English Medium Class 10 - CBSE Question Bank Solutions

It is given that –1 is one of the zeroes of the polynomial x³ + 2x² – 11x – 12. Find all the zeroes of the given polynomial.

If (x + a) is a factor of (2x² + 2ax + 5x + 10), then find the value of a.

If (a – b), a and (a + b) are zeros of the polynomial 2x³ – 6x² + 5x – 7, write the value of a.

If x³ + x² – ax + b is divisible by (x² – x), write the values of a and b.

State division algorithm for polynomials.

Determine the prime factorisation of the following positive integer:

 20570

Determine the prime factorisation of the following positive integer:

58500

Determine the prime factorisation of the following positive integer:

45470971

Find the LCM and HCF of the following pair of integers and verify that LCM × HCF = Product of the two numbers.

26 and 91

Find the LCM and HCF of the following integers by applying the prime factorisation method:

40, 36 and 126

Find the LCM and HCF of the following integers by applying the prime factorisation method:

 84, 90 and 120

Find the LCM and HCF of the following integers by applying the prime factorisation method:

 24, 15 and 36

Write down the decimal expansions of the following rational numbers by writing their denominators in the form 2^m × 5ⁿ, where m, n are non-negative integers.

\[\frac{3}{8}\]

Write down the decimal expansions of the following rational numbers by writing their denominators in the form 2^m × 5ⁿ, where m, n are non-negative integers.

\[\frac{13}{125}\]

Write down the decimal expansions of the following rational numbers by writing their denominators in the form 2^m × 5ⁿ, where m, n are non-negative integers.

\[\frac{129}{2^2 \times 5^7}\]