Write in Standard Form p(x)=1/2x^2+3x-4x^3+6x^4-1

$p (x) = \frac{1}{2} x^{2} + 3 x - 4 x^{3} + 6 x^{4} - 1$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$p (x) = a x^{2} + b x + c$

Step 2

Combine $\frac{1}{2}$ and $x^{2}$ .

$p (x) = \frac{x^{2}}{2} + 3 x - 4 x^{3} + 6 x^{4} - 1$

Step 3

Simplify the expression.

Move $3 x$ .

$p (x) = \frac{x^{2}}{2} - 4 x^{3} + 6 x^{4} + 3 x - 1$

Move $\frac{x^{2}}{2}$ .

$p (x) = - 4 x^{3} + 6 x^{4} + \frac{x^{2}}{2} + 3 x - 1$

Reorder $- 4 x^{3}$ and $6 x^{4}$ .

$p (x) = 6 x^{4} - 4 x^{3} + \frac{x^{2}}{2} + 3 x - 1$

Step 4

Reorder terms.

$p (x) = 6 x^{4} - 4 x^{3} + \frac{1}{2} x^{2} + 3 x - 1$