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