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How do you write a polynomial in standard form, then classify it by degree and number of terms $x-6{{x}^{2}}$?

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Last updated date: 25th Feb 2024
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Views today: 7.38k
IVSAT 2024
Answer
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Hint: In this problem we need to classify the polynomial by the degree and number of the terms. For this problem we need to rearrange the terms in the given equation. We will arrange the given terms in ascending or descending order. After arranging the terms, we will observe the given equation and write the highest power of the terms in the equation. From this we will classify the given equation based on the degree. After that we will calculate the number of terms in the given equation and classify the given equation based on the number of terms.

Complete step by step solution:
Given equation $x-6{{x}^{2}}$.
Rearranging the above equation in ascending order, then we will get
$\Rightarrow -6{{x}^{2}}+x$
In the above equation we can observe that the highest power of the above equation is $2$. So, we can classify the above equation as the ‘Quadratic equation’.

In the given polynomial we can observe that the number of terms is also $2$. So, we can classify the above polynomial as ‘Binomial’.

Note: In this problem we have the highest power as $2$ so we have called it a Quadratic equation. Here are some names of the polynomial for different degrees.
$1$- Linear
$2$- Quadratic
$3$- Cubic
$4$- Quartic
$5$- Quintic
$6$- Hextic
$7$- Haptic
$8$- Octic
$9$- Nonic
$10$- Decic
Names of the different polynomials having different number of terms are
$1$- Monomial
$2$- Binomial
$3$- Trinomial
$4$- Quadrinomial