Question

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Answer 1

Given :-

• 3x² + 7x + 3 - 5x

To find :-

• Classify based on terms.

Lets understand!

If there is one term in an expression it is called as monomial, If it has 2 unlike terms it is called binomial , If it has 3 unlike terms it is called trinomial and if there are 4 unlike terms it is polynomial.

Here, In this question there are four terms but there are like terms too. If we simplify them, we will get 3 unlike terms.

So, As we know, if there are 3 unlike terms it is a trinomial.

Therefore, 3x² + 7x + 3 - 5x is a trinomial.

Solution :-

Eq - 3x² + 7x + 3 - 5x

Now, simplify like terms :-

➜ 3x² + 7x -5x +3

➜ 3x² + 2x +3

Now, Here there are 3 terms in the polynomial.

They are:-

1. 3x²
2. 2x
3. 3

Therefore, 3x² + 7x + 3 - 5x is a trinomial.

Extra :-

If classified by degree, It is quadratic.

Know more :-

You can use these further, in solving any expressions :-

$\boxed{\begin{array}{cc}\boxed{\bigstar\:\:\textbf{\textsf{Algebric\:Identity}}\:\bigstar}\\\\1)\bf\:(A+B)^{2} = A^{2} + 2AB + B^{2}\\\\2)\sf\: (A-B)^{2} = A^{2} - 2AB + B^{2}\\\\3)\bf\: A^{2} - B^{2} = (A+B)(A-B)\\\\4)\sf\: (A+B)^{2} = (A-B)^{2} + 4AB\\\\5)\bf\: (A-B)^{2} = (A+B)^{2} - 4AB\\\\6)\sf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\7)\bf\:(A-B)^{3} = A^{3} - 3AB(A-B) + B^{3}\\\\8)\sf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})\\\\\end{array}}$

Answer 2

$\Large{\underbrace{\underline{\sf{Understanding\: the\: Concept}}}}$

Here in this question, concept of polynomial is used. We have given an equation and we have to classify it on the basis of terms. We can see that the given term is a polynomial. Polynomial is a form of equation that involves coefficients and variable.

Such like:

$\leadsto$ 3x²+5x+7

Here:-

$\leadsto$ Coefficient of x² is 3

$\leadsto$ Coefficient of x is 5

$\leadsto$ Variable is x

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We understand about polynomial. Now let's classify them on the basis of number of terms.

A polynomial on the basis of terms can be classified as:

$\boxed{\begin{array}{c| c }\bf{Number\; of \;terms}&\bf{Na{me}\; of \:polynomial}\\\\1&\sf Monomial\\2&\sf Binomial\\3&\sf Trinomials\end{array}}$

NOTE→A polynomial which has more than 3 terms don't have any classified name and can be terms as generally by polynomial.

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We have given polynomial:-

3x²+7x+3-5x

To find the number of terms first we have simply it and had to write in simplest form.

So let's do it!!

$\leadsto$ 3x²+7x+3-5x

Now simply like terms:

$\leadsto$ 3x²+7x-5x+3

$\leadsto$ 3x²+2x+3

Now we can see that there are 3 terms in this polynomial.

Which are:-

• 3x²

•2x

•3

Since it has 3 terms, it is a form of trinomial.

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