# How To Write A Polynomial In Factored Form

Here’s how the action of constructed analysis works, step-by-step.

Divide (3{x^3} – 4x 5) by ((x 2)) and accompaniment the caliber and remainder.

First, accomplish abiding the polynomial is listed in adjustment of bottomward powers.

Missing admiral charge be replaced by a zero. (3{x^3} – 4x 5) has coefficients (3), (0), (- 4) and (5). The (0) is there because there’s no ({x^2}).

Another way of autograph ((x 2)) is (x = – 2). So (- 2) is the divisor.

First address the catechism in this form:

Bring bottomward the aboriginal accessory (in this archetype (3)) and address it beneath the line. Accumulate it by the divisor ((- 2)) and abode the artefact ((- 6)) beneath the abutting accessory but aloft the line.

Now add the artefact you accept aloof affected (in our archetype (- 6)) to the accessory aloft it, ((0)). Address the consistent cardinal ((- 6)) beneath the line. Accumulate this new cardinal by the divisor ((- 2)) and abode the answer, ((12)) beneath the abutting coefficient.

Continue like this until no added ethics remain.

The aboriginal three numbers beneath the band are the coefficients of the caliber and the aftermost cardinal is the remainder.

Now that we accept the coefficients of the quotient, we address its announcement by abbreviation the aboriginal amount by one.

So for our example, the acknowledgment is:

[3{x^3} – 4x 5]

[= (x 2)(3{x^2} – 6x 8) – 11]

where ((x 2)) is the divisor, ((3{x^2} – 6x 8)) is the caliber and (- 11) is the remainder.

If you see that your acknowledgment has a accepted agency in the quotient, again you can simplify. Bring the agency to the advanced of the brackets and accumulate the divisor – bethink that the adjustment is not important for multiplication.

How To Write A Polynomial In Factored Form – How To Write A Polynomial In Factored Form
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