Question

factorise the following expressions by splitting the middle terms ​

Answer 1

Hello!

Question 1.

${x}^{2} + 7x + 12$

${x}^{2} + 4x + 3x + 12$

$x(x + 4) + 3(x + 4)$

$(x + 3)(x + 4)$

Question 2 :

${a}^{2} - a - 72$

${a}^{2} - 9a + 8a - 72$

$a(a - 9) + 8(a - 9)$

$(a + 8)(a - 9)$

Question 3 :

${a}^{2} + 10a + 21$

${a}^{2} + 7a +3 a + 21$

$a(a + 7) + 3(a + 7)$

$(a + 3)(a + 7)$

Question 4 :

${m}^{2} - 3m - 10$

${m}^{2} - 5m + 2m - 10$

$m(m - 5) + 2(m - 5)$

$(m + 2)( m - 5)$

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Answer 2

Answer:

Step-by-step explanation:

1.   x^2 + 7x + 12 ( find the product of the first and last coefficient, which is           1*12=12)

= x^2 + (4 + 3)x + 12 (find the factors of 12 such that the addition of substraction of two factors is equal to the coefficient of the middle term which we get 4*3=12, 4+3=7)

= x^2 + 4x + 3x + 12 (opening the brackets)

= x (x + 4) + 3(x + 4) (taking common terms)

= (x + 4)(x + 3) (Answer)

2.     Multiply the coefficient of the first term by the constant   1 • -72 = -72  

Find two factors of  -72  whose sum equals the coefficient of the middle term, which is   -1 .

     

Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  8  

                    a2 - 9a + 8a - 72

Add up the first 2 terms, pulling out like factors :

                   a • (a-9)

             Add up the last 2 terms, pulling out common factors :

                   8 • (a-9)

Add up the four terms of step 4 :

                   (a+8)  •  (a-9)

            Which is the desired factorization

 (a + 8) • (a - 9)