Question

Show x-2 is a factor of polynomial f (x) equals to 2x cube-3x square-17x+30and hence factorise f(x)?​

Answer 1

Answer:

HEYA MATE HERE'S YOUR REQUIRED STEPS:-

Let f(x)=x-2

Hence, x-2=0

x=2 ----1

NOW USING THE VALUE OF X, WE GET--

2x^3-3x^2-17x+30

f(x)=2(2)^3 -3(2)^2-17×2+30

f(2)=16-12-34+30

f(2)=4-4

f(2)=0 Hence x-2 is a factor having remainder 0

2x^3-3x^2-17x+30. (NOW factorising...)

=2x^3-4x^2+x^2-2x-15x+30

= 2x^2(x-2)+x(x-2)-15(x-2)

=(2x^2+x-15)(x-2). (TAKING x-2 common)

=(2x^2+6x-5x-15)(x-2)

={2x(x+3)-5(x+3)}(x-2)

(x+3)(x-2)(2x-5) are the factors of 2x^3-3x^2-17x+30

(NOTE: THE USER HAS FACTORISED BASED ON THE HIGHEST DEGREE OF POLYNOMIAL THAT IS 2x^3 SO x-2 IS USED THRICE TO ALLOW TO FACTORISE)