Simplifying Polynomial Expressions Solutions

To simplify a polynomial expression: 
- Combine all like terms . 
- Write the expression in descending order by the power of the exponents. 
Simplifying the expression may require the distributive property as well as adding and subtracting like terms.  
Once the expression is simplified and in descending power order, a polynomial expression can be classified by the degree of the exponent on the leading term and the number of terms.

Simplify.

$(14 x^{2} - 22 x + 1) - (x^{2} + 7 x - 11) (14 x^{2} - 22 x + 1) + (- x^{2} - 7 x + 11)$

$13 x^{2} - 29 x + 12$

This is a quadratic trinomial.

Find the product.

$(2 x + 3) (- x^{2} + 11 x - 4)$

$- 2 x^{3} + 22 x^{2} - 8 x + - 3 x^{2} + 33 x - 12 - 2 x^{3} + 19 x^{2} + 25 x - 12$

This is a cubic polynomial with 4 terms.