Professor P. Bishop FIU: MAC1147 R.6 Polynomial Division; Synthetic DivisionDivision: Write dividend and divisor in standard form, leaving a space or inserting zero for anymissing terms. (1) Divide lead term of dividend by lead term of divisor; (2) multiply divisor by resultof step 1; (3) write product under like terms in dividend; (4) subtract; (5) repeat steps 1 through 3with result of step 4 until last term of dividend has been used. Check: (Quotient)(Divisor) + Remainder= Dividend.1. (-5x4 + 3x3 – 5x + 2)  (3x – 2 + x2)Synthetic division is used to divide a polynomial of degree 1 or higher by a binomial g(x) of the formx – c. [1] Write the dividend in descending order. [2] Copy the coefficients into the division symbol,remembering to insert a zero for each missing power of x. Outside the division symbol, write thedivisor c (number only) with the opposite sign. This is Row 1. [3] Copy the lead coefficient into row3 directly under the row 1 number. [4] Multiply the entry in row 3 by c and place the result in row 2directly under the next term. [5] Add the quantities in row 1 and row 2, and write the result directlyunderneath it in row 3. [6] Repeat steps 4 and 5 until no more entries are available in row 1. [7] Thefinal entry in row 3 is the remainder R; the other entries are the coefficients in descending order of thequotient q(x) whose degree is one degree less than the dividend. To check. dividend = divisor timesquotient plus remainder: f(x) = g(x) . q(x) + R.Use synthetic division to find the quotient q(x) and remainder R when f(x) is divided by g(x):2.( ) ( )= + - = -f x x x ; g x x23 5 43. ( ) ( )=- + + = +f x x x ; g x x5 22 3 10 74. ( ) ( )= + - = -f x . x . x . ; g x x .33 2 5 8 7 3 1 85. ( ) ( )= - - - = +f x x x x ; g x x6 4 23 55 114 27 4Use synthetic division to determine whether x – c is a factor of f(x):6.( ) ( )= + - + - = +f x x x x x ; g x x4 3 28 15 4 47. ( ) ( )= + - + = +f x x x x ; g x x4 315 5 157. Find the sum of a + b +c + d if x x x dax bx cx x- + += + + +- -3 224 3 5 85