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Question

Use the factor theorem to determine whether (x-1) is a factor of:

(iii) 22x3+52x2-72


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Solution

Checking for the factor.
Factor theorem: Let g(x) be a polynomial of degree greater than or equal to 1 and a be a real number. Then the following holds:

g(a)=0(x-a) is a factor of g(x)

(x-a) is a factor of g(x) g(a)=0.

Let g(x)=22x3+52x2-72

According to the factor theorem, if (x-1) is a factor of g(x) then g(1)=0.

Substitute 1 for x in the function g(x) to obtain g(1)

g(1)=22(1)3+52(1)2-72g(1)=22+52-72g(1)=0

As g(1)=0, (x-1) is a factor of g(x).

Hence, (x-1) is a factor of the given polynomial.


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