Question

explain it also
I will mark as brainlist plz answer the questions plz!​

Answer 1

$\Large{\underline{\underline{\bf{Solution :}}}}$

☯ Question : 1(i)

$\sf{\rightarrow x - 1 = 0} \\ \\ \sf{\rightarrow x = 1} \\ \\ \bf{Put \: value \: of \: x \: in \: polynomial.} \\ \\ \sf{\rightarrow 2(1)^4 + 3(1)^3 - 5(1)^2 + 4(1) - 1} \\ \\ \sf{\rightarrow 2 + 3 - 5 + 4 - 1} \\ \\ \sf{\rightarrow 9 - 6} \\ \\ \sf{\rightarrow 3}$

$\Large{\implies{\boxed{\boxed{\sf{Remainder : 3}}}}}$

→ Also refer to 1st Attachment.

$\rule{150}{2}$

★ (ii)

$\sf{\rightarrow x - 2 = 0} \\ \\ \sf{\rightarrow x = 2} \\ \\ \bf{Put \: value \: of \: x \: in \: polynomial.} \\ \\ \sf{\rightarrow (2)^4 - 2(2)^3 - 3(2)^2 + 4(2) + 1} \\ \\ \sf{\rightarrow 16 - 16 - 12 + 8 + 1} \\ \\ \sf{\rightarrow 25 - 28} \\ \\ \sf{\rightarrow -3}$

$\Large{\implies{\boxed{\boxed{\sf{Remainder : -3}}}}}$

→ Also refer to second attachment.

$\rule{150}{2}$

★ (iii)

$\sf{\rightarrow x - 4 = 0} \\ \\ \sf{\rightarrow x = 4} \\ \\ \bf{Put \: value \: of \: x \: in \: polynomial.} \\ \\ \sf{\rightarrow + 3(4)^3 - 57 + 4(4) - 1} \\ \\ \sf{\rightarrow 192 - 57 + 16 - 1} \\ \\ \sf{\rightarrow 208 - 58} \\ \\ \sf{\rightarrow 150}$

$\Large{\implies{\boxed{\boxed{\sf{Remainder : 150}}}}}$

→ Also refer to third attachment.

$\rule{150}{2}$

★ (iv)

$\sf{\rightarrow x - 3 = 0} \\ \\ \sf{\rightarrow x = 3} \\ \\ \bf{Put \: value \: of \: x \: in \: polynomial.} \\ \\ \sf{\rightarrow 2(3)^5 - (3)^4 - 4(3)^3 - 5(3)^2 + 4(3) - 1} \\ \\ \sf{\rightarrow 486 - 81 - 108 - 45+ 12 - 1} \\ \\ \sf{\rightarrow 498 - 235} \\ \\ \sf{\rightarrow 263}$

$\Large{\implies{\boxed{\boxed{\sf{Remainder : 263}}}}}$

→ Also refer to fourth attachment.

$\rule{400}{4}$

☯ Question : 2 (i)

→ (2x + 1)(3x - 1)

Firstly, we will multiply 2x by 3x and (-1) then we will multiply (1) by 3x and (-1).

→ 6x² - 2x + 3x - 1

→ 6x² - x - 1

$\Large{\implies{\boxed{\boxed{\sf{6x^2 - x - 1}}}}}$

$\rule{150}{2}$

★ (ii)

→ (x + 2)(4x - 3)

Firstly, we will multiply x by 4x and (-3) then we multiply 2 by 4x and (-3).

→ 4x² - 3x + 8x - 6

→ 4x² - 5x - 6

$\Large{\implies{\boxed{\boxed{\sf{4x^2 - 5x - 6}}}}}$

$\rule{150}{2}$

★ (iii)

→ (5x - 2)(3x + 1)

Firstly, we will multiply 5x by 3x and 1 then we will multiply (-2) by 3x and 1.

→ 15x² + 5x - 6x - 2

→15x² - x + 2

$\Large{\implies{\boxed{\boxed{\sf{15x^2 - x + 2}}}}}$

$\rule{150}{2}$

★ (iv)

→ (2x - 4)(5x - 1)

Firstly, we will multiply 2x by 5x and (-1) then we will multiply (-4) by 5x and (-1).

→ 10x² - 2x - 20x - 4

→ 10x² - 22x - 4

$\Large{\implies{\boxed{\boxed{\sf{10x^2 - 22x - 4}}}}}$