Question

Question 10 multiple choice

Answer 1

Answer: Choice B

(x-1)(x^3+x^2+5x+6)

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Explanation:

The 1 in the upper left box means that x = 1 is a root of the original polynomial.

So this means x-1 is a factor of the original polynomial.

This is because x = 1 leads to x-1 = 0 after subtracting 1 from both sides.

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The 0 in the last position of the bottom row shows we got a remainder of 0.

Getting a remainder 0 tells us that (x-1) is a factor of the polynomial. This synthetic division table confirms our initial guess.

The other values in that bottom row (1, 1, 5, 6) form coefficients to the polynomial 1x^3+1x^2+5x+6, or simply x^3+x^2+5x+6

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So we know that (x-1) and (x^3+x^2+5x+6) are factors

Meaning that,

x^4+4x^2+x-6 = (x-1)(x^3+x^2+5x+6)

You can confirm this by expanding out the right hand side (distribution rule).