Question

divide 12 - 7 x minus 5 x square by 3 minus 5 x​

Answer 1

Answer:

Quotient ⇒ – x + 2

Remainder ⇒ 18

Step-by-step explanation:

Here, we are asked to divide a polynomial by a polynomial. That is,

• $\sf { \dfrac{12-7x-5x^2}{3 - 5x} }$

As arithmetic, it is a quite tedious process, so let's understand step by step.

Step 1 : Arrange the polynomials in descending order and set up in the form of a long division.

➝ Dividend in descending order = $\sf { -5x^2-7x + 12}$

➝ Divisor in descending order = $\sf {-5x + 3}$

Step 2 : Divide the first term of the dividend $\sf { (5x^2) }$ by the first term of the divisor $\sf { (-5x) }$ and write the product below the dividend. Then, subtract as an ordinary subtraction.

Step 3 : Now, the remainder is the new dividend. Divide first term of the remainder $\sf { (-10x) }$ by $\sf { (-5x) }$ . Write the quotient $\sf { (2) }$ above the dividend after $\sf { (-x) }$ .

Step 4 : Multiply $\sf { (-5x- 3) }$ with $\sf { (2) }$ and subtract.

We got the answer,

• Quotient ⇒ – x + 2
• Remainder ⇒ 18

Verification :

Division algorithm states that,

• Dividend = Divisor × Quotient + Remainder

L.H.S :

➝ $\sf { -5x^2-7x + 12}$

R.H.S :

→ (-5x - 3)(-x + 2) + 18

→ -5x(-x + 2) - 3(-x + 2) + 18

→ 5x² -10x + 3x - 6 + 18

→ 5x² -7x + 12

$\therefore$ L.H.S = R.H.S

Hence, verified!