Determine the LCM of the given polynomials. Leave your answer in factored form. \( x^{2}+10 x+25 \) and \( x^{2}+11 x+30 \)

a) \( \frac{12 a b}{4 a}= \)

5) Qual a expressão cujo desenvolvimento logarítmico é dado abaixo ( \( a, b \), c são reais positivos)? a) \( \log _{2} a+\log _{2} b-\log _{2} c \) b) \( \frac{1}{3} \log a-\frac{1}{2} \log c-\frac{3}{2} \log b \) c) \( 2+\frac{1}{3} \log _{2} a+\frac{1}{6} \log _{2} b-\log _{2} c \) d) \( \frac{1}{2} \log (a-b)+\log a-\log (a+b) \)

4. Find the value of \( k \) so that the equation \( k x^{2}+k x+1=-4 x^{2}-x \) have equal roots. 5. For what values of \( m \) will the equation \( x^{2}-2(5+2 m) x+3(7+10 m)=0 \) have equal roots? 6. If the roots of the equation \( \left(a^{2}+b^{2}\right) x^{2}-2(a c+b c) x+\left(c^{2}+c^{2}\right)=0 \) are cqual, then prove the \( a \) c \( c \)

Use the distributive property to remove the parentheses, \[ (y+5) 7 \]

6) \( (x-8)(x-3)(x-5)=(x-5)(x-3)(x-6) \)