Question

In each of the following equations, take x as the given numbers and compute the numbers y.

i. y = x², x = -5, x = 5

ii. y = x² + 3x + 2, x = -2

iii. y = x² + 5x + 4, x = -2, x = -3

iv. y = x³ + 1, x = -1

v. y = x³ + x² + x + 1

Answer 1

i. y = x², x = -5 , x = 5

If x = -5, y = x² = (-5)² = -5 × -5 = 25

If x = 5, y = x² = (5)² = 5 × 5 = 25

ii. y = x² + 3x + 2, x = -2

If x = -2, y = x² + 3x + 2 = (-2)² + 3x(-2) + 2

= 4 – 6 + 2 = -2 + 2 = 0

iii. y = x² + 5x + 4, x = -2 , x = -3

If x = -2, y = x² + 5x + 4 = (-2)² + 5x(-2) + 4

= 4 – 10 + 4 = -6 + 4 = -2

If x = -3, y = x² + 5x + 4 = (-3)² + 5x(-3) + 4

= 9 – 15 + 4 = -6 + 4 = -2

iv. y = x³ + 1, x = -1

If x = -1, y = x³ + 1 = (-1)³ + 1

= (-1)(-1)(-1) + 1 = 1 × (-1) + 1 = 0

v. y = x³ + x² + x + 1, x = -1

If x = -1, y = x³ + x² + x + 1 = (-1)³ + (-1)² + (-1) + 1 

= -1 + 1 – 1 + 1 = 0