HCF of x2-9 and x-32 is -a- HCF of x2-x-6 and x2-4 is b- - Then a - b is

The correct option is B nbsp;x^2+x 6 Let us factorize nbsp;the given expressions. nbsp;x^2 9= x^2 3^2 nbsp;= (x+3)(x 3) (x+3)^2 nbsp; nbsp;= (x+3)(x+3 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

GCD of Polynomials

HCF of x2-9 a...

Question

HCF of $(x^{2} - 9)$ and $(x + 3)^{2}$ is 'a'. HCF of $x^{2} + x - 6$ and $x^{2} - 4$ is 'b'. Then $a \times b$ is ____.

$x^{2} + x - 8$

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

$x^{2} + x - 6$

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

$x^{2} - x - 6$

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

$x^{3} + x - 6$

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

Open in App

Solution

The correct option is B
$x^{2} + x - 6$

Let us factorize the given expressions.

$x^{2} - 9 = x^{2} - 3^{2} = (x + 3) (x - 3)$

$(x + 3)^{2} = (x + 3) (x + 3)$

So, the HCF, $a = (x + 3)$

$x^{2} + x - 6 = (x + 3) (x - 2)$

$x^{2} - 4 = (x + 2) (x - 2)$

So, the HCF, $b = (x - 2)$

Hence, $a \times b = (x + 3) (x - 2) = x^{2} + x - 6$

Suggest Corrections

Similar questions

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)

Q. Find the HCF and LCM of

3 x^{2} - 6 x

x^{2} - 4 x + 4

and

x^{2} + x - 6

Q. If

(x - k)

is the HCF of

x^{2} + 5 x + 6

and

x^{2} - 9

, then find the value of a.

Q. Find the HCF of

p (x) = x^{2} - x - 12

and

q (x) = x^{2} - 9

Q. If

(x - 3) (x - 2)

is the HCF of the polynomials

x^{2} - 2 x - 3) (2 x^{2} + a x - 2)

and

(x^{2} + x - 2) (3 x^{2} + b x - 3)

, then

a & b

Join BYJU'S Learning Program

HCF of (x2−9) and (x+3)2 is 'a'. HCF of x2+x−6 and x2−4 is 'b'. Then a×b is ____.

The correct option is B x2+x−6 Let us factorize the given expressions. x2−9=x2−32=(x+3)(x−3) (x+3)2=(x+3)(x+3) So, the HCF, a=(x+3) x2+x−6=(x+3)(x−2) x2−4=(x+2)(x−2) So, the HCF, b=(x−2) Hence, a×b=(x+3)(x−2)=x2+x−6

HCF of $(x^{2} - 9)$ and $(x + 3)^{2}$ is 'a'. HCF of $x^{2} + x - 6$ and $x^{2} - 4$ is 'b'. Then $a \times b$ is ____.