solve 4.
solve 4. ANSWER THE FOLLOWING. 1. Determine the remainder when p(x) = xa-3x2+2x+3 is divided by x 1. 2. Check whether p(x) = x3-5x2+4x-3 is a multiple of g(x) = x-2. 3. For what value of a, is the polynomial x3-ax2-2x+5a-7 a multiple of (I-a)? 4. If ax2+bx+c is exactly divisible by (x-1) and (x-2) and leaves remainder 6 wren divided by (X+l), find the values of a, b and c. 5. Without actual division, prove that (X+l) exactly divides the polynomial 6. If the polynomials x3+2x2-5ax-7 and x3+ax2-12x+6, leaves the remainder RI and R2 an x-2 resoectivelv and if 2R1+R2-6=0, find the value of a.

Hi, f (x) = {ax}^{2} + bx + c now x - 1 and x - 2 exactly divides so using remainder theorem f (1) = f (2) = 0 a + b + c = 0 . . . . . (1) 4 a + 2 b + c = 0 . . . . . . (2) and remainder is 6 when f (x) divided by x + 1, so f (- 1) = 6 a - b + c = 6 . . . . (3) Subtracting (1) from (3), we get - 2 b = 6 b = - 3 putting the value of b in (1) and (2), we get a + c = 3 . . . . (4) 4 a + c = 6 . . . . . (5) subtracting (4) from (5), we get 3 a = 3 \Rightarrow a = 1 Now, from (1), we get 1 + (- 3) + c = 0 \Rightarrow c = 2 Regards

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