Question

Define factor theorem with example.​

Answer 1

Answer:

hey mate here is your answer:-

If p(x) is a polynomial of degree n > 1 and a is any real number, thenx – a is a factor of p(x), if p(a) = 0, andp(a) = 0, if x – a is a factor of p(x).Let’s look at an example to understand this theorem better.Example:Examine whether x + 2 is a factor of x3 + 3x2 + 5x + 6.Solution: To begin with, we know that the zero of the polynomial (x + 2) is –2. Let p(x) = x3 + 3x2 + 5x + 6Then, p(–2) = (–2)3 + 3(–2)2 + 5(–2) + 6 = –8 + 12 – 10 + 6 = 0According to the factor theorem, if p(a) = 0, then (x – a) is a factor of p(x). In this example, p(a) = p(- 2) = 0

If p(x) is a polynomial of degree n > 1 and a is any real number, thenx – a is a factor of p(x), if p(a) = 0, andp(a) = 0, if x – a is a factor of p(x).

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