Chapter 8.3, Problem 47HP

To determine

To write: A binomial and a trinomial involving a single variable. Then find their product.

Answer to Problem 47HP

  $x^3+6x^2+15x+14$

Explanation of Solution

Given:

Any binomial and a trinomial of single variable

Calculation:

Any binomial of variable x is given by $\left(x+2\right)$

Any trinomial of variable x is given by $x^2+4x+7$

Now, find their product $\left(x+2\right)\left(x^2+4x+7\right)$

Applying the distributive property

  $x\cdot x^2+x\cdot 4x+x\cdot 7+2\cdot x^2+2\cdot 4x+2\cdot 7$

Apply the product property of exponent $x^a\cdot x^b=x^{a+b}$

  $x^3+4x^2+7x+2x^2+8x+14$

Combine the like terms

  $x^3+6x^2+15x+14$