Question

Factorise ➡️

(a² - 2a)² - 23(a² - 2a) + 120
__!

Answer 1

✨нєγα ∂єαя✨

Refer the attachment for the solution ^^

Answer 2

$\huge\bigstar\mathfrak\blue{\underline{\underline{SOLUTION:}}}$

The given polynomial is,

$( {a}^{2} - 2a) {}^{2} - 23( {a}^{2} - 2a) + 120 = 0........(1) \\ let \: {a}^{2} - 2a = x.............(2)$

So, equation (1) becomes,

${x}^{2} - 23x + 120 = 0 \\ = > {x}^{2} - 15x - 8x + 120 = 0 \\ = > x(x - 15) - 8(x - 15) = 0 \\ = > (x - 15)(x - 8) = 0 \\ = > x = 15 \: or \: x = 8$

Substitute value of x in equation (2), we have,

When x= 15

${a}^{2} - 2a = 15 \\ = > {a}^{2} - 2a - 15 = 0 \\ = > {a}^{2} - 5a + 3a - 15 = 0 \\ = > a(a - 5) + 3(a - 5) = 0 \\ = > (a - 5)(a + 3) = 0 \\ = > a = 5 \: or \: a = - 3$

When x= 8

${a}^{2} - 2a = 8 \\ = > {a}^{2} - 2a - 8 = 0 \\ = > {a}^{2} - 4a + 2a - 8 = 0 \\ = > a(a - 4) + 2(a - 4) = 0 \\ = > (a - 4)(a + 2) = 0 \\ = > a = 4 \: or \: a = - 2$

Hence, a= 5,-3,4, & -2.

hope it helps ☺️