Question

lesson polynomial.
please do 1. 2. 3. 4. 5.​

Answer 1

★ Solution (1) :-

$\sf \longrightarrow {x}^{3} - {2x}^{2} - x + 2$

$\sf \longrightarrow {x}^{3} - x - {2x}^{2} + 2$

$\sf \longrightarrow \{(x \times x \times x) - x \} - (2 \times x \times x + 2)$

$\sf \longrightarrow x(x \times x - 1) - 2(x \times x + 1)$

$\sf \longrightarrow x({x}^{2} - 1) - 2( {x}^{2} + 1)$

★ Solution (2) :-

$\sf \longrightarrow {x}^{3} - {3x}^{2} - 9x - 5$

$\sf \longrightarrow {x}^{3} - 5 - {3x}^{2} - 9x$

$\sf \longrightarrow \{(1 \times x \times x \times x) - 1 \times 5 \} - (3 \times x \times x - 3 \times 3 \times x)$

$\sf \longrightarrow 1(x \times x \times x - 5) - 3(x \times x + 3 \times x)$

$\sf \longrightarrow 1( {x}^{3} - 5) - 3( {x}^{2} + 3x)$

★ Solution (3) :-

$\sf \longrightarrow {x}^{3} + {13x}^{2} + 32x + 20$

$\sf \longrightarrow \{(x \times x \times x) + 13 \times x \times x \} + (2 \times 2 \times 2 \times 2 \times 2 \times x + 2 \times 2 \times 5)$

$\sf \longrightarrow x \times x(x + 13) + 2 \times 2(2 \times 2 \times 2 \times x + 5)$

$\sf \longrightarrow {x}^{2} (x + 13) + 4(8x + 5)$

★ Solution (4) :-

$\sf \longrightarrow {2y}^{3} + {y}^{2} - 2y - 1$

$\sf \longrightarrow {2y}^{3} + {y}^{2} - 2y - 1$

$\sf \longrightarrow \{(2 \times y \times y \times y) + y \times y \} - 1 \times 2 \times y - 1 \times 1$

$\sf \longrightarrow y \times y(2 \times y + 1) - 1(2 \times y + 1)$

$\sf \longrightarrow {y}^{2} (2y + 1) - 1(2y + 1)$

Hence solved !!