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

User DennisV
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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

User Hagen Von Eitzen
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