Question

split the middle term
(a)-6x+7x-3
(b)-
${2x}^{2 } + 9x + 10$
(c)-
${x}^{2} - 23x + 42$
(d)-
${x}^{2} + 5x + 6$
(e)-
${x}^{2} + x - 56$
split the middle term .and answer the question please.

Answer 1

$\bold{Answer :}$

(a)

{ Question needs a little correction }

Now, 6x² + 7x - 3

= 6x² + (9 - 2)x - 3

= 6x² + 9x - 2x - 3

= 3x (2x + 3) - 1 (2x + 3)

= (2x + 3) (3x - 1)

(b)

Now, 2x² + 9x + 10

= 2x² + (4 + 5)x + 10

= 2x² + 4x + 5x + 10

= 2x (x + 2) + 5 (x + 2)

= (x + 2) (2x + 5)

(c)

Now, x² - 23x + 42

= x² - (21 + 2)x + 42

= x² - 21x - 2x + 42

= x (x - 21) - 2 (x - 21)

= (x - 21) (x - 2)

(d)

Now, x² + 5x + 6

= x² + (3 + 2)x + 6

= x² + 3x + 2x + 6

= x (x + 3) + 2 (x + 3)

= (x + 3) (x + 2)

(e)

Now, x² + x - 56

= x² + (8 - 7)x - 56

= x² + 8x - 7x - 56

= x (x + 8) - 7 (x + 8)

= (x + 8) (x - 7)

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