Factorise by grouping: x² - 5x + 2x - 10

Step-by-step explanation:

To factor by grouping, first divide the polynomial into 2 groups with parentheses.

Factor the greatest common factor (GCF) out of both binomials.

For the first binomial, the GCF is x.

For the second binomial, the GCF is 2.

Factor out the common binomial which is (x-5).

The factorized form of x²-5x+2x-10 is (x+2)(x-5)

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

step-by-step explanation: