1.

Show that,(i) x + 3 is a factor of 69 + 11c – x2 + x3(ii) 2x – 3 is a factor of x + 2x3 -9x2 +12

Answer»

(i) According to the question,

Let p(x) = 69 + 11x − x2 + x3 and g(x) = x + 3

g(x) = x + 3

zero of g(x) ⇒ g(x) = 0

x + 3 = 0

x = – 3

Therefore, zero of g(x) = – 3

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

p( – 3) = 69 + 11( – 3) –( – 3)2 + ( – 3)3

= 69 – 69

= 0

Since, the remainder = zero,

We can say that,

g(x) = x + 3 is factor of p(x) = 69 + 11x − x2 + x3

(ii) According to the question,

Let p(x) = x + 2x3 – 9x2 + 12 and g(x) =2x−3

g(x) = 2x – 3

zero of g(x) ⇒ g(x) = 0

2x – 3 = 0

x = 3/2

Therefore, zero of g(x) = 3/2

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

P(3/2) = 3/2 + 2(3/2)– 9(3/2)2 + 12

= (81 – 81) / 4

= 0

Since, the remainder = zero,

We can say that,

g(x) = 2x – 3 is factor of p(x) = x + 2x3 – 9x2 + 12



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