Find the numerical value of m if the expression x3 + mx2 + 7x − 6 has a remainder of −4 whendivided by x + 2.
Question
Find the numerical value of m if the expression has a remainder of when divided by .
Solution
To find the value of m, we can use the Remainder Theorem which states that the remainder of a polynomial f(x) divided by (x-a) is equal to f(a).
In this case, our polynomial is f(x) = x^3 + mx^2 + 7x - 6 and we are dividing by x + 2, so a = -2.
Substituting a = -2 into the polynomial gives us the remainder, which is -4.
So, we have:
(-2)^3 + m(-2)^2 + 7(-2) - 6 = -4 -8 + 4m - 14 - 6 = -4 4m - 28 = -4 4m = 24 m = 24 / 4 m = 6
So, the numerical value of m is 6.
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