Q5 of 64 Page 30

Examine the validity of the following statements:

(x — 1) is a factor of p(x) = x4 — 2x3 + 3x —2

Given, p(x) = x4 — 2x3 + 3x —2


For (x – 1) to be a factor of p(x), the condition: p(1) = 0; should be satisfied.


p(1) = (1)4 – 2(1)3 + 3(1) – 2


= 1 – 2 + 3 – 2


= 0


Thus, (x – 1) is a factor of the given polynomial.


⇒ The given statement is valid.


More from this chapter

All 64 →
5

Examine the validity of the following statements:

(x + 1) is a factor of p(x) = 3x3 + 2x2 + 7 x + 8

 5

Examine the validity of the following statements:

(x + 2) is a factor of p(x) = x3 + x2 + x + 2

 5

Examine the validity of the following statements:

(x — 3) is a factor of p(x) = x2 — 2x — 3

 6

Factorize the following polynomials:

p(x) = x3 —x2—x + 1