Question

Is the polynomial prime? 7x2-35x+2x-10

Answer 1

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.

$7x^2-35x+2x-10$

$7x^2-33x-10$

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}$

What is the formula for the quadratic roots?

$\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=7,\:b=-33,\:c=-10$

$x_{1,\:2}=\frac{-\left(-33\right)\pm \sqrt{\left(-33\right)^2-4\cdot \:7\left(-10\right)}}{2\cdot \:7}$

$x_{1,\:2}=\frac{-\left(-33\right)\pm \sqrt{\left(-33\right)^2-4\cdot \:7\left(-10\right)}}{2\cdot \:7}$

$x_{1,\:2}=\frac{-\left(-33\right)\pm \:37}{2\cdot \:7}$

$x_1=\frac{-\left(-33\right)+37}{2\cdot \:7},\:x_2=\frac{-\left(-33\right)-37}{2\cdot \:7}$

$x=5,\:x=-\frac{2}{7}$

Therefore the factor is (x-5) and (7x+2).

can be factored

∴ not a prime polynomial.

To learn more about the prime polynomial visit:

brainly.com/question/26388060

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