Contents of Collecting and Ordering Terms

Collecting and Ordering Terms

The Sort command on the Polynomials submenu collects numeric coefficients of terms of a polynomial expression and returns the terms in order of decreasing degree. The Collect command on the Polynomials submenu collects all coefficients of terms of a polynomial expression, but does not necessarily sort the terms by degree. Specify your choice of polynomial variable in the dialog box that appears.

$\blacktriangleright$ Polynomials + Sort

5t² +2t - 16t⁵ + t³ -2t² +9 + at² = -16t⁵ + t³ +3t² + at² + 2t + 9 (The variable is t.)

x² +3x + 5 - 3x³ +5x² +4x³ +13 + 2x⁴ = 2x⁴ + x³ +6x² + 3x + 18

5t² +3xt² -16t⁵ + y³ -2xt² +9 = t²x + 5t² -16t⁵ + y³ + 9 (The variable is x.)

5t² +3xt² -16t⁵ + y³ -2xt² +9 = -16t⁵ + xt² +5t² + y³ + 9 (The variable is t.)

$\blacktriangleright$ Polynomials + Collect

5t² +2t - 16t⁵ + t³ -2t² +9 + at² = -16t⁵ + t³ + $\left(\vphantom{ 3+a}\right.$ 3 + a $\left.\vphantom{ 3+a}\right)$ t² + 2t + 9 (The variable is t.)

x² +3x + 5 - 3x³ +5x² +4x³ +13 + 2x⁴ = 6x² +3x + 18 + x³ +2x⁴ (The variable is x.)

5t² +3xt² -16t⁵ + y³ -2xt² +9 = 5t² + xt² -16t⁵ + y³ + 9 (The variable is x.)

5t² +3xt² -16t⁵ + y³ -2xt² +9 = -16t⁵ + $\left(\vphantom{ x+5}\right.$ x + 5 $\left.\vphantom{ x+5}\right)$ t² +9 + y³ (The variable is t.)

For some expressions, you may want to apply both commands.

$\blacktriangleright$ Polynomials + Collect, Polynomials + Sort

(The variable is x)

5t² +3xt² -16t⁵ + y³ -2xt² +9 = 5t² + xt² -16t⁵ + y³ +9 = t²x + 5t² -16t⁵ + y³ + 9

$\blacktriangleright$ Polynomials + Sort, Polynomials + Collect

(The variable is x)

5t² +3xt² -16t⁵ + y³ -2xt² +9 = t²x + 5t² -16t⁵ + y³ +9 = t²x + 5t² -16t⁵ + y³ + 9
x³b + e + x²c + x² + x⁴k + x - x³d + a = kx⁴ - dx³ + bx³ + x² + cx² + x + e + a = kx⁴ + $\left(\vphantom{ -d+b}\right.$ - d + b $\left.\vphantom{ -d+b}\right)$ x³ + $\left(\vphantom{ c+1}\right.$ c + 1 $\left.\vphantom{ c+1}\right)$ x² + x + e + a