Respuesta :
The given polynomial is not a prime polynomial.
Given the polynomials, we have to choose the polynomial which is prime.
A polynomial with integer coefficients that cannot be factored into lower degree polynomials is Prime polynomials.
[tex]7x^2-35x+2x-10[/tex]
[tex]7x^2-33x-10[/tex]
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}[/tex]
What is the formula for the quadratic roots?
[tex]\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\mathrm{For\:}\quad a=7,\:b=-33,\:c=-10[/tex]
[tex]x_{1,\:2}=\frac{-\left(-33\right)\pm \sqrt{\left(-33\right)^2-4\cdot \:7\left(-10\right)}}{2\cdot \:7}[/tex]
[tex]x_{1,\:2}=\frac{-\left(-33\right)\pm \sqrt{\left(-33\right)^2-4\cdot \:7\left(-10\right)}}{2\cdot \:7}[/tex]
[tex]x_{1,\:2}=\frac{-\left(-33\right)\pm \:37}{2\cdot \:7}[/tex]
[tex]x_1=\frac{-\left(-33\right)+37}{2\cdot \:7},\:x_2=\frac{-\left(-33\right)-37}{2\cdot \:7}[/tex]
[tex]x=5,\:x=-\frac{2}{7}[/tex]
Therefore the factor is (x-5) and (7x+2).
can be factored
∴ not a prime polynomial.
To learn more about the prime polynomial visit:
https://brainly.com/question/26388060
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