6 days ago

What is the quotient (2x4 – 3x3 – 3x2 + 7x – 3) ÷ (x2 – 2x + 1)?

Mathematics

2 answers:

Inessa [12.3K]6 days ago

8 0

Answer:

Quotient: $2x^2+x-3$

Refer to the attached document.

Step-by-step explanation:

Provided: $(2x^4-3x^3-3x^2+7x-3)\div (x^2-2x+1)$

A rational expression is provided, and we need to compute the quotient.

We will utilize long division to obtain the quotient.

Initially, we eliminate $2x^4$ by $x^2$

$x^2-2x+1$ ) $2x^4-3x^3-3x^2+7x-3$ ( $2x^2+x-3$

$-2x^4+4x^3-2x^2$

$x^3-5x^2+7x$

$-x^3+2x^2-x$

$-3x^2+6x-3$

$3x^2-6x+3$

$0$

Thus, the result of the division is $2x^2+x-3$

babunello [11.4K]6 days ago

5 0

Here are two polynomials:

1. The dividend - $f(x)=2x^4 - 3x^3 - 3x^2 + 7x - 3$

2. The divisor - $g(x)=x^2 - 2x + 1$ .

As the divisor is a perfect square $g(x)=x^2 - 2x + 1=(x-1)^2$ , it is necessary to determine the result of dividing f(x) by (x-1):

$f(x)=2x^4 - 3x^3 - 3x^2 + 7x - 3=(x-1)(2x^3-x^2-4x+3)=(x-1)(x-1)(2x^2+x-3)=(x-1)^2(2x^2+x-3)=g(x)(2x^2+x-3).$

Thus, the quotient obtained is $2x^2+x-3$ .

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