Answer:
[tex]2x(x+3)(x + 4)[/tex]
Step-by-step explanation:
To factor [tex]2x^3+14x^2+24x[/tex]
First, factor out the common term [tex]2x[/tex]:
[tex]\implies 2x(x^2+7x+12)[/tex]
Now factor the expression in the parantheses: [tex]x^2+7x+12[/tex]
Find two numbers that multiply to 12 and sum to 7: 3 and 4
Rewrite [tex]7x[/tex] as the sum of these 2 numbers:
[tex]\implies x^2+3x + 4x+12[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies x(x+3) + 4(x+3)[/tex]
Factor out the common term [tex](x+3)[/tex]:
[tex]\implies (x+3)(x + 4)[/tex]
Therefore, the final factorization of the polynomial is:
[tex]\implies 2x (x+3)(x + 4)[/tex]
