Answer: The correct answer is option D
Explanation:
To factorize a polynomial, we need to find the expressions that can be multiplied to get the original polynomial. There are different methods to factorize polynomials, such as finding the greatest common factor, grouping terms, using identities, or applying the factor theorem⁴⁵⁶.
For the given polynomial x-17x² +16, we can use the following steps to factorize it:
- First, we can rearrange the terms in descending order of the degree of x, so we get -17x² + x + 16.
- Next, we can look for two numbers that add up to 1 and multiply to -272, which is the product of the coefficient of x² and the constant term. One such pair of numbers is -16 and 17.
- Then, we can split the middle term x into -16x + 17x and group the terms into two pairs, so we get (-17x² - 16x) + (17x + 16).
- Next, we can factor out the greatest common factor from each pair of terms, so we get -x(17x + 16) + 1(17x + 16).
- Then, we can factor out the common factor of (17x + 16) from both terms, so we get (17x + 16)(-x + 1).
- Finally, we can simplify the signs and write the factors in ascending order of the degree of x, so we get (x - 1)(x + 16).
Therefore, the complete factorization of x-17x² +16 is (x - 1)(x + 16).