f(m)=(m-12)(m-7) −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 −3 -2.5 −2 -1.5 −1 -0.5 0 0.5 1 1.5 2 2.5 3 x y
Exercício( m − 12 ) ( m − 7 ) \left(m-12\right)\left(m-7\right) ( m − 12 ) ( m − 7 )
Solução explicada passo a passo
1
Aplicamos a regra: ( x + a ) ( x + b ) \left(x+a\right)\left(x+b\right) ( x + a ) ( x + b ) = x 2 + ( a + b ) x + a b =x^2+\left(a+b\right)x+ab = x 2 + ( a + b ) x + ab a = − 12 a=-12 a = − 12 b = − 7 b=-7 b = − 7 x = m x=m x = m x + b = m − 7 x+b=m-7 x + b = m − 7 x + a = m − 12 x+a=m-12 x + a = m − 12
m 2 + ( − 12 − 7 ) m − 12 ⋅ − 7 m^2+\left(-12-7\right)m-12\cdot -7 m 2 + ( − 12 − 7 ) m − 12 ⋅ − 7
2
Aplicamos a regra: a + b a+b a + b = a + b =a+b = a + b a = − 12 a=-12 a = − 12 b = − 7 b=-7 b = − 7 a + b = − 12 − 7 a+b=-12-7 a + b = − 12 − 7
m 2 − 19 m − 12 ⋅ − 7 m^2-19m-12\cdot -7 m 2 − 19 m − 12 ⋅ − 7
3
Aplicamos a regra: a b ab ab = a b =ab = ab a b = − 12 ⋅ − 7 ab=-12\cdot -7 ab = − 12 ⋅ − 7 a = − 12 a=-12 a = − 12 b = − 7 b=-7 b = − 7
m 2 − 19 m + 84 m^2-19m+84 m 2 − 19 m + 84
Resposta final para o problema m 2 − 19 m + 84 m^2-19m+84 m 2 − 19 m + 84