Warm Up Solutions

Write the expression in standard form, including all terms from degree n to degree 0, the constant. Name all of the coefficients and constants.

$7 x^{2} - x^{3} + 5 x^{4} + 8$

$5 x^{4} - x^{3} + 7 x^{2} + 0 x + 8 coefficients : 5, - 1, 7, 0 constant : 8$

Note

Recall that the standard form of polynomials has terms listed in descending order by degree.

Q: What is the degree of this expression?
A: 4, quartic

Q: Name the missing degree term.
A: 0x, linear or degree 1

$12 - 2 x - 7 x^{3} + 10 x$

$- 7 x^{3} + 0 x^{2} + 8 x + 12 coefficients : - 7, 0, 8 constant : 12$

Note

Q: What is the leading coefficient of the expression?
A: –7

Q: What is the constant, or degree zero term?
A: 12

Solve using mental math.

$3 x - 1 = 0$

$\begin{array}{rcl} 3 x & = & 1 \\ x & = & \frac{1}{3} \end{array}$

$5 x + 3 = 0$

$\begin{array}{rcl} 5 x & = & - 3 \\ x & = & - \frac{3}{5} \end{array}$