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Zanzabum
3 years ago
9

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
Mathematics
2 answers:
klio [65]3 years ago
4 0

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

VikaD [51]3 years ago
4 0

Answer:

B. x-2

Step-by-step explanation:

100% on the test

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