Question

The model represents x2 – 9x + 14. An algebra tile configuration showing only the Product spot. 24 tiles are in the Product spot: 1 is labeled + x squared, 9 are labeled negative x, and 14 are labeled +. Which is a factor of x2 – 9x + 14? x – 9 x – 2 x + 5 x + 7



The answer is x-2

Answer 1

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 $p(9)$:

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

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:

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

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

Answer 2

Answer:

B. x-2

Step-by-step explanation:

100% on the test