ANSWER[tex]q(x) = 7x + 4[/tex]
EXPLANATION
We want to find the quotient when [tex]7{x}^{2}-3x-9[/tex] is divided by x-1
We can quickly perform a synthetic division.
We write out the coefficients of the polynomial
[tex]7{x}^{2}-3x-9[/tex]
7 -3 -9
1| 7 4
7 4 -5
To obtain the top row.When we equate the divisor to zero, we get;[tex]x - 1 = 0[/tex][tex]\implies\:x=1[/tex]
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 [tex]7x + 4[/tex] and the remainder is -5
Remember this polynomial can be written as:
Dividend= Divisor * Quotient + Remainder
[tex]7x^2-3x-9=(x-1)(7x+4)-5[/tex]
Therefore Quotient=7x+4
