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

Answer:

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

Step-by-step explanation:

Answer 2

Answer:

-1, 2, 0.5, 0.5

Step-by-step 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

-----------------------------------

             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