What is $(2 t^{2} - 3 t + 2) (2 t^{3} + t^{2} - t)$ ?

4 t^{5} + 4 t^{4} - t^{3} + 5 t^{2} - 2 t

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4 t^{5} - 4 t^{4} - t^{3} + 5 t^{2} - 2 t

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4 t^{5} - 4 t^{4} - t^{2} + 5 t^{2} - 2 t

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4 t^{5} - 4 t^{4} - t^{3} + 5 t^{2} + 2 t

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Solution

The correct option is B $4 t^{5} - 4 t^{4} - t^{3} + 5 t^{2} - 2 t$
$(2 t^{2} - 3 t + 2) (2 t^{3} + t^{2} - t)$
Multiply the coefficients and add the exponents of the variable.
$=$ $2 t^{2} .2 t^{3} + 2 t^{2} . t^{2} - 2 t^{2} . t - 3 t .2 t^{3} - 3 t . t^{2} - 3 t . - t + 2.2 t^{3} + 2. t^{2} - 2. t$
$=$ $4 t^{5} + 2 t^{4} - 2 t^{3} - 6 t^{4} - 3 t^{3} + 3 t^{2} + 4 t^{3} + 2 t^{2} - 2 t$
$=$ $4 t^{5} - 4 t^{4} - t^{3} + 5 t^{2} - 2 t$

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\sqrt{- 1}

\frac{[(t - 1) (2 t + 1 - i \sqrt{3}) (2 t + 1 + i \sqrt{3})]}{4}

5 t^{2} - \frac{17}{2} t + \frac{3}{2} = 0

t = \frac{1}{5}, \frac{3}{2}

a = 2 t - 2

(m / s^{2})

t

t = 0, u = 2 m / s, x = 4 m

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