Factor 3z^2+24z+48

Math
3z2+24z+48
Factor 3 out of 3z2+24z+48.
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Factor 3 out of 3z2.
3(z2)+24z+48
Factor 3 out of 24z.
3(z2)+3(8z)+48
Factor 3 out of 48.
3z2+3(8z)+3⋅16
Factor 3 out of 3z2+3(8z).
3(z2+8z)+3⋅16
Factor 3 out of 3(z2+8z)+3⋅16.
3(z2+8z+16)
3(z2+8z+16)
Factor using the perfect square rule.
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Rewrite 16 as 42.
3(z2+8z+42)
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
8z=2⋅z⋅4
Rewrite the polynomial.
3(z2+2⋅z⋅4+42)
Factor using the perfect square trinomial rule a2+2ab+b2=(a+b)2, where a=z and b=4.
3(z+4)2
3(z+4)2
Factor 3z^2+24z+48

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