Question

(׳v+ ײ - 5 × - 2 ) ÷ (× - 2)​

Answer 1

$\textbf{Correct\:Question\: : }$

◆ (x³+ x² - 5x - 2) ÷ (x-2)

$\textbf{Solution\: :}$

Here,

• p(x) = x³+ x² - 5x - 2

• g(x) = x - 2

Using Long Division Method

(Refer to the attachment)

• Quotient obtained = x² + 3x + 1

• Remainder obtained = 0

$\textbf{Verification\: :}$

We know that,

★ Dividend = Divisor × Quotient + Remainder

Put the values

→ x³+ x² - 5x - 2 = (x - 2)(x² + 3x + 1) + 0

→ x³+ x² - 5x - 2 = x(x² + 3x + 1) - 2(x² + 3x + 1) + 0

→ x³+ x² - 5x - 2 =( x³+ 3x² + x - 2x² - 6x - 2 ) + 0

→ x³+ x² - 5x - 2 =( x³+ 3x² - 2x² - 6x + x - 2 ) + 0

→ x³+ x² - 5x - 2 = x³+ x² - 5x - 2 + 0

→ x³+ x² - 5x - 2 = x³+ x² - 5x - 2

Hence,Verified!

Answer 2

Question:

Your question is having a mistake, the correct question is :

(x³ + x² - 5x - 2) ÷ (x - 2)

Answer:

☯ $\boxed{\sf The\:remainder\:is\:0}$

☯ $\boxed{\sf The\:quotient\:is\:x^2 + 3x + 1}$

Step-by-step explanation:

Check attachment for the solution.

As we know,

• p(x) = x³ + x² - 5x - 2

• g(x) = x - 2

We got,

• Quotient = x² + 3x + 1

• Remainder = 0

To verify,

• Dividend = Divisor × Quotient + Remainder

= x³ + x² - 5x - 2 = (x - 2) × (x² + 3x + 1) + 0

= x³ + x² - 5x - 2 = x(x² + 3x + 1) - 2(x² + 3x + 1) + 0

= x³ + x² - 5x - 2 = (x³ + 3x² + x - 2x² - 6x - 2) + 0

= x³ + x² - 5x - 2 = x³ + x² - 5x - 2 + 0

= x³ + x² - 5x - 2 = x³ + x² - 5x - 2

Hence, verified!

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