Answer:
5x² + 15x + 10 = 5(x + 1)(x +2)
4x² - 6x - 4 = 2(2x +1)(x -2)
2x² - 7x - 15 = (x -5 )(2x +3)
Explanation:
Factorize:
5x² + 15x + 10
Sum = 15
Product = 5*10 = 50
Factor = 5 , 10 {5*10 = 50 & 5 + 10 = 15}
Rewrite the middle term using the factors.
5x² + 15x + 10 = 5x² + 10x + 5x + 10
= 5x(x + 2) + 5(x +2)
= (x +2)(5x + 5)
= 5(x +1)(x+ 2)
4x² - 6x - 4
Sum = -6
Product = 4*(-4) = -16
Factors = 2 , (-8) {2 +(-8) = -6 & 2*(-8) = -16}
Rewrite the middle term,
4x² - 6x - 4 = 4x² - 8x + 2x - 4
= 4x(x - 2) + 2(x - 2)
= (x - 2)(4x + 2)
= (x -2) 2(2x + 1)
= 2(2x + 1)(x - 2)
2x² - 7x - 15
Sum = -7
Product = -30
Factor = 3 , (-10) {3 +(-10) = -7 & 3*(-10) = -30}
Rewrite the middle term,
2x² - 7x - 15 = 2x² - 10x + 3x - 15
= 2x(x - 5) + 3(x - 5)
= (x - 5)(2x + 3)