Question

p(x)=3x cube+x square+2x+5 is divied by g(x)=x square +2x+1​

Answer 1

Answer:

Step-by-step explanation:

Let p(x) = 3x³ + x² + 2x + 5  ,  q(x) = 3x - 5  and r(x) = 9x + 10

To find : g(x) such that it divided p(x)

we use the division algorithum,

a = bq + r

where a = dividend  , b = divisor ,  q =  quotient and r = remainder

⇒ p(x) = g(x)× q(x) + r(x)

⇒ 3x³ + x² + 2x + 5 = g(x)× (3x - 5) + (9x + 10)

3x³ + x² + 2x + 5 - (9x + 10) = g(x)× (3x - 5)

3x³ + x² - 7x - 5 = g(x)× (3x - 5)

Long Division is attached.

g(x) is quotient of the division.

Therefore, g(x) = x² + 2x + 1

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