When the function f(x) = 2x^n + ax^2 - 6 is divided by (x - 1), the remainder is -7 and when divided by (x + 3), the remainder is 129. Calculate the value of "a" and "n" and hence write the polynomial function completely.

Step-by-step explanation:

Step-by-step explanation:

From the fact that the remainder is -7 after we divide by x -1 , then we know that f(1) = -7. But f(1) = 2 + a - 6.

So 2 + a - 6 = -7

a - 4 = -7

a = 4 - 7

a = -3.

Also we know that when divided by x + 3 the remainder is 129. Hence f( -3) = 129

129 = f(-3) = 2 (-3)^ n + (-3)(-3)^2 -6

129 = 2 (-3)^n -27 - 6

129 = 2 (-3)^n -33

129 + 33 = 2(-3)^n

162 = 2 (-3)^n

81 = (-3)^n

Hence n =4 and therefore f(x) = 2x^4 -3x^2 - 6.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

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step-by-step explanation: