Question

prove that x^4+5x^3+8x^2-10x+12 is exactly divisible by x^2-5x+6.

Answer 1

Firstly we will factorise x2-5x+6

=x2-5x+6

=x2-3x+2x+6

=x(x-3)+2(x+3)

=x(x-3)-2(x-3)

=(x-3) (x-2)

So we will now see

whether (x-3) and (x-2)

is a factor of x4 - 5x3 + 8x2 - 10x +12

p(x)= x4 - 5x3 + 8x2 - 10x +12

p(2)

=(2)4-5(2)3+8(2)2-10(2)+12

=16-40+32-20+12

=60-60

=0

now,

p(3)

=(3)4-5(3)3+8(3)2-10(3)+12

=81-135+72-30+12

=0

therefore

x4 - 5x3 + 8x2 - 10x +12

is divisible by x2 - 5x + 6.

hope it helpzzz

Please mark me as BRAINLIST...