Question

निम्नलिखित बहुपद युग का म.स.ज्ञात कीजिए

8(x³-x²+x) और 28 (x³+1)

Answer 1

हल-

8(x³-x²+x) के गुणनखंड

$= 2 \times 2 \times 2 \times x( {x}^{2} - x + 1)$


तथा 28 (x³+1) के गुणनखंड

$= 2 \times 2 \times 7 \times x(x + 1)( {x}^{2} - x + 1)$


सर्व भाजक व्यंजन = 2 × 2 × (x² - x +1)


$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 4( {x}^{2} - x + 1) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$



अतः म.स . = 4 (x² - x +1 )

Answer 2

$\huge\boxed{\texttt{\fcolorbox{Red}{aqua}{Hey Mate!!!!}}}$

$<b>$
First we find out factors of both.
$8(x {}^{3} - x {}^{2} + x) \\ = 2 \times 2 \times 2 \times x(x {}^{2} - x + 1)$
And
$28(x {}^{3} + 1) \\ = 28(x + 1)(x {}^{2} + 1 {}^{2} - x \times 1) \\ = 2 \times 2 \times 7(x + 1)(x {}^{2} - x + 1)$
Now Highest Common factors in both are
$hcf = 2 \times 2(x {}^{2} - x + 1) \\ hcf = 4(x {}^{2} - x + 1)$
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