Question

Division of polynomials.
Find quotient and remainder by long division
(a) x2 + 3x + 4 = x + 1​

Answer 1

$\sf\large\underline{Given:}$

• $\rm{Dividend=x^2+3x+4}$
• $\rm{Divisor=x+1}$

$\sf\large\underline{To\: Find:}$

• $\rm{Quotient\:and\: remainder}$

Now calculate it by long division method:-]

x+1)x²+3x+4(x+2

x²+x+4

_(-)_(-)____

2x+4

2x+2

____(-)_(-)___

2

$\sf\large{Hence,}$

$\rm{\implies Quotient=x+2}$

$\rm{\implies Remainder=2}$

$\sf\large\underline{Verification:}$

• To Verifiy the division. We have to apply the formula here]

$\sf\large\underline{Formula\: used:}$

$\rm{\implies Dividend=Divisor\times\: Quotient+remainder}$

$\rm{\implies x^2+3x+4=(x+1)(x+2)+2}$

$\rm{\implies x^2+3x+4=x^2+3x+2+2}$

$\rm{\implies x^2+3x+4=x^2+3x+4}$

$\sf\large\underline{Hence,\:Verified}$

Answer 2

$\huge\sf\pink{Answer}$

☞ Quotient = x+2

☞ Remainder = 2

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ x² + 3x + 4 = x + 1

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

✪ The quotient and the remainder?

$\rule{110}1$

$\huge\sf\purple{Steps}$

$\sf x + 1) \: {x}^{2} + 3x + 4(x + 2 \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: {x}^{2} + x \\ \: \: \: \: \: \: \: \: \: \: \: \: ( - ) \: \: ( - )\\ \underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\:\:\:\:\:\: \: \: \: \: \:} \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2x + 4 \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2x +2 \\ \qquad \qquad \: \: \: \: \: \: ( - ) \: ( - ) \\ \underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\:\:\:\:\:\:\: \: \: \: \: \: \: \: \: \: } \\ \sf \qquad \qquad \qquad \: \: \: \: \: \: \: \: \: 2$

$\rule{170}3$