What is the standard form of y= (x+5)(4x-7) ?

1 Answer
mason m
Nov 15, 2015

4x^2+27x+35

Explanation:

The "standard form" of a polynomial refers to its order. In standard form, terms are listed in order of descending degree.

Degree refers to the sum of the exponents in a single term. For example, the degree of 12x^5 is 5, since that is its only exponent. The degree of -3x^2y is 3 because the x is raised to the 2 and the y is raised to the 1, and 2+1=3. Any constant, like 11, has a degree of 0 because it can technically be written as 11x^0 since x^0=1.

In (x+5)(4x+7), we first have to distribute all of the terms. This leaves us with 4x^2+7x+20x+35, which simplifies to be 4x^2+27x+35.

Now, all we have to do is make sure we are in standard form. The degrees, as they are currently listed, go in the order 2rarr1rarr0, which is in descending order. Therefore, the polynomial in standard form is color(red)(4x^2+27x+35

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