Question

Using factor theorem show that (2x+1) is a factor of 2x²+3x²-11x-6
Plz help me........

Answer 1

Step-by-step explanation:

let P(x)=2x^2+3x^2-11x-6

if 2x+1 is factor of p(x)

then, 2x+1=0

or,x=-1/2

By factor theorm

P(-1/2)=2×(-1/2)^2+3×(-1/2)^2-11×(-1/2)-6

=2×1/4+3×1/4+11/2-6

=1/2+3/4+11/2-6

=27/4-6

=3/4

So,2x+1 is not a factor of P(x)

Answer 2

Hey.. here's your answer.

Answer:

No, 2x +1 is not a factor of p (x).

Step-by-step explanation:

$p(x) = 2 {x}^{2} + 3 {x}^{2} - 11x - 6$

put 2x+1 = 0

2x = -1

$x = \frac{ - 1}{2}$

put the value of x in p(x).

$2( \frac{ - 1}{2} ) ^{2} + 3 ({ \frac{ - 1}{2} })^{2} - 11( \frac{ - 1}{2}) - 6 \\ \frac{2}{4} + \frac{3}{4} + \frac{11}{2} - 6 \\ \frac{2 + 3 + 22}{4} - 6 \\ \frac{27}{4} - 6 \\ \frac{27 - 24}{4} \\ \frac{3}{4}$

Since, the remainder is 3/4 which is not equal to 0.

Therefore, 2x +1 is not a factor of p (x).

Hope this will help you.