Check whether p(x) is a multiple of g(x) or not(i) p(x) = x3 – 5x2�

1.	Check whether p(x) is a multiple of g(x) or not(i) p(x) = x3 – 5x2 + 4x – 3, g(x) = x – 2.(ii) p(x) = 2x3 – 11x2 – 4x+ 5, g(x) = 2x + l
Answer» (i) p(x) = x³ – 5x² + 4x – 3, g(x) = x – 2. According to the question, g(x)=x – 2, Then, zero of g(x), g(x) = 0 x – 2 = 0 x = 2 Therefore, zero of g(x) = 2 So, substituting the value of x in p(x), we get, p(2) =(2)³ – 5(2)² + 4(2) – 3 = 8 – 20 + 8 – 3 = – 7 ≠ 0 Hence, p(x) is not the multiple of g(x) since the remainder ≠ 0. (ii) p(x) = 2x³ – 11x² – 4x+ 5, g(x) = 2x + l According to the question, g(x)= 2x + 1 Then, zero of g(x), g(x) = 0 2x + 1 = 0 2x = – 1 x = – ½ Therefore, zero of g(x) = – ½ So, substituting the value of x in p(x), we get, p(–½) = 2 × ( – ½ )³ – 11 × ( – ½ )² – 4 × ( – 1/2) + 5 = – ¼ – 11/4 + 7 = 16/4 = 4 ≠ 0 Hence, p(x) is not the multiple of g(x) since the remainder ≠ 0.

Check whether p(x) is a multiple of g(x) or not(i) p(x) = x3 – 5x2 + 4x – 3, g(x) = x – 2.(ii) p(x) = 2x3 – 11x2 – 4x+ 5, g(x) = 2x + l

Answer»

(i) p(x) = x³ – 5x² + 4x – 3, g(x) = x – 2.

According to the question,

g(x)=x – 2,

Then, zero of g(x),

g(x) = 0

x – 2 = 0

x = 2

Therefore, zero of g(x) = 2

So, substituting the value of x in p(x), we get,

p(2) =(2)³ – 5(2)² + 4(2) – 3

= 8 – 20 + 8 – 3

= – 7 ≠ 0

Hence, p(x) is not the multiple of g(x) since the remainder ≠ 0.

(ii) p(x) = 2x³ – 11x² – 4x+ 5, g(x) = 2x + l

According to the question,

g(x)= 2x + 1

Then, zero of g(x),

g(x) = 0

2x + 1 = 0

2x = – 1

x = – ½

Therefore, zero of g(x) = – ½

So, substituting the value of x in p(x), we get,

p(–½) = 2 × ( – ½ )³ – 11 × ( – ½ )² – 4 × ( – 1/2) + 5

= – ¼ – 11/4 + 7

= 16/4

= 4 ≠ 0

Hence, p(x) is not the multiple of g(x) since the remainder ≠ 0.