Chapter 8.4, Problem 4CB

To determine

the binomial factor of the given trinomial form using algebra tiles.

Answer to Problem 4CB

The two binomial factors of the given trinomial form using algebra tiles are $\left(x+5\right)\left(x+2\right)$

Explanation of Solution

Given info:

The trinomial form is given as $x^2+7x+10$

Formula used:

Calculation:

Finding the binomial factors using algebra tiles as follows:

1. Take coefficient of $x^2$ , $x$ and constant as a number of tiles. From the trinomial $x^2+7x+10$

A blue colour tile represents the coefficient of $x^2$

A Green colour represents the coefficient of $x$

A Yellow colour represents the constant in 1’s

2. Form the rectangle using the tiles.

  

3. Always arrange $x^2$ in the upper left corner of the rectangle, in order to make perfect rectangular tiles we can add extra $\pm x$ tiles and 1’s at the bottom right corner of the rectangle.
4. The binomial factors are taken as length of the rectangle and width of the rectangle.
5. The length of the rectangle is the vertically right side addition of the tiles.
6. The width of the rectangle is the horizontal bottom addition of the tiles.
7. The length of the rectangle is $x+1+1+1+1+1=x+5$ .
8. The width of the rectangle is $x+1+1=x+2$

Hence, the two binomial factors using algebra tiles are $\left(x+5\right)\left(x+2\right)$

Conclusion:

Thus, the two binomial factors using algebra tiles are $\left(x+5\right)\left(x+2\right)$