Question

x^4-20x^3+33x^2-20x+4​

Answer 1

SOLUTION

TO FACTORISE

$\sf{4 {x}^{4} - 20 {x}^{3} + 33 {x}^{2} - 20x + 4}$

EVALUATION

Here the given expression is

$\sf{4 {x}^{4} - 20 {x}^{3} + 33 {x}^{2} - 20x + 4}$

For x = 2 the value of the expression is zero

So (x - 2) is a factor of the expression

$\sf{4 {x}^{4} - 20 {x}^{3} + 33 {x}^{2} - 20x + 4}$

$\sf{ = 4 {x}^{4} - 8 {x}^{3} - 12{x}^{3} + 24{x}^{2} + 9 {x}^{2} - 18x - 2x + 4}$

$\sf{ = 4 {x}^{3}(x - 2) - 12{x}^{2} (x - 2) + 9 {x}^{} (x - 2) - 2(x - 2)}$

$\sf{ = (x - 2)(4 {x}^{3} - 12{x}^{2} + 9 {x}^{} - 2)}$

$\sf{ = (x - 2)(4 {x}^{3} - 8 {x}^{2} -4{x}^{2} + 8x + x - 2)}$

$\sf{ = (x - 2) \bigg[4 {x}^{2} (x - 2) -4x(x - 2)+ ( x - 2) \bigg] }$

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

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

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

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