Question

Factorise 10x² - 18x³ + 14x⁴.​

Answer 1

Solution:-

$\tt\longmapsto{}$ $\sf{10x^2 = 2 × 5 × x × x}$

$\tt\longmapsto{}$ $\sf{18x^2 = 2 × 3 × 3 × x × x × x}$

$\tt\longmapsto{}$ $\sf{14x^4 = 2 × 7 × x × x × x × x}$

★ The common factors of the three terms are 2, x and x.

Therefore,

$\sf{10x^2 - 18x^3 + 14x^4}$

$\sf{= (2 × x × x × 5) - (2 × x × x × 3 × 3 × x) + (2 × x × x × 7 × x × x)}$

$\sf{2 × x × x ×[(5 - (3 × 3 × x) + (7 × x × x)]}$

⠀⠀⠀⠀$\boxed{\sf{\purple{(Combining\: the\: three\: terms)}}}$

$\sf{= 2x^2 × (5 - 9x + 7x^2)}$

$\sf{= 2x^2 (7x^2 - 9x + 5)}$

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Answer 2

$\huge \sf {\orange {\underline {\pink{\underline{Answer :-}}}}}$

$\tt\longmapsto{}$ $\sf{10x^2 = 2 × 5 × x × x}$

$\tt\longmapsto{}$ $\sf{18x^2 = 2 × 3 × 3 × x × x × x}$

$\tt\longmapsto{}$ $\sf{14x^4 = 2 × 7 × x × x × x × x}$

★ The common factors of the three terms are 2, x and x.

Therefore,

$\sf{10x^2 - 18x^3 + 14x^4}$

$\sf{= (2 × x × x × 5) - (2 × x × x × 3 × 3 × x) + (2 × x × x × 7 × x × x)}$

$\sf{2 × x × x ×[(5 - (3 × 3 × x) + (7 × x × x)]}$

⠀⠀⠀⠀$\boxed{\sf{\purple{(Combining\: the\: three\: terms)}}}$

$\sf{= 2x^2 × (5 - 9x + 7x^2)}$

$\sf{= 2x^2 (7x^2 - 9x + 5)}$

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