☛ Factoriser une expression littérale - facteur commun

Énoncé
Factoriser les expressions suivantes.

\(A(x)=5x+15\)

\(B(a)=6a-a^2\)

\(C(y)=7y-7\)

\(D(z)=-5z^2-25z\)

\(E(b)=-3b(b+6)+7(b+6)\)

\(F(n)=n(5n-2)+(2n-3)(5n-2)\)

\(G(t)=(t+1)(5t-6)-(5t-6)(-1+4t)\)

\(H(m)=(m+3)(6m+2)-(m+3)^2\)

\(I(c)=(3c+2)(c+5)-(3c+2)\)

\(J(s)=(4s+8)(s-1)+(s+1)(s+2)\)

Solution
\(A(x)=5\times x+5\times 3=5(x+3)\)

\(B(a)=6\times a-a\times a=a(6-a)\)

\(C(y)=7\times y-7\times 1=7(y-1)\) 

\(D(z)=-5z\times z-5z\times 5\\D(z)=-5z\times z+(-5z)\times 5\\D(z)=-5z(z+5)\) 

\(E(b)=(b+6)(-3b+7)\)

\(F(n)=(5n-2)[n+(2n-3)]\\F(n)=(5n-2)(n+2n-3)\\F(n)=(5n-2)(3n-3)\\ F(n)=(5n-2)(3\times n-3\times 1)\\F(n)=3(5n-2)(n-1)\) 

\(G(t)=(5t-6)[(t+1)-(-1+4t)]\\G(t)=(5t-6)(t+1+1-4t)\\G(t)=(5t-6)(-3t+2)\) 

\(H(m)=(m+3)(6m+2)-(m+3)(m+3)\\H(m)=(m+3)[(6m+2)-(m+3)]\\ H(m)=(m+3)(6m+2-m-3) \\H(m)=(m+3)(5m-1)\)

\(I(c)=(3c+2)(c+5)-(3c+2)\times 1=(3c+2)(c+5-1)=(3c+2)(c+4)\)

\(J(s)=4(s+2)(s-1)+(s+1)(s+2)\\J(s)=(s+2)[4(s-1)+(s+1)]\\J(s)=(s+2)(4s-4+s+1)\\J(s)=(s+2)(5s-3)\)