Question

f(x) = 4x4 − 8x3 − 3x2 + 7x − 2 = (x + 1)(4x3 − 12x2 + 9x − 2) Based on the sythetic division shown, 1 2 is of the polynomial.

Answer 1

Second half of the question: Based on the synthetic division shown, 1/2 is DEFINITELY A ROOT of the polynomial.

Explanation:

Answer 2

-1, 2, 0.5, 0.5

Explanation:

`4x^4 - 8x^3 - 3x^2 + 7x - 2`

Using synthetic division for x=-1 we find that

-1 4 -8 -3 7 -2

-4 12 -9 2

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4 -12 9 -2 0

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Thus quotient is
`4x^3 - 12x2 + 9x - 2`

Again try synthetic division by x-2

2 4 -12 9 -2

8 -8 2

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4 -4 1 0

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Thus quotient is
`4x^2-4x+1\\=(2x-1)^2`

Hence zeroes of the polynomial f(x) are

-1, 2, 0.5, 0.5