Question

using factor theorem factorise 2 x power 4 - 7 x cube minus 13 x square + 63 X - 45​

Answer 1

$2x ^{4} - 7x ^{3} - 13x ^{2} + 63x - 45$

on using the hit and trial method

on putting the value of x is 3 and polynomial become zero .

$2 \times 3 ^{4} - 7 \times 3 ^{3} - 13 \times {3}^{2} + 63 \times 3 - 45$

$162 - 189 - 117 + 189 - 45 = 0$

$162 - 162 = 0$

$0 = 0$

it means x minus 3 is the g X

on dividing the polomial p x by gX

$x - 3 \div 2 {x}^{4} - 7 {x}^{3} - 13 {x}^{2} + 63x - 45$

we get the quotient

$2 {x}^{3} - {x}^{2} - 16x + 15$

now also the use of hit and trial method

X-1 is the gX divided the 2 x cube minus x square - 16 x + 15

we will get quotient

$2 {x}^{2} + x - 15$

now factorise it

$2 {x}^{2} + 6x - 5x - 15$

$2 x(x + 3) - 5(x + 3)$

$(x + 3)(2x - 5)(x - 3)(x - 1)$

Answer 2

hope it would help you

written in short but you should solve it complexly with all steps.