1. ## Algebra + Polynomials

The polynomial 13 $x^2$+ $kx$+35 is to be factored into two linear prime binomials with integer coefficients. This can be done if $k$ is:
a)any even number
b) some even number
c) any odd number
d) some odd number
e) zero

Im thinking its either c or d but im not sure which?

2. for the solutions to be integers firstly consider

and therefore make sure you are finding real numbers first, integers are a subset of real numbers. In your case a = 13, b=k & c=35

$b^2-4ac >0$

$k^2-4(13)(35) >0$

$k^2-1820 >0$

$k^2>1820$

$k>\sqrt{1820} \approx 42$

Now we know what to expect for k.

As 13 is a prime number you can expect your solution to look like

$(13x+A)(x+B)$ where $A\times B = 35$. Try factors of 35 for A & B and expand this equation to find the middle term to be >42.