Question

4. Factorise the following expressions :
(i) x2 + 11x - 60
(ii) x2 - x - 42
(iv​

Answer 1

Answer:

x^2+15x-4x-60

x(x+15)-4(x+15)

(x+15)(x-4)

x^2 - x-42

x^2 - 7x+6x-42

x(x-7)+6(x-7)

(x-7) (x+6)

Answer 2

The first term is, x2 its coefficient is 1 .

The first term is, x2 its coefficient is 1 .The middle term is, -11x its coefficient is -11 .

The first term is, x2 its coefficient is 1 .The middle term is, -11x its coefficient is -11 .The last term, "the constant", is -60

The first term is, x2 its coefficient is 1 .The middle term is, -11x its coefficient is -11 .The last term, "the constant", is -60 Step-1 : Multiply the coefficient of the first term by the constant 1 • -60 = -60

The first term is, x2 its coefficient is 1 .The middle term is, -11x its coefficient is -11 .The last term, "the constant", is -60 Step-1 : Multiply the coefficient of the first term by the constant 1 • -60 = -60 Step-2 : Find two factors of -60 whose sum equals the coefficient of the middle term, which is -11 .

The first term is, x2 its coefficient is 1 .The middle term is, -11x its coefficient is -11 .The last term, "the constant", is -60 Step-1 : Multiply the coefficient of the first term by the constant 1 • -60 = -60 Step-2 : Find two factors of -60 whose sum equals the coefficient of the middle term, which is -11 . -60 + 1 = -59

The first term is, x2 its coefficient is 1 .The middle term is, -11x its coefficient is -11 .The last term, "the constant", is -60 Step-1 : Multiply the coefficient of the first term by the constant 1 • -60 = -60 Step-2 : Find two factors of -60 whose sum equals the coefficient of the middle term, which is -11 . -60 + 1 = -59 -30 + 2 = -28

The first term is, x2 its coefficient is 1 .The middle term is, -11x its coefficient is -11 .The last term, "the constant", is -60 Step-1 : Multiply the coefficient of the first term by the constant 1 • -60 = -60 Step-2 : Find two factors of -60 whose sum equals the coefficient of the middle term, which is -11 . -60 + 1 = -59 -30 + 2 = -28 -20 + 3 = -17

The first term is, x2 its coefficient is 1 .The middle term is, -11x its coefficient is -11 .The last term, "the constant", is -60 Step-1 : Multiply the coefficient of the first term by the constant 1 • -60 = -60 Step-2 : Find two factors of -60 whose sum equals the coefficient of the middle term, which is -11 . -60 + 1 = -59 -30 + 2 = -28 -20 + 3 = -17 -15 + 4 = -11

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and 4

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and 4 x2 - 15x + 4x - 60

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and 4 x2 - 15x + 4x - 60Step-4 : Add up the first 2 terms, pulling out like factors :

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and 4 x2 - 15x + 4x - 60Step-4 : Add up the first 2 terms, pulling out like factors : x • (x-15)

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and 4 x2 - 15x + 4x - 60Step-4 : Add up the first 2 terms, pulling out like factors : x • (x-15) Add up the last 2 terms, pulling out common factors :

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and 4 x2 - 15x + 4x - 60Step-4 : Add up the first 2 terms, pulling out like factors : x • (x-15) Add up the last 2 terms, pulling out common factors : 4 • (x-15)

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and 4 x2 - 15x + 4x - 60Step-4 : Add up the first 2 terms, pulling out like factors : x • (x-15) Add up the last 2 terms, pulling out common factors : 4 • (x-15)Step-5 : Add up the four terms of step 4 :

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and 4 x2 - 15x + 4x - 60Step-4 : Add up the first 2 terms, pulling out like factors : x • (x-15) Add up the last 2 terms, pulling out common factors : 4 • (x-15)Step-5 : Add up the four terms of step 4 : (x+4) • (x-15)

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and 4 x2 - 15x + 4x - 60Step-4 : Add up the first 2 terms, pulling out like factors : x • (x-15) Add up the last 2 terms, pulling out common factors : 4 • (x-15)Step-5 : Add up the four terms of step 4 : (x+4) • (x-15) Which is the desired factorization

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