Answer:
[tex]12x^3+102x^2+114x-84[/tex]
Step-by-step explanation:
Given polynomials:
[tex]\begin{cases} 6x^2+39x-21\\6x^2+54x+84 \end{cases}[/tex]
Factor the polynomials:
Polynomial 1
[tex]\implies 6x^2+39x-21[/tex]
[tex]\implies 3(2x^2+13x-7)[/tex]
[tex]\implies 3(2x^2+14x-x-7)[/tex]
[tex]\implies 3[2x(x+7)-1(x+7)][/tex]
[tex]\implies 3(2x-1)(x+7)[/tex]
Polynomial 2
[tex]\implies 6x^2+54x+84[/tex]
[tex]\implies 6(x^2+9x+14)[/tex]
[tex]\implies 6(x^2+7x+2x+14)[/tex]
[tex]\implies 6[x(x+7)+2(x+7)][/tex]
[tex]\implies 6(x+2)(x+7)[/tex]
[tex]\implies 2 \cdot 3(x+2)(x+7)[/tex]
The lowest common multiplier (LCM) of two polynomials a and b is the smallest multiplier that is divisible by both a and b.
Therefore, the LCM of the two polynomials is:
[tex]\implies 2 \cdot 3(x+7)(x+2)(2x-1)[/tex]
[tex]\implies (6x^2+54x+84)(2x-1)[/tex]
[tex]\implies 12x^3+108x^2+168x-6x^2-54x-84[/tex]
[tex]\implies 12x^3+102x^2+114x-84[/tex]
