factor out the greatest common factor. if the greatest common factor is 1, just retype the…
factor out the greatest common factor. if the greatest common factor is 1, just retype the polynomial.\n24z^4 - 40z^2
Answer
Explanation:
Step1: Find the GCF of coefficients
Find the GCF of (24) and (40). Prime - factorize: (24 = 2^3\times3), (40=2^3\times5). The GCF of (24) and (40) is (2^3 = 8).
Step2: Find the GCF of variables
For the variable (z), in (z^4) and (z^2), use the rule (GCF(z^m,z^n)=z^{\min(m,n)}). Since (\min(4,2) = 2), the GCF of (z^4) and (z^2) is (z^2).
Step3: Factor out the GCF
Factor out (8z^2) from (24z^4-40z^2). (24z^4-40z^2=8z^2(3z^{4 - 2}-5z^{2 - 2})) (=8z^2(3z^2 - 5))
Answer:
(8z^2(3z^2 - 5))