Practice Questions on HCF and LCM of Two Polynomials
Q1: Find the HCF and LCM of the expressions 3x2 – 6x+3 and 6x2 -12x +6.
Q2: Determine the HCF and LCM of the polynomials x4 – 16 and x4 – 4x2 + 4.
Q3: Find the HCF and LCM of the expressions 9x2 – 16 and 3x2 – 4.
Q4: Find the HCF and LCM of the polynomials 3x3+ 6x2 – 9x.
Q5: Determine the HCF and LCM of the polynomials 4x3 – 8x2 and 6x3 – 12x2.
HCF and LCM of Polynomials
HCF (Highest Common Factor) and LCM (Least Common Multiple) of polynomials are concepts similar to those for integers. The HCF of two polynomials is the largest polynomial that divides both polynomials without leaving a remainder, while the LCM is the smallest polynomial that is a multiple of both polynomials.
To find the HCF of polynomials, we take the common factors among all the factors of two polynomials, and for LCM, we take the product of all their unique factors. In this article, we will discuss how to find HCF and LCM for polynomials, with some solved examples as well.
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