Question

Factor the following expression completely… (Hint factor out the GCF first)

Answer 1

15x⁴ + 55x³ + 30x² = 5x² (x + 3) (3x + 2)

Step-by-step explanation:

Factorize:

15x⁴ = 3 * 5 * x⁴

55x³ = 11 * 5 * x³

30x² = 6 *5 * x²

GCF = 5x²

15x⁴ + 55x³ + 30x² = (5x²*3x²) + (5x² * 11x) + (5x² *6)

= 5x² (3x² + 11x + 6)

3x² +11x + 6

Sum = 11

Product = 3 *6 = 18

Factor = 2 , 9 {2 +9 = 11 & 2*9 = 18}

3x² + 11x + 6 = 3x² + 9x + 2x + 6 {Rewrite the middle term using factors}

= 3x(x + 3) + 2(x +3)

= (x + 3)(3x + 2)

15x⁴ + 55x³ + 30x² = 5x²(x + 3)(3x + 2)

Answer 2

Given:

The expression is given

`15x^4+55x^3+30x^2`

Step-by-step explanation:

To factor out completely the expression.

Take common from the expression.

`5x^2(3x^2+11x+6)`

Now factorize the quadratic equation in the bracket.

`5x^2(3x+2)(x+3)`

Answer:

Hence the factor of the expression is

`5x^2(3x+2)(x+3)`