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Factor the polynomial by its greatest common monomial factor.

20y^(6)-15y^(4)+40y^(2)=

Factor the polynomial by its greatest common monomial factor. $\newline$ $20 y^{6}-15 y^{4}+40 y^{2}=$

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Solve exponential equations using natural logarithms

Full solution

Q. Factor the polynomial by its greatest common monomial factor.

\newline

20 y^{6}-15 y^{4}+40 y^{2}=

Identify GCF and lowest power: Identify the greatest common factor (GCF) of the coefficients and the lowest power of $y$ in all terms. $\newline$ The coefficients are $20$ , $-15$ , and $40$ . The GCF of these numbers is $5$ . $\newline$ The variable parts are $y^6$ , $y^4$ , and $y^2$ . The lowest power of $y$ is $y^2$ . $\newline$ So, the greatest common monomial factor is $20$ $0$ .
Divide by GCF: Divide each term of the polynomial by the greatest common monomial factor. $\newline$ $20y^6 \div 5y^2 = 4y^4$ $\newline$ $-15y^4 \div 5y^2 = -3y^2$ $\newline$ $40y^2 \div 5y^2 = 8$
Write factored form: Write the factored form of the polynomial using the greatest common monomial factor. $\newline$ The polynomial $20y^6 - 15y^4 + 40y^2$ factored by the greatest common monomial factor $5y^2$ is: $\newline$ $5y^2(4y^4 - 3y^2 + 8)$

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