Question

Dvide the polynomial_3xpower4 -4x power3 - 3x-1_by (x-1)
b
y Long Divison method.
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Answer 1

Answer:

3 x ki power 3 minus x square minus x minus 4

Answer 2

Correct Question:

Divide the polynomial 3x⁴ - 4x³ - 3x - 1 divided by (x-1)

Answer:

Quotient = 3x³ - x² - x - 4

Step-By-Step-Explaination:

Given:

• P(x) = 3x⁴ - 4x³ - 3x - 1

• g(x) = x - 1

To Find:

• Quotient = [ q(x) ]

• Remainder = [ r(x) ]

Procedure:

➝ Finding the quotient by Remainder Theorem :-

Let p(x) = 3x⁴ - 4x³ - 3x - 1

and

g(x) = x - 1

Zero of x - 1 :-

$\: \: \: \: \: \sf \implies \: x - 1 = 0 \\ \\ \: \: \: \: \: \sf \implies \: x = 1$

Putting x = 1 :-

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: p(1) = 3 {(1)}^{4} - 4 {(1)}^{3} - 3(1) - 1$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: p(1) = 3 - 4 - 3 - 1$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: p(1) = - 1 - 4$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: p(1) = - 5$

r(x) = -5

* Long division method has been attached in the attachment.