Question

Add (1.3t3 + 0.4t2 – 24t) + (8 – 18t + 0.6t2) For each term in the second polynomial, enter the letter showing where that term should be placed to add the polynomials vertically. 1.3t3 + 0.4t2 + (–24t) ____=0.6t^2 ____=0t^3 ____=8 ____=-18t

Answer 1

(1.3t3 + 0.4t2 – 24t) + (8 – 18t + 0.6t2) 

In adding polynomials, make sure that each term is grouped together. 

1.3t³ + 0.4t² - 24t
         + 0.6t² - 18t  + 8
1.3t³ + 1.0t² - 42t + 8

In a polynomial equation, arrangement of each term is dependent on the exponential number. It should be from the highest exponent to the lowest. 

Answer 2

You can use the fact that only coefficients of like terms can be added together.

The addition will be done as

$1.3t^3 + (0.4 + 0.6)t^2 + (-24 - 18)t + 8$

What are like terms?

Those terms which have same variables raised with same powers.

For example, $5t^3$ and $6t^3$ are like terms since variable is same, and it is raised to same power 3.

For example $5t^3$ and $6t^2$ are not like terms as the variables are same but powers aren't same.

What are coefficients?

Constants who are in multiplication with variables are called coefficients of those variables.

For example, in $10x^2$ we have 10 as coefficient of $x^2$

Using those above facts, and the fact that only like terms' coefficients can be added, we have:

$= 1.3t^3 + 0.4t^2 - 24t + (8 - 18t + 0.6t^2)\\= 1.3t^3 + 0.4t^2 + 0.6t^2 - 24t - 18t + 8\\= 1.3t^3 + (0.4 + 0.6)t^2 + (-24 - 18)t + 8 \\= 1.3t^3 + 1 \times t^2 -32t + 8\\= 1.3t^3 + t^2 - 42t + 8 \text{\: \: (1 is already factor of all numbers so no need to write it)}$

Learn  more about like terms here:

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