In the expansion of (x-7)(3x**2+kx-3) the coefficient of x**2 is 0. i) Find the value of k ii) Find the coefficient of x. iii) write the fully expanded equation in terms of x
i) multiply out: 3x3+kx2-3x-21x2-7kx+21 simplify: 3x3+(k-21)x2+(-7k-3)x+21 the coefficient of x2 is 0 and therefore k-21=0 k=21.
ii)from i) the coefficient of x is (-7k-3) k=21 and therefore the required answer is (-7*21)-3 =-147-3 =-150 iii) from i) and ii): 3x3+(k-21)x2+(-7k-3)x+21 -> 3x**3-150x+21
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