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Add
4x^(3)-2x^(2)+1 to
7x^(2)+12 x

$1$ . Add $4 x^{3}-2 x^{2}+1$ to $7 x^{2}+12 x$

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Understanding negative exponents

Full solution

Q.

1

. Add

4 x^{3}-2 x^{2}+1

to

7 x^{2}+12 x

Write Expressions: Write down the expressions to be added. $\newline$ We have two polynomials: $4x^3 - 2x^2 + 1$ and $7x^2 + 12x$ .
Align Like Terms: Align the like terms. $\newline$ We align the terms with the same powers of $x$ : $\newline$ $(4x^3 - 2x^2 + 0x + 1) + (0x^3 + 7x^2 + 12x + 0)$
Add Coefficients: Add the coefficients of the like terms. $\newline$ Add the coefficients of $x^3$ terms: $4x^3 + 0x^3 = 4x^3$ $\newline$ Add the coefficients of $x^2$ terms: $-2x^2 + 7x^2 = 5x^2$ $\newline$ Add the coefficients of $x$ terms: $0x + 12x = 12x$ $\newline$ Add the constant terms: $1 + 0 = 1$
Write Final Expression: Write the final expression. $\newline$ Combine the results from Step $3$ to get the final expression: $\newline$ $4x^3 + 5x^2 + 12x + 1$

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