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3x4 plus 5x3 plus x2 - 5 divided by x 2 =[(3x4) + (5x3) + (x2 - 5)]/x2 =(12 + 15 + x2 -5)/x2 =(27 - 5 + x2)/x2 =(22 + x2)/x2
Since the polynomial has three zeroes it has a degree of 3. So we have:(x - -5)[x - (2 + i)][x - (2 - i)]= (x + 5)[(x - 2) - i][(x - 2) + i]= (x + 5)[(x - 2)2 - i2]= (x + 5)[x2 - 2(x)(2) + 22 - (-1)]= (x + 5)(x2 - 4x + 4 + 1)= (x + 5)(x2 - 4x + 5)= x(x2 - 4x + 5) + 5(x2 - 4x + 5)= x3 - 4x2 + 5x + 5x2 - 20x + 25= x3 + x2 - 15x + 25Thus,P(x) = x3 + x2 - 15x + 25
x2 + 3x - 40 = x2 + 8x - 5x - 40 = x(x + 8) - 5(x + 8) = (x - 5)(x + 8)
x2 + 1x - 30 = (x + 6) (x - 5)
(X + 5)(X + 1) FOIL this. X2 + 1X + 5X + 5 Gather terms. X2 + 6X + 5 ----------------------------those were the factors