Question

add the given polynomials using the vertical format.

1. $(7x^{3}+2x + 4)$ and $(5x^{2}-4)$
2. $(5x^{4}-7x^{2}+6)$ and $(9x^{4}-2x^{3}+6x^{2})$

Explanation:

Step1: Align like terms (Q3)

$$\begin{align*} &7x^3 + 0x^2 + 2x + 4\\ +&\ 0x^3 + 5x^2 + 0x - 4\\ \hline \end{align*}$$

Step2: Add like terms (Q3)

$$7x^3 + 5x^2 + 2x + (4-4) = 7x^3 + 5x^2 + 2x$$

Step3: Align like terms (Q4)

$$\begin{align*} &5x^4 + 0x^3 - 7x^2 + 0x + 6\\ +&\ 9x^4 - 2x^3 + 6x^2 + 0x + 0\\ \hline \end{align*}$$

Step4: Add like terms (Q4)

$$(5+9)x^4 + (0-2)x^3 + (-7+6)x^2 + 6 = 14x^4 - 2x^3 - x^2 + 6$$

Answer:

1. $7x^3 + 5x^2 + 2x$
2. $14x^4 - 2x^3 - x^2 + 6$