Q. 274.3( 3 Votes )

# If (x^{3}

Answer :

If (x - 2) is a factor of the polynomial (x^{3} + mx^{2} – x + 6) then it must satisfy it.

So, putting x = 2 the polynomial must be zero.

Putting x = 2 and equating to zero.

= (23 + m2^{2} –2 + 6)

= 4m + 12 = 0

= m = -3

If we divide f(x) = (x^{3} + mx^{2} –x + 6) by (x - 3) remainder can be find at value of –

(x - 3) = 0

Or x = 3

So we will put x = 3 in f(x) = (x^{3} + mx^{2} – x + 6)

f(3) = (3^{3} + m3^{2} – 3 + 6)

= 30 + 9m

So remainder = 30 + 9m

= 30 + 9(-3) = 30 - 27 = 3

So, r = 3.

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