Write in Standard Form 3x+2x2-4x+3x2-5x

Question

Solvely Expert · Accepted Answer

Solution:

Step 1:

First, combine like terms and organize the polynomial in descending powers of $x$ . The standard form is $a x^{2} + b x + c$ .

Step 2:

Combine $3 x$ and $- 4 x$ . The expression now looks like $2 x^{2} - x + 3 x^{2} - 5 x$ .

Step 3:

Next, add $2 x^{2}$ to $3 x^{2}$ . This simplifies to $5 x^{2} - x - 5 x$ .

Step 4:

Finally, combine $- x$ and $- 5 x$ . The polynomial in standard form is $5 x^{2} - 6 x$ .

Knowledge Notes:

To write a polynomial in standard form, one must follow certain steps:

Combine like terms: Like terms are terms that have the same variables raised to the same power. In this case, terms with $x^{2}$ are combined, and terms with $x$ are combined.
Arrange in descending order: The terms should be written starting from the highest power to the lowest power of the variable. The standard form for a quadratic polynomial is $a x^{2} + b x + c$ , where $a$ , $b$ , and $c$ are constants.
Simplify the expression: This involves performing addition or subtraction on the coefficients of like terms.

In the given problem, the terms $2 x^{2}$ and $3 x^{2}$ are like terms, as are $3 x$ , $- 4 x$ , and $- 5 x$ . These are combined to simplify the polynomial to its standard form.

The process of simplifying polynomials is foundational in algebra and is used in various applications, including solving quadratic equations, graphing parabolas, and optimizing functions.

Write in Standard Form 3x+2x^2-4x+3x^2-5x

Answer