Question

Use the long division method to find the result when 3, x, cubed, minus, 7, x, squared, minus, 6, x, plus, 163x

3
−7x
2
−6x+16 is divided by 3, x, minus, 73x−7. If there is a remainder, express the result in the form q, left bracket, x, right bracket, plus, start fraction, r, left bracket, x, right bracket, divided by, b, left bracket, x, right bracket, end fractionq(x)+
b(x)
r(x)
​
.

Answer 1

Dividing 3x^3 - 7x^2 - 6x + 163x by 3x - 73 using long division results in x^2 - 24x + 177 with a remainder of 36842.

To perform long division with polynomials, you divide the highest degree term of the numerator by the highest degree term of the denominator. In this case, divide 3x^3 by 3x to get x^2, and then multiply the entire divisor 3x - 73 by x^2. Subtract the result from the numerator, and repeat the process until the degree of the remainder is less than the degree of the divisor.

Here are the steps:

```

x^2 - 24x + 177

____________________________

3x - 73 | 3x^3 - 7x^2 - 6x + 163x

- (3x^3 - 73x^2)

___________________

66x^2 - 6x

- (66x^2 - 1602x)

___________________

1596x + 163x

- (1596x - 36579)

___________________

36842

```

So, the result of dividing 3x^3 - 7x^2 - 6x + 163x by 3x - 73 is x^2 - 24x + 177 with a remainder of 36842. Therefore, the expression in the form q(x) + r(x)/b(x) is:

`\[ (x^2 - 24x + 177) + (36842)/(3x - 73) \]`

The question probable may be:

How is the long division method applied to divide 3x^3 - 7x^2 - 6x + 163x by 3x - 73? If there's a remainder, express the result in the form
`\(q(x) + (r(x))/(b(x))\).`