30xexponet2-5x-10 answer this please? which expressions are equivalent to the following
-5(-6x2 + x + 2)
5x(6x − x − 2)
(10x − 5)(3x − 5)
3x(2x − 1) + 2(2x − 1)
5(2x − 1)(3x + 2)
5(2x + 1)(3x − 2)

5(2x+1)(3x-2)

Step-by-step explanation:

30x²-5x-10 is a quadratic expression with the highest power of the unknown variable x being 2

It is equivalent to ax²+bx+c

Step 1

Factorise the expression

30x² - 5x- 10

=5(6x²-x-2)

Step 2

Solve the reduced form of the quadratic expression in the bracket

Note that in solving quadratic expressions,

ax²×c = acx²

We find two factors of acx² that can be added to give bx

In comparison,

ax² ~ 6x²

c ~ -2

ax²×c ~ 6x²×-2

= -12x²

We find factors of -12x² that can be added to give -x

Factors of -12x² are

1x × -12x

2x × -6x

3x × -4x

-1x × 12x

-2x × 6x

-3x × 4x

From all the factors listed, only 3x and -4x can be added to give -x

3x + (-4x) = 3x - 4x = -x

Step 3

5(6x² - x - 2) = 5(6x² + 3x - 4x - 2)

=5[(6x²+3x)+(-4x-2)]

Step 3

Factorise the expression bracket by bracket

5[(6x²+3x)+(-4x-2)]

=5[3x(2x+1)-2(2x+1)]

Step 4

5[3x(2x+1)-2(2x+1)]

= 5(2x+1)(3x-2)

Therefore, 30x²-5x-10 is equivalent to 5(2x+1)(3x-2)

step-by-step explanation: 2