If $f (x) = (x + 2) (x^{2} + 8 x + 15)$ and $g (x) = (x + 3) (x^{2} + 9 x + 20)$ then find the HCF of $f (x)$ and $g (x)$ .

x + 3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x^{2} + 8 x + 15

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

x + 4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x^{2} + 9 x + 20

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $x^{2} + 8 x + 15$
Prime factorisation of $(x + 2) (x^{2} + 8 x + 15) = (x + 2) \times [(x + 3) \times (x + 5)]$
Prime factorisation of $(x + 3) (x^{2} + 9 x + 20) = (x + 3) \times [(x + 4) \times (x + 5)]$
So,HCF $= (x + 3) \times (x + 5) = (x^{2} + 8 x + 15)$

Suggest Corrections

Similar questions

Q. Apply division algorithm to find the quotient q(x) and remainder r(x) in dividing f(x) by g(x) in each of the following :

(i) f(x) = x³ − 6x² + 11x − 6, g(x) = x² + x + 1
(ii) f(x) = 10x⁴ + 17x³ − 62x² + 30x − 3, g(x) = 2x² + 7x + 1
(iii) f(x) = 4x³+ 8x + 8x² + 7, g(x) = 2x² − x + 1
(iv) f(x) = 15x³ − 20x² + 13x − 12, g(x) = 2 − 2x + x²

Q. If

f (x) = (x - 2) (x^{2} - x - a), g (x) = (x + 2) (x^{2} + x - b)

and their HCF is

x^{2} - 4,

then find

a - b

(

a

and

b

are constants)

$\frac{x^{2} - 8 x + 15}{x^{2} - 9 x + 18} = \frac{x - 5}{x - 6}$

On dividing f(x) = x³ - 3x² + x + 2 by a polynomial g(x) the quotient and remainder q(x) and r(x) are (x – 2) and (-2x + 4) respectively, then g(x) is

Q. Let

f (x) = \frac{3}{x - 2} - \frac{1}{x + 3}

and

g (x) = \frac{x^{2} - 4 x + 19}{x^{2} + x - 6}

. If

f (x) = g (x)

, then

x =

Join BYJU'S Learning Program

If f(x)=(x+2)(x2+8x+15) and g(x)=(x+3)(x2+9x+20) then find the HCF of f(x) and g(x).

The correct option is C x2+8x+15Prime factorisation of (x+2)(x2+8x+15)=(x+2)×[(x+3)×(x+5)]Prime factorisation of (x+3)(x2+9x+20)=(x+3)×[(x+4)×(x+5)]So,HCF =(x+3)×(x+5)=(x2+8x+15)

If $f (x) = (x + 2) (x^{2} + 8 x + 15)$ and $g (x) = (x + 3) (x^{2} + 9 x + 20)$ then find the HCF of $f (x)$ and $g (x)$ .

The correct option is C $x^{2} + 8 x + 15$
Prime factorisation of $(x + 2) (x^{2} + 8 x + 15) = (x + 2) \times [(x + 3) \times (x + 5)]$
Prime factorisation of $(x + 3) (x^{2} + 9 x + 20) = (x + 3) \times [(x + 4) \times (x + 5)]$
So,HCF $= (x + 3) \times (x + 5) = (x^{2} + 8 x + 15)$