Question

divide x⁴+3x²-10 by x²+5 by long division method
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Answer 1

Required Answer:-

Question:

• Divide x⁴ + 3x² - 10 bt x² + 5 by long division method.

Solution:

x² + 5 )  x⁴ + 3x² - 10  ( x² - 2

            x⁴ + 5x²

          (—)    (—)

      ——————————

                  -2x² - 10

                  -2x² - 10

                   (—)   (—)

      ——————————

                         0

Therefore,

→ Q = x² - 2

→ R = 0

Answer:

• Q = x² - 2
• R = 0

Verification:

We know that,

→ Dividend = Divisor × Quotient + Remainder

→ LHS = x⁴ + 3x² - 10

RHS,

→ Divisor = x² + 5

→ Quotient = x² - 2

→ Remainder = 0

Therefore,

Divisor × Quotient + Remainder

= (x² + 5) × (x² - 2) + 0

= x²(x² - 2) + 5(x² - 2) + 0

= x⁴ - 2x² + 5x² - 10

= x⁴ + 3x² - 10

= LHS (Proved)

→ Therefore, our answer is correct (Verified)

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