Question

If P(x)= 5x3 2x + 2 is divided by 5x-2,the reminder is:
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Answer 1

Answer:78/25

Step-by-step explanation:

Using factor theorem, x=2/5

Substitute in equation

5(2/5)³+2(2/5)+2

5(8/125)+2(2/5)+2

8/25+4/5+2

(8+20+50)/25

78/25 is the remainder

Answer 2

★ Given :

(Dividend)p(x) = 5x³ + 2x + 2

Divisor = 5x - 2

★ To find :

The remainder when p(x) is divided by 5x - 2..

★ Solution :

We know that,

$\purple{Remainder\:theorem}$ - The remainder theorem states that when a polynomial, f(x), is divided by a linear polynomial , x - a, the remainder of that division will be equivalent to f(a)...

by applying remainder theorem..

5x - 2 = 0

5x = 2

$x = \frac{2}{5}$

p(x) = 5x³ + 2x + 2

$p\left(\frac{2}{5}\right) =$

$5 \times \left( \frac{2}{5}\right)^{3} + 2 \times \frac{2}{5} + 2$

$= 5 \times \frac{8}{125} + \frac{4}{5} + 2$

$= \frac{8}{25} + \frac{4}{5} + 2$

$= \frac{(8+ 20 + 50)}{25}$

$\leadsto \frac{78}{25}$

$\purple{\therefore \: Remainder = \frac{78}{25}}$