Question

Pʟᴇᴀsᴇ ʜᴇʟᴘ ᴍᴇ ᴡɪᴛʜ ᴛʜᴇ ᴀʙᴏᴠᴇ sᴜᴍ..!!!

Tʜᴀɴᴋ ʏᴏᴜ..!!! ​

Answer 1

Question:

Divide the polynomial x³ - 5x² + 3x - 3 by x² - 2, and find the quotient and the remainder. Hence express your result in the form :

Dividend = Divisor × Quotient + Remainder

Answer:

Quotient = x - 5

Remainder = 5x - 13

Step-by-step explanation:

The number which we divide is dividend and the number by which we divide is divisor.

• Dividend = x³ - 5x² + 3x - 3  

• Divisor = x² - 2

$\sf\Large\qquad\qquad \ \ \ \ x-5\\ \begin{array}{cc} \cline{2 - 2}\sf x^2-2 )&\sf \ x^3-5x^2+3x-3\\&\sf _{-} x^3 \ \ \ \ \ \ _{+}-2x \ \ \ \\ \cline{2-2}& \sf \ \ \ \ \ \ -5x^2+5x-3\\ &\sf \ \ \ \ \ \ _{+}-5x^2 \ \ \ \ _{-}+10 \\ \cline{2-2} & \sf \ \ \ \ \ \ \ \ \ \ \ \ 5x-13 \\ \cline{2-2} \end{array}$

Quotient = x - 5

Remainder = 5x - 13

Dividend = Divisor × Quotient + Remainder

x³ - 5x² + 3x - 3 = (x² - 2) (x - 5) + (5x - 13)

__________________________

Verification :

⇒ (x² - 2) (x - 5) + (5x - 13)

⇒ x²(x - 5) - 2(x - 5) + 5x - 13

⇒ x³ - 5x² - 2x + 10 + 5x - 13

⇒ x³ - 5x² + 3x - 3

Answer 2

Refer The Attachment ⬆️

• Quotient = x-5
• Remainder = 5x-13

$\boxed{\tt{@MrMonarque}}$

Hope It Helps You ✌️