If 4x2 - 6x - m is divisible by x - 3, the value of m is exact divisor ofa.9b.45c.20d.36
Question
If 4x² - 6x - m is divisible by x - 3, the value of m is an exact divisor of:
a. 9
b. 45
c. 20
d. 36
Solution
To determine the value of m, we need to use the factor theorem. According to the factor theorem, if a polynomial is divisible by x - c, then the polynomial evaluated at c will be equal to zero.
In this case, we are given that 4x^2 - 6x - m is divisible by x - 3. So, we can set x - 3 equal to zero and solve for x:
x - 3 = 0 x = 3
Now, we substitute x = 3 into the polynomial:
4(3)^2 - 6(3) - m = 0 36 - 18 - m = 0 18 - m = 0 m = 18
Therefore, the value of m is 18.
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