, equals
What is the remainder, r(x)r(x)r, left parenthesis, x, right parenthesis?
r(x)=r(x)=r, left parenthesis, x, right parenthesis, equals
Answers
Given: a(x) = x⁵ + 2x⁴ - x³ + 2 , b(x) = x³ + 3 a(x) = b(x)q(x) + r(x)
To find : q(x) & r(x)
Solution:
a(x) = x⁵ + 2x⁴ - x³ + 2
b(x) = x³ + 3
x² + 2x - 1
x³ + 3 _| x⁵ + 2x⁴ - x³ + 2 |_
x⁵ + 3x²
_______________
2x⁴ - x³ - 3x² + 2
2x⁴ + 6x
__________________
- x³ - 3x² - 6x + 2
-x³ -3
________________
-3x² - 6x + 5
a(x) = b(x)q(x) + r(x)
x⁵ + 2x⁴ - x³ + 2 = ( x³ + 3) (x² + 2x - 1) + ( -3x² - 6x + 5)
q(x) = x² + 2x - 1
r(x) = -3x² - 6x + 5
Learn more:
Divide the polynomial 6x³ + 8x² by the monomial 2x. What is the ...
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Answer:
Given: a(x) = x⁵ + 2x⁴ - x³ + 2 , b(x) = x³ + 3 a(x) = b(x)q(x) + r(x)
To find : q(x) & r(x)
Solution:
a(x) = x⁵ + 2x⁴ - x³ + 2
b(x) = x³ + 3
x² + 2x - 1
x³ + 3 _| x⁵ + 2x⁴ - x³ + 2 |_
x⁵ + 3x²
_______________
2x⁴ - x³ - 3x² + 2
2x⁴ + 6x
__________________
- x³ - 3x² - 6x + 2
-x³ -3
________________
-3x² - 6x + 5
a(x) = b(x)q(x) + r(x)
x⁵ + 2x⁴ - x³ + 2 = ( x³ + 3) (x² + 2x - 1) + ( -3x² - 6x + 5)
q(x) = x² + 2x - 1
r(x) = -3x² - 6x + 5
Learn more:
Divide the polynomial 6x³ + 8x² by the monomial 2x. What is the ...
brainly.in/question/4737681
On dividing a polynomial p(x) by x2 - 4, quotient and remainder ...
brainly.in/question/15921981
Divide the polynomial (6x³ + 11x² - 10x - 7) by the binomial (2x + 1 ...
brainly.in/question/4743553
Step-by-step explanation: