Question

FACTORISE IT BY FACTOR THEOREM:
12x^3-4x^2-3x-1

Answer 1

$\bigstar$ Factor Theorem :  x – a is a factor of the polynomial p(x), if p(a) = 0. Also, if x – a is a factor of p(x), then p(a) = 0, where a is any real number.

Here the equation that you have given is somewhat wrong , the correct equation is taken.

$\bigstar$ 12x³+4x²-3x-1

Factor the first two terms:

$\star$ 4x²(3x+1)-3x-1

Notice that we can factor out the negative - from the last two terms:

$\star$ 4x²(3x+1)-(3x+1)

This means we can factor this by grouping. The factoring is already done, so we are left with:

$\star$ (3x+1)(4x^2–1)

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