Use the FOIL method to simplify the product of the polynomials.
B
b
In each pair compare the coefficients of the resulting polynomial with the digits of the resulting number.
A
a
i. x^2+2x+1, 121
ii. x^2+3x+2, 132
iii. x^2+4x+3, 143
B
b
The coefficients of the resulting polynomial are the same as the digits in the result of the product of two numbers.
Practice makes perfect
a
We have to simplify each pair of products. Let's do it one at a time.
i.
We will start by simplifying the product of the polynomials using the FOIL method. Recall that the word F OI L stands for First, Outer, Inner, and Last.
Let's now simplify the above expression by multiplying and combining like terms.
Let's take a look at the first pair of products and their results.
(x+1)(x+1) & = 1x^2+ 2x+ 1
11* 11 & = 1 2 1
We can see that the coefficients of the resulting polynomial are the same as the digits in the result of the product of two numbers. It is not a coincidence. It has happened because the coefficients of the two binomials correspond to the digits of the two numbers as well.
(1x+1)(1x+1)
11*11
Let's check if this is true for the other two pairs of products, starting with pair ii.
(1x+1)(1x+2) & = 1x^2+ 3x+ 2
11* 12 & = 1 3 2
Again, we can see that the coefficients correspond with the digits. Finally, let's check pair iii.
(1x+1)(1x+3) & = 1x^2+ 4x+ 3
11* 13 & = 1 4 3
Therefore, the similarity between the answers in each pair is that the coefficients of the resulting polynomial are the same as the digits in the result of the product of two numbers.
