(2x + 3) is a factor of which of the given expressions?radio_button_unchecked4x3 + 6x2 - x - 6radio_button_unchecked4x3 + x2 - 3x - 27radio_button_unchecked2x3 + 6x2 - 3x - 27radio_button_unchecked2x3 + 5x2 - x - 6
Question
(2x + 3) is a factor of which of the given expressions?radio_button_unchecked4x3 + 6x2 - x - 6radio_button_unchecked4x3 + x2 - 3x - 27radio_button_unchecked2x3 + 6x2 - 3x - 27radio_button_unchecked2x3 + 5x2 - x - 6
Solution
To find out which expression has (2x + 3) as a factor, we need to set (2x + 3) equal to zero and solve for x.
Step 1: Set the factor equal to zero 2x + 3 = 0
Step 2: Solve for x 2x = -3 x = -3/2
Now, we substitute x = -3/2 into each of the given expressions. If the result is zero, then (2x + 3) is a factor of that expression.
Step 3: Substitute x = -3/2 into each expression
For 4x^3 + 6x^2 - x - 6: = 4(-3/2)^3 + 6(-3/2)^2 - (-3/2) - 6 = -27 + 13.5 + 1.5 - 6 = -18 ≠ 0
For 4x^3 + x^2 - 3x - 27: = 4(-3/2)^3 + (-3/2)^2 - 3(-3/2) - 27 = -27 + 2.25 + 4.5 - 27 = -47.25 ≠ 0
For 2x^3 + 6x^2 - 3x - 27: = 2(-3/2)^3 + 6(-3/2)^2 - 3(-3/2) - 27 = -13.5 + 13.5 + 4.5 - 27 = -22.5 ≠ 0
For 2x^3 + 5x^2 - x - 6: = 2(-3/2)^3 + 5(-3/2)^2 - (-3/2) - 6 = -13.5 + 11.25 + 1.5 - 6 = -6.75 ≠ 0
None of the given expressions have (2x + 3) as a factor.
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