Question

The polynomial which when divided by –x² + x – 1 gives a quotient x – 2 and remainder 3, is
A. x³ – 3x² + 3x – 5
B. –x³ – 3x² – 3x – 5
C. –x³ + 3x² – 3x + 5
D. x³ – 3x² – 3x + 5

Answer 1

Answer:

a=bq+r

a= (–x² + x – 1) × (x–2)+3

a=–x³ + x² – x + 2x²– 2x + 2 + 3

[ a=–x³ + 3x² – 3x + 5 ]

✓✓✓✓✓✓✓✓✓✓✓✓

Answer 2

Given :  polynomial which when divided by –x² + x – 1 gives a quotient x – 2 and remainder 3.

 

Concept :

DIVISION ALGORITHM for polynomials :  

f(x) = g(x)  × q(x) + r(x)

Dividend =  Divisor ×  Quotient + Remainder

 

Solution :  

We have,  g(x) = -x² + x -1 , q(x) = x - 2 and r(x) = 3

 f(x) = g(x)  × q(x) + r(x)

= (-x² + x -1) (x - 2) + 3  

= -x³ + x² - x +2x² -2x + 2 + 3  

= -x³ + x² + 2x² - x -2x +2+3

= -x³ + 3x² - 3x +5

Hence, the polynomial f(x) is -x³ +3x² - 3x +5 .

The correct option is (c) : -x³ +3x² - 3x +5 .

HOPE THIS ANSWER WILL HELP YOU……

 

Some more questions :  

If the polynomial $f(x)=ax^{3}+bx-c$ is divisible by the polynomial $g(x)=x^{2}+bx+c$, then ab=

(a) 1

(b) $\frac{1}{c}$

(c) -1

(d) $-\frac{1}{c}$

https://brainly.in/question/7407444

 

Apply division algorithm to find the quotient q(x) and remainder r(x) in dividing f(x) by g(x) in each of the following:

$f(x)= x^{3} -6x^{2} + 11x -6,g(x)=x^{2}+x+1$

https://brainly.in/question/7060874