Question

SPLITTING THE MIDDLE TERM
1) x2-11x-782
2) x2+27x+162
3) x2-12x-325
IRREVELANT ANSWERS WOULD BE REPORTED​

Answer 1

$\large\underline{\underline{\sf{\color{lime}{SOLUTION :-}}}}$

1) $\sf{x^2-11x-782}$

$\sf{= x^2+23x-34x-782}$

$\sf{= x(x+23) -34(x+23)}$

$\sf{= (x+23)(x-34)}$

→ x = -23 or 34.

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2) $\sf{x^2+27x+162}$

$\sf{= x^2+18x+9x+162}$

$\sf{= x(x+18)+9(x+18)}$

$\sf{= (x+18)(x+9)}$

→ x = 18 or -9.

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3) $\sf{x^2-12x-325}$

$\sf{= x^2+13x-25x-325}$

$\sf{= x(x+13)-25(x+13)}$

$\sf{= (x+13)(x-25)}$

→ x = -13 or 25.

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Answer 2

Answer:

1) \sf{x^2-11x-782}x

2

−11x−782

\sf{= x^2+23x-34x-782}=x

2

+23x−34x−782

\sf{= x(x+23) -34(x+23)}=x(x+23)−34(x+23)

\sf{= (x+23)(x-34)}=(x+23)(x−34)

→ x = -23 or 34.

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2) \sf{x^2+27x+162}x

2

+27x+162

\sf{= x^2+18x+9x+162}=x

2

+18x+9x+162

\sf{= x(x+18)+9(x+18)}=x(x+18)+9(x+18)

\sf{= (x+18)(x+9)}=(x+18)(x+9)

→ x = 18 or -9.

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3) \sf{x^2-12x-325}x

2

−12x−325

\sf{= x^2+13x-25x-325}=x

2

+13x−25x−325

\sf{= x(x+13)-25(x+13)}=x(x+13)−25(x+13)

\sf{= (x+13)(x-25)}=(x+13)(x−25)

→ x = -13 or 25.