The H.C.F and L.C.M of two expressions are $(a - 7)$ and $(a^{3} - 10 a^{2} + 11 a + 70)$ respectively. If one of the expressions is $(a^{2} - 12 a + 35)$ , find the other.

Open in App

Solution

Given, $H = (a - 7)$
$A = (a^{2} - 12 a + 35)$
$L = (a^{3} - 10 a^{2} + 11 a + 70)$
$B = ?$
We have $A \times B = H \times L$
$∴ B = \frac{H \times L}{A} = H \times \frac{L}{A}$
$∴ \frac{L}{A} = \frac{a^{3} - 10 a^{2} + 11 a + 70}{a^{2} - 12 a + 35}$
$∴$ $B = (a - 7) (a + 2)$
$= a^{2} - 5 a - 14$

Suggest Corrections

Similar questions

The H.C.F. and L.C.M of two expression are (a − 7) and (a³ − 10a² + 11a + 70) respectively. If one of the expressions is (a² − 12a + 35) find the other.

Q. The HCF of two polynomials is

h (a) = a - 7

and their LCM is

m (a) = a^{3} - 10 a^{2} + 11 a + 70

. If one of the polynomial is

p (a) = a^{2} - 12 a + 35

, and if the leading coefficient of

q (a)

is positive, find the other polynomial

q (a)

Q. The H.C.F. and L.C.M. of two expressions are

(x - 3)

and

(x^{3} - 5 x^{2} - 2 x + 24)

respectively. If one of the expression is

(x^{2} - 7 x + 12)

, find the other.

The H.C.F. and L.C.M. of two expression are (x − 3) and (x³ − 5x² − 2x + 24) respectively. If one of the expression is (x² − 7x + 12) find the other.

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.

Join BYJU'S Learning Program

The H.C.F and L.C.M of two expressions are (a−7) and (a3−10a2+11a+70) respectively. If one of the expressions is (a2−12a+35), find the other.

Given, H=(a−7)A=(a2−12a+35)L=(a3−10a2+11a+70)B=?We have A×B=H×L∴B=H×LA=H×LA∴LA=a3−10a2+11a+70a2−12a+35∴ B=(a−7)(a+2)=a2−5a−14

The H.C.F and L.C.M of two expressions are $(a - 7)$ and $(a^{3} - 10 a^{2} + 11 a + 70)$ respectively. If one of the expressions is $(a^{2} - 12 a + 35)$ , find the other.