Question

without actual division,prove that 2x³+13x²+x-70 is divisible by x-2​

Answer 1

$The \: polynomial p(x)=2x^3+13x^2+x−70.</p><p>Now p(2)=2(2)^3+13(2)^2+2−70</p><p>=16+52+2−70=0</p><p>∴ By \: factor \: theorem, x-2 \: is \: a \: factor \: of \: p(x)</p><p>i.e. p(x)=2x^3+13x^2+x−70 is \: exactly \: divisible \: by \: x-2.</p><p></p><p>$

Here is ur Answer dear friend☺

Answer 2

Answer:

The polynomial p(x)=2x 3+13x 2+x−70.

Now p(2)=2(2) 3+13(2) 2+2−70

=16+52+2−70=0

∴ By factor theorem, x-2 is a factor of p(x)

i.e. p(x)=2x 3+13x 2+x−70 is exactly divisible by x-2.

hope it helps you