Question

What is the quotient? 7x^2-3x-9 divided by x-1

Answer 1

ANSWER
`q(x) = 7x + 4`

Step-by-step explanation

We want to find the quotient when
`7{x}^(2)-3x-9` is divided by x-1

We can quickly perform a synthetic division.

We write out the coefficients of the polynomial

`7{x}^(2)-3x-9`

7 -3 -9

1| 7 4

7 4 -5

To obtain the top row.When we equate the divisor to zero, we get;
`x - 1 = 0`
`\implies\:x=1`

This gives the 1 in the far left.The first two numbers in the last row are the coefficients of the quotient. The last number in the last row is the remainder.Therefore the quotient is
`7x + 4` and the remainder is -5

Remember this polynomial can be written as:

Dividend= Divisor * Quotient + Remainder

`7x^2-3x-9=(x-1)(7x+4)-5`

Therefore Quotient=7x+4