which polynomial is prime?\n$3x^{3}+3x^{2}-2x - 2$\n$3x^{3}-2x^{2}+3x - 4$\n$4x^{3}+2x^{2}+6x +…
which polynomial is prime?\n$3x^{3}+3x^{2}-2x - 2$\n$3x^{3}-2x^{2}+3x - 4$\n$4x^{3}+2x^{2}+6x + 3$\n$4x^{3}+4x^{2}-3x - 3$
Answer
Explanation:
Step1: Try factoring by grouping for each polynomial
For (3x^{3}+3x^{2}-2x - 2):
Group the terms: ((3x^{3}+3x^{2})+(-2x - 2)=3x^{2}(x + 1)-2(x + 1)=(x + 1)(3x^{2}-2))
For (3x^{3}-2x^{2}+3x - 4):
Group the terms: ((3x^{3}-2x^{2})+(3x - 4)=x^{2}(3x - 2)+(3x - 4)). There is no common - factor to factor out further.
For (4x^{3}+2x^{2}+6x + 3):
Group the terms: ((4x^{3}+2x^{2})+(6x + 3)=2x^{2}(2x + 1)+3(2x + 1)=(2x + 1)(2x^{2}+3))
For (4x^{3}+4x^{2}-3x - 3):
Group the terms: ((4x^{3}+4x^{2})+(-3x - 3)=4x^{2}(x + 1)-3(x + 1)=(x + 1)(4x^{2}-3))
Answer:
(3x^{3}-2x^{2}+3x - 4)