Question

if x2 -x -6 and x2 +3x -18 have acommon factor (x-a) then find the value of a​

Answer 1

Answer:

Step-by-step explanation:

since the first and second polynomials have the same factor. p(a) of the first polynomial = p(a) of the second. the answer we get is a = 3

Answer 2

$\underline{\boxed{\bold{Question}}}$  

↠ If x² - x - 6 and x² + 3x - 18 have a common factor (x - a) Then find the value of a.

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$\underline{\boxed{\bold{Important\;Information}}}$  

↠ Every 2 degree polynomial is has factors. Factors may be real or imaginary depending on Discriminant D = b² - 4ac

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$\underline{\boxed{\bold{Given}}}$

↠ First Polynomial  = x² - x - 6

↠ Second Polynomial  = x² + 3x - 18

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$\underline{\boxed{\bold{Answer}}}$

Let's Start !

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Let's Factorize first polynomial by splitting the middle term.

Polynomial  = x² - x - 6 = 0

$:\implies x^{2} - x -6 = 0$

$:\implies x^{2} - 3x + 2x -6 = 0$

$:\implies x(x-3) + 2(x -3) = 0$

$:\implies( x-3)(x+2)=0$

 

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$\boxed{\boxed{\bold{\therefore Factors\;of\;polynomial\;x^{2}-x-6 \;are\; (x-3)\; and \;(x+2)}}}$

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Let's Factorize second polynomial by splitting the middle term.

Polynomial  = x² + 3x - 18

$:\implies x^{2} +3x-18=0$

$:\implies x^{2} +6x-3x -18 = 0$

$:\implies x(x+6) - 3(x +6) = 0$

$:\implies( x - 3)(x +6) = 0$

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$\boxed{\boxed{\bold{\therefore Factors\;of\;polynomial\;x^{2} +3x -18 \;are \;(x-3)\; and \;(x+6)}}}$

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∴ x² - x - 6 = (x - 3)(x + 2)

∴ x² + 3x - 18 = (x - 3)(x + 6)

$\boxed{\boxed{\bold{\therefore Common\;factor\;is\;(x-3)}}}$

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Comparing (x - 3) with (x - a)

$:\implies ( x - 3)= (x - a)$

$\boxed{:\implies a = 3}$

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$\boxed{\boxed{\bold{\therefore Value\;of\;A = 3}}}$

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Hope this helps u.../

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