HCF of - x-2-9 nbsp- nbsp- and -x-3-2 is -a- nbsp-HCF of nbsp-x-2-x-6 and x-2-4 is -b- Then nbsp-a- b is -nbsp-x-2-x-6-nbsp-x-2-x-8 nbsp-nbsp-x-2-x-6-nbsp-x-3-x-6-

The correct option is A 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 ...

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Byju's Answer

Standard IX

Mathematics

GCD by Factorization

HCF of ( x^2-...

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 ____.

$x^{2} + x - 8$

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$x^{2} + x - 6$

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$x^{2} - x - 6$

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$x^{3} + x - 6$

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

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Similar questions

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 ____.

Q. 17.If HCF of x2-x-6 and x2+9 x+14 is x+m then the value of m is A. 1 B.2 C.-2 D.-1

Find the HCF of $(x - 2)^{2}$ , $x^{2} - 4$ and $x^{2} + x - 6$ .

Q. Find the HCF and LCM of

3 x^{2} - 6 x

x^{2} - 4 x + 4

and

x^{2} + x - 6

Q. For what values of

a

and

b

the polynomials

p (x) = (x^{2} + 5 x + 6) (x^{2} + 2 x - a)

and

q (x) = (x^{2} - x - 2) (x^{2} + 7 x + b)

have

(x + 2) (x - 2)

as their HCF.

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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 ____.