|Mathematics and Statistics Assessment||Quadratic and Other Polynomial Expressions, and Functions|
…so he measures practically everything in terms of the length of his longest paintbrush,
which we can call p.
In order to submit his mural, he needs to find the equation for the area of his mural, in terms of “p.”
He measures the length of one side as p plus 3...
…and the width as p-squared minus 4p plus 2.
Knowing that the area formula is length times width,
multiplying the two will give him the area of the world record mural.
We can find the product between the two polynomials by splitting up the p plus 3…
…to get p times p-squared minus 4p plus 2…
plus 3 times p-squared minus 4p plus 2.
Using the distributive property we can start distributing.
P times p squared equals p-cubed, plus p times negative 4p
which is negative 4p squared, plus p times 2 equals 2p…
…PLUS 3 times p squared is 3p squared...
...plus 3 times negative 4p is minus 12p plus 3 times 2 which is 6.
Now we can combine like terms.
There's no other p-cubed terms, so we can leave it as p-cubed.
We have two p squared terms, negative 4p squared and 3p squared.
So let's combine like terms.
Negative 4p squared plus 3p squared equals negative p squared.
We have two p terms, so we again can combine like terms.
2p minus 12p equals negative 10p.
We only have one constant number, 6, so we can just leave that as it is.
After we combine all like terms we get the answer as
p cubed minus p squared minus 10 p plus 6.
Poor Shmonet. It seems his paintbrush is roughly the length of a toothpick.
Well, that’s just one more thing he can bring up in therapy.