In Exercises use synthetic division to perform the indicated division. Write the polynomial in the form p(x) = d(x)q(x) + r(x)[tex](4x^{2} -5x+3)[/tex] ÷ [tex](x+3)[/tex]

The polynomial in the form p(x) = d(x)q(x) + r(x) is p(x) = (x + 3)(4x - 17) + 54Step-by-step explanation:In synthetic division we equate the divisor by 0 to find the value of x x + 3 = 0 ⇒ x = -3Step 1 : Write down the coefficients of the f(x) , put x = -3 at the left                            -3        4      -5      3                                     ____________Step 2 : Bring down the first coefficient to the bottom row.                         -3        4       -5       3                                   ________________                                     4 Step 3 : Multiply it by -3, and carry the result into the next column.                        -3        4       -5        3                                   ____-12________                                     4Step 4 : Add down the column                        -3        4       -5        3                                   ____-12________                                    4      -17 Step 5 : Multiply it by -3, and carry the result into the next column                        -3        4        -5        3                                   _____-12___51_____                                    4        -17Step 6 : Add down the column                       -3        4         -5         3                                  _____-12____51___                                   4        -17         54 The quotient is (4x - 17) and the remainder is 54The factors of (4x² - 5x + 3) are:d(x) = (x + 3) and q(x) = (4x - 17)The remainder r(x) = 54The polynomial in the form p(x) = d(x)q(x) + r(x) is p(x) = (x + 3)(4x - 17) + 54Learn more:You can learn more about polynomial in brainly.com/question/12700460#LearnwithBrainly