Question

Find the H.C.F of the following expressions:

(1) x³ − 7x² + 14x − 8 and x³ − 6x² + 11x − 6

(2) 4a² − 11a² + 25a + 7 and 2a³ − 5a² + 11a + 7

(3) x³ − 86x + 35 − 6x² and x³ + 40 − 5x² − 99x

(4) a³ − a² − 7a + 3; a³ − 5a² + 9a − 9 and a³ − 4a² + 4a − 3.

Answer 1

(1) We need to find the H.C.F. of and .

To find the H.C.F. of the given expressions, we need to follow the steps below.

(a) Arrange the terms of the expressions in descending order of powers.

(b) If the powers of the first terms are same, then consider the form which has a smaller co-efficient as the divisor.

(c) Continue the division process till the remainder of one of the expressions reduces to zero.

(d) The last divisor is the H.C.F. of the two expressions.

Hence, the H.C.F. of the two expressions is.

(2) The given expressions areand

Use the steps of division method to find the H.C.F. of the given expressions.

Hence, H.C.F. of the given expressions is.

(3) The given expressions areand

We use the division method to find the H.C.F. of the given expressions.

Hence, the H.C.F. of the given expressions is.

(4) The given expressions are, and

We use the division method to find the H.C.F. of the first two given expressions.

Thus, the H.C.F. ofandis a –3

We now find the H.C.F. of a –3 and

Hence, the H.C.F. of the given expressions is.