2 Answers

Jimmygchen · Answer 1 · 2020-06-25T07:18:00+0000

I didn't get all the part with the tiles, but here's the general answer:

given a polynomial

p(x)=ax^2+bx+c

we have that
x-k is a factor of
p(x) if and only if k is a root of
p(x) , i.e. if

p(k)=ak^2+bk+c=0

So, given the polynomial

p(x)=x^2-9x+14

We can check if
x-9 is a factor by evaluating
p(9) :

$p(9)=81-81+14=14\\eq 0$

So,
x-9 is not a factor.

Similarly, we can evaluate
$p(2),\ p(-5),\ p(-7)$ to check if
$x-2,\ x+5,\ x+7$ are factors:

$p(2)=4-18+14=0,\quad p(-5)=25+45+14=84\\eq 0,\quad p(-7)=49+63+14=126 \\eq 0$

So, only
x-2 is a factor of
x^2-9x+14

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