Question

which of the following shows $8x^{3}y + x^{2} - 14z - 2 + 5y^{2}x$ written in standard form? (2 points)

$\circ$ $-14z + 8x^{3}y + 5y^{2}x - 2 + x^{2}$

$\circ$ $x^{2} - 2 - 14z + 5y^{2}x + 8x^{2}y$

$\circ$ $8x^{3}y + x^{2} + 5y^{2}x - 14z - 2$

$\circ$ $8x^{3}y + 5y^{2}x + x^{2} - 14z - 2$

Explanation:

Step1: Define standard form for polynomials

Standard form of a polynomial orders terms by descending degree (sum of exponents of variables in each term).

Step2: Calculate degree of each term

• $8x^3y$: $3+1=4$
• $x^2$: $2$
• $-14z$: $1$
• $-2$: $0$
• $5y^2x$: $2+1=3$

Step3: Order terms by descending degree

Arrange terms from highest to lowest degree: $8x^3y$ (degree 4), $5y^2x$ (degree 3), $x^2$ (degree 2), $-14z$ (degree 1), $-2$ (degree 0).

Answer:

D. $8x^3y + 5y^2x + x^2 - 14z - 2$