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Chapter 7 - Coordinate Geometry. Chapter 8 - Introduction to Trigonometry. Chapter 9 - Some Applications of Trigonometry. Chapter 11 - Constructions. Chapter 12 - Areas Related to Circles. Chapter 13 - Surface Areas and Volumes. Chapter 14 - Statistics. Chapter 15 - Probability. If you practice it regularly, then you will better understand all the concepts of the chapter. Still, if you find yourself in any problem, our expert teachers will always help you. Factor theorem: Sometimes a polynomial having values that are unknown and one of its factors are provided and we have to calculate the value of that unknown value.

Sometimes, a linear polynomial is given and we have to verify whether it is a factor of given polynomial f x of degree greater than 1 or not. For solving such types of problems factor theorem is required. In this segment, we will study division algorithms for polynomials. If any two polynomials like p x and g x along with one polynomial of the two is not equal to 0 i. The outcome of the above numerical is known as the Division Algorithm for polynomials.

In other words, we can say that when p x divided by g x , we get q x as quotient and r x as remainder. Organize the terms of the dividend and the divisor in descending order of their degrees. The first term of the dividend must be divided by the first term of the divisor to obtain the first term of the quotient. Multiply the whole divisor by the first term if the quotient and subtract the result obtained from the dividend.

Observe the remainder as the new dividend and proceed as earlier. Repeat the procedure till a remainder Ch 13 Maths Class 10 Vedantu Diy is derived which is either 0 or whose degree is less than that of the divisor. Verifying the division algorithm for polynomials. Let us consider the following example. To find the Quotient and Remainder using a division algorithm.

By division algorithm, we have. A line drawn runs through these points to derive the graph of the given polynomial. We construct a table containing the values of y corresponding to various values of x:.

We now plot the points -4, 16 , -3, 7 , -2, 0 , -1, -5 , 0 -8 , 1, 9 , 2, 8 , 3, -5 , 4, 0 , 5, 7 and 6, 16 on a graph paper and draw a smooth free hand curve passing through these points.

Such a curve is called a parabola. The lowest point of the graph 1, 9 is called the vertex of Class 10 Maths Ch 12 All Formulas Us the parabola.

This line is called the axis of the parabola. For a polynomial of degree n, the number of zeroes can be utmost n or less. For example, for a quadratic, polynomial the no.

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