ANSWER[tex]q(x) = 7x + 4[/tex]EXPLANATIONWe 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 -91| 7 4 7 4 -5To 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 -5Remember 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