Respuesta :
Polynomial are mathematical expressions involving variables raised with non-negative integers and coefficients. The factors of the polynomial are (2x+5)(x+7)(x-1), thus , the correct option is C.
What is a polynomial?
Polynomial are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
Example:
x² + 3x + 5 is a polynomial.
The complete question is:
Which of the following is the complete factorization of the polynomial below? 2x³ + 17x² + 16x - 35
- (2x+5)(x-7)(x-1)
- (2x-5)(x+7)(x+1)
- (2x+5)(x+7)(x-1)
- (2x+5)(x-7)(x+1)
The factorization of the polynomial can be done as shown below,
2x³ + 17x² + 16x - 35
Writing all the factors of the leading coefficeient and the constant term,
q = ±1, ±2
p = ±1, ±5, ±7, ±35
Further write the factors in the p/q form,
p/q = ±(1/2), ±1, ±(5/2), ±5, ±(7/2), ±7, ±(35/2), ±35.
Testing the factor 1 in the polynomial we will get,
P(1) = 0
Thus, (x-1) is a factor of the polynomial.
Now, if we divide the polynomial by the factor(x-1), then the quotient will be (2x²+19x+35).
Further, factorizing the factor (2x²+19x+35),
2x²+19x+35
= 2x² + 14x + 5x + 35
= (2x+5)(x+7)
Hence, the factors of the polynomial are (2x+5)(x+7)(x-1), thus , the correct option is C.
Learn more about Polynomials:
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