Question

Divide. (6x³ + 2x² + 3x −4) ÷ (x² + 3x +4)​

Answer 1

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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