Question

divide the polynomial 3x⁴-:4x³-3x-1 by x-1​

Answer 1

Answer:

x−13x 4−4x 3 −3x−1

=−5

Step-by-step explanation:

Let p(x) = 3x⁴-4x³-3x-1 and g(x) = x-1,

x-1) 3x⁴-4x³+0-3x-1(3x³-x²-x-4

3x⁴ -3x³

___________________

-x³ + 0 -3x. -x³ + x²

___________________

-x² - 3x - 1

-x² + x

___________________

- 4x - -4x + 4

____________________

Remainder (-5)

Dividend = 3x⁴-4x³-3x-1,

Divisor = x-1,

Quotient = 3x³-x²-x-4,

Remainder = -5

Therefore,

frac{3x^{4}-4x^{3}-3x-1 }{x-1}= -5 x−13x 4 −4x −3x−1

=−5

Answer 2

$\sf\huge {\underline{\underline{{Solution}}}}$

How to solve ?

Since,the given polynomial having degree 4 and we have to divide it by x-1 having degree 1 so,in order to make the same degree of polynomial x-1 must be Multiply with degree 3

=>( x-1 )x³= x⁴-x³

Now,to make the coefficient same Multiply it with 3

=> 3x⁴-3x³

Now,divide the given polynomial with 3x⁴-3x³

=> 3x⁴-4x³

=> 3x⁴-3x³

=> $(-)(+)$

__________

-x³-3x-1

Now ,again Multiply x-1 with -x² to make the degree of 3.

=> -x²(x-1)= -x³+x²

=> -x³-3x-1

=> -x³+x²

=>$(+)(-)$

__________

-x²-3x-1

Now ,divide the x-1 with -x in order to make the degree of 2.

=> -x(x-1)= -x²+x

=>-x²-3x-1

=>-x²+x

=>(+)(-)

________

-4x-1

Now, Multiply x-1 with -4

=> -4x-1

=>-4x+4

=>(+)(-)

______

-5

Therefore, Remainder = -5

Quotient = 3x³-x²-x-4

Dividend = 3x⁴-4x³-3x-1

Divisor= x-1

Now, check by using division algorithm:

Dividend= Divisor x quotient+remainder

3x⁴-4x³-3x-1 = (x-1)(3x³-x²-x-4)-5

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$= 3x⁴-x³-x²-4x-3x³+x²+x+4-5

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$= 3x⁴-4x³-4x+x+4-5

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$= 3x³-4x³-3x-1