6x³ + 2x² + 3x - 4 is not exactly divisible by x² + 3x - 4.
Given,
The expression : 6x³ + 2x² + 3x - 4
We have to divide the given expression by x² + 3x - 4.
Let's take 6x³ + 2x² + 3x - 4 as p(x) and x² + 3x - 4 as g(x).
If p(x) is divisible by the factors of g(x), then p(x) is divisible by g(x).
So, let's factorize x² + 3x - 4
x² + 3x - 4 = (x - 1) (x + 4)
Now,
p(x) = 6x³ + 2x² + 3x - 4
By using remainder theorem,
If p(1) = 0 and p(4) = 0, then p(x) is divisible by g(x).
So,
p(1) = 6 × 1³ + 2 x 1² + 3 x 1 -4
p(1) = 6 + 2 + 3 - 4
p(1) = 11 - 4
p(1) = 7
Next,
p(4) = 6 x 4³ + 2 x 4² + 3 x 4 - 4
p(4) = 6 x 64 + 2 x 16 + 12 - 4
p(4) = 384 + 32 + 12 - 4
p(4) = 424
Here, p(1) and p(4) is not 0.
So, p(x) is not divisible by g(x).
That is, 6x³ + 2x² + 3x - 4 is not exactly divisible by x² + 3x - 4.
Learn more about divisibility here:
brainly.com/question/1591815
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