Question

Subtract $5{x^2} + 2x - 11$ from $3{x^2} + 8x - 7$. How do you express a result as a trinomial?

Answer 1

Hint: In this question we will subtract $5{x^2} + 2x - 11$ from $3{x^2} + 8x - 7$. First, we will remove all the parentheses and as we distribute the negative sign, we will change each sign after the subtraction sign. And, we will combine like terms and evaluate it, which is the required trinomial equation.

Complete step-by-step answer:
Now let us subtract $5{x^2} + 2x - 11$ from $3{x^2} + 8x - 7$.
$ = 3{x^2} + 8x - 7 - \left( {5{x^2} + 2x - 11} \right)$
$ = 3{x^2} + 8x - 7 - 5{x^2} - 2x + 11$
$ = - 2{x^2} + 6x + 4$
Hence, when we subtract $5{x^2} + 2x - 11$ from $3{x^2} + 8x - 7$we get $ - 2{x^2} + 6x + 4$.
The trinomial equation is nothing but a polynomial involving three terms which is connected by plus or minus notations.
Hence, the required trinomial equation is $ = - 2{x^2} + 6x + 4$.
So, the correct answer is “$- 2{x^2} + 6x + 4$”.

Note: To subtract two polynomials, first we need to remove all the parentheses. We can write the problem vertically rather than horizontally because it makes the next step much easier. When adding, distribute the positive sign, which does not change any of the signs. When subtracting, distribute the negative sign, which changes each sign after the subtraction sign. Next, we can combine like terms. This step is much easier if things are written vertically because like terms are written above one another. Remember that to combine like terms the variable and the power of each variable must be exactly the same. Horizontal addition works fine for simple polynomials.