Factorise the following:
a) x^2 - 5x - 6
b) x^2 + 3x – 40
c) x^2 - 7x - 30

a) (x+6)(x-1)

b) (x+8)(x-5)

c) (x+3)(x-10)

Step-by-step explanation:

The final answer would always have to be two brackets with x and the relevant variables.

x²: You know the possible factors that can be multiplied together would be x and x. Each factor would have to be in different brackets, so we get (x + smth else)(x +smth else)

When factorising quadratic expressions, you need to find the correct pair of factors, that when multiplied together, becomes the constant of the expression. They also need to become the middle term when they are multiplied with the term in the bracket and then added together.

Possible factors for a):

1. 1 × 6 = 6

2. 2 × 3 = 6

You know 1 - 6 = -5, so we shall use the factors 6 and 1.

(x+6)(x-1) = x² -x + 6x - 6

              = x² + 5x - 6

Thus, (x+6)(x-1) is the answer.

Possible factors for b):

1. 1 × 40 = 40

2. 2 × 20 = 40

3. 4 × 10 = 40

4. 5 × 8 = 40

You know 8 - 5 = 3, so we shall use the factors 8 and 5.

(x+8)(x-5) = x² -5x + 8x - 40

               = x² + 3x - 40

Thus, (x+8)(x-5) is the answer.

Possible factors for c):

1. 1 × 30 = 30

2. 2 × 15 = 30

3. 3 × 10 = 30

4. 5 × 6 = 30

You know 3 - 10 = -7, so we shall use the factors 3 and 10.

(x+3)(x-10) = x² -10x + 3x - 30

               = x² - 7x - 40

Thus, (x+3)(x-10) is the answer.

a)

x² - 5x - 6

= x² + x - 6x - 6

= x(x + 1) -6(x + 1)

= (x - 6) (x + 1)

b)

x² + 3x - 40

= x² + 8x - 5x - 40

= x(x + 8) -5(x + 8)

= (x - 5) (x + 8)

c)

x² - 7x - 30

= x² - 10x + 3x - 30

= x(x - 10) + 3(x - 10)

= (x + 3) (x - 10)

question

what is the value of the third quartile of the data set represented by this box plot? a. 19 b. 21 c. 26 d. 29

answer

c

step-by-step explanation:

given expression is .

now we need to simplify the given expression .

we know that square root is equivalent to the power 1/2. so that means we can take half of the exponents to get the square root of given expression.

expanding that will give a very very large number so let's keep answer in exponent form.