1. Arrange both the polynomial is same order of exponent . It would be good to have terms arrange from highest exponent to lowest exponent i.e
For example
$S(x) = x^2 + 5x^3 + 1 +10x$
$P(x) = x^3 + x^2 + 5 +10x$

Arranging them as per suggestion above

$S(x) = 5x^3 +x^2+ 10x +1$
$P(x) = x^3 + x^2 + 10x +5$

2. Add the like term . By like term ,we mean same exponent terms. There are two method to add like terms. We either can group them horizontally and add it. We can add vertically
Horizontally
$S(x) + P(x)$
$=x^2 + 5x^3 + 1 +10x + (x^3 + x^2 + 5 +10x)$
Arranging both the polynomial in same order
$=5x^3 +x^2+ 10x +1 + (x^3 + x^2 + 10x +5 )$
Opening the parenthesis and grouping the like terms. In addition,no sign are changed when parenthesis are opened
$= 5x^3 + x^3 + x^2+x^2 + 10x +10x + 1+5$
$=6x^3+2x^2+20x+6$

Vertically
$S(x) = x^2 + 5x^3 + 1 +10x$
$P(x) = x^3 + x^2 + 5 +10x$

Arranging both the polynomial in same order

$S(x) = 5x^3 +x^2+ 10x +1$
$P(x) = x^3 + x^2 + 10x +5$

Similarly we can add three or more polynomials

Example-1
$(2x^3 - x+1+x^2) + (x^3 + 6x - 7) + (-3x^2 - 11 + 2x)$
Arranging them in same order
$=(2x^3 + x^2 - x+1) + (x^3 + 6x - 7) + (-3x^2 + 2x - 11)$

Opening the parenthesis and grouping the like terms
$=2x^3+x^3 +x^2-3x^2 -x +6x+2x +1-7-11$
$=3x^3-2x^2+7x-16$

## Subtracting polynomials

We many times need to subtract the two polynomial .It is very similar to adding polynomials only.Subtracting polynomials just means Subtracting the like terms.We need to follow below steps for Subtraction of polynomial
1. Arrange both the polynomial is same order of exponent . It would be good to have terms arrange from highest exponent to lowest exponent i.e
For example
$S(x) = x^2 + 5x^3 + 1 +10x$
$P(x) = x^3 + x^2 + 5 +10x$

Arranging them as per suggestion above

$S(x) = 5x^3 +x^2+ 10x +1$
$P(x) = x^3 + x^2 + 10x +5$

2. Subtract the like term . By like term ,we mean same exponent terms. There are two method to subtract like terms. We either can group them horizontally and subtract it. We can add vertically
Horizontally
$S(x) - P(x)$
$=x^2 + 5x^3 + 1 +10x - (x^3 + x^2 + 5 +10x)$
Arranging both the polynomial in same order
$=5x^3 +x^2+ 10x +1 -(x^3 + x^2 + 10x +5 )$
Opening the parenthesis and grouping the like terms. In Subtract, sign are reversed when parenthesis are opened i.e + becomes - and - becomes +
$= 5x^3 - x^3 + x^2 - x^2 + 10x -10x + 1-5$
Subtract the like term
$=4x^3 - 4$

Vertically
$S(x) = x^2 + 5x^3 + 1 +10x$
$P(x) = x^3 + x^2 + 5 +10x$

Arranging both the polynomial in same order

$S(x) = 5x^3 +x^2+ 10x +1$
$P(x) = x^3 + x^2 + 10x +5$

Similarly we can add three or more polynomials

Example-1
$(2x^3 - x+1+x^2) - (x^3 + 6x - 7) - (-3x^2 - 11 + 2x)$
Arranging them in same order
$=(2x^3 + x^2 - x+1) - (x^3 + 6x - 7) - (-3x^2 + 2x - 11)$

Opening the parenthesis and grouping the like terms
$=2x^3- x^3 +x^2+3x^2 -x -6x-2x +1+7+11$
$=x^3+4x^2-9x+18$

Reference Books for class 9 Math

Given below are the links of some of the reference books for class 9 Math.

1. Mathematics for Class 9 by R D Sharma One of the best book for studying class 9 level mathematics. It has lot of problems to be solved.
2. Secondary School Mathematics for Class 9 by R S Aggarwal This is also as good as R.D. Sharma. Either this or the book by R.D. Sharma will do. I find book R.S. Aggarwal little bit more challenging than the one by R.D. Sharma.
3. Pearson IIT Foundation Series - Maths - Class 9 Buy this book if you want to challenge yourself further and want to prepare for JEE foundation.
4. Pearson IIT Foundation Physics, Chemistry & Maths combo for Class 9 Only buy if you are prepared to study extra topics and want to take your studies a step further. You might need help to understand topics in these books.

You can use above books for extra knowledge and practicing different questions.

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