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

Nov 15, 2015

$4 {x}^{2} + 27 x + 35$

#### 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 $12 {x}^{5}$ is $5$, since that is its only exponent. The degree of $- 3 {x}^{2} y$ 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 $11 {x}^{0}$ since ${x}^{0} = 1$.

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

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 $2 \rightarrow 1 \rightarrow 0$, which is in descending order. Therefore, the polynomial in standard form is color(red)(4x^2+27x+35