The factor mathematicstheorem is really just to test to determine whether or not (a-x) is a factor P(x). So if we have a polynomial and we are trying to determine the factor, what that means is if (a-x) is a factor of the polynomial then P (a) is equal to zero. This is just to understand that if the value, when plugged upon the zero that means that (x-a) is a factor. But this may be just the special case of the remainder theorem.
We will find out the remainder is equals to zero. By understanding the examples determining which binomials are factors of P(x) = x3- 6x2 + 3x + 10. If A is (x-2), B is (x+1) or C is (3x-2). We need to remember that if it is a factor then when we plug it into the polynomial we are going to get the remainder of zero. If the remainder is anything but zero then it is not a factor. Let’s look at the first one A. as (x-2).we are trying to figure out if binomial is x-2 we are going to get the polynomial.so we will put 2 into the equation as P(2)= 23- 6(2)2 + 3(2) + 10 , simplifying the equation we get zero.
Yes. x-2 is a factor of a polynomial. Let’s try with B. (x+1) into the equation as P (-1) = (-1) 3- 6(-1)2 +3(-1) + 10 and we get as zero, so yes even B is a factor. In the C. we need to find the value of x by assuming 3x-2=0.x=2/3, substituting it into the equation now. P(2/3) = (2/3) 3- 6 (2/3)2 + 3(2/3) +10 we get after simplifying the fractions -66/27+324/27 here the fraction will not come to zero and this C will not be the factor of the given polynomial.
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