I need some assistance on the math question shown. Please write work on PAPER and please do it order. Polynomials Math 30-1

Find the remainder when f(x) is divided by x - k. 1) (x) =5x3 - 25x2 + 29x - 36 k = 3 /1 Factor each to linear and irreducible quadratic factors and find all rational zeros. Your work must be shown ALGEBRAICALLY for full marks. 2) f(x) = 2x4 - 5x3 -4x2 + 3x 12 3) When 2x + kx" + 2x - 12 is divided by x - 4, the remainder is 252. Determine the value of k. 12 4) A certain polynomial function, P(x), is divided by x + 2. The quotient is 3x - 2x + 3 and the remainder is -8. What is the equation of P(x)? /1 5) When mx' - 2x" + nx - 4 is divided by x + 2, the remainder is 4. When mx - 2x- + nx - 4 is divided by x - 1, the remainder is -11. Determine the values of m and n. 126) Ann, Stan, and Fran are triplets. They were born 4 years before their sister, Kim. This year, the product of their four ages is 49 092 greater than the sum of their ages. How old is Kim? 12 7) The graph of a polynomial function, P(x) has a double root at -3, a single root at -5, and a double root at 4. P(x) also passes through the point Q(-2, 3). . Determine the equation of P(x) and write your final answer in factored form. /2 . What is the value of the y-intercept for P(x). /1 8) The graph of f(x) is shown below. Write the equation of the polynomial, with lowest possible multiplicity. N 129) Sketch a graph with the least possible degree of each polynomial function. leading coefficient is negative; zero of 3 has multiplicity 3; zero of 2 has multiplicity 2; zero of 4 has multiplicity 1.. (MUST SHOW REASONING and WORK) 12