Question

1- Fatore o polinômio ax²+bx²-7x².

2- Escreva a forma fatorada do polinômio 8a⁵b+12³.

3- Fatore as expressões.

a) x²-4

b) 4a²-9b²

4-Verifique se os polinômios são trinômios quadrados perfeitos:

a) x²+12x+64 e) a²x²+2ax+1

b) a²-22a+121 f) y²-2y+4

c) 4b²+10b+25 g) x²+5x+16​​​

Answer 1

$\large\boxed{\begin{array}{l}\tt 1)~\sf ax^2+bx^2-7x^2=x^2\cdot(a+b-7)\\\tt 2)~\sf 8a^5b+12^3=8\cdot(a^5b+216)\\\rm 3)\\\tt a)~\sf x^2-4=(x+2)\cdot(x-2)\\\tt b)~\sf 4a^2-9b^2=(2a+3b)\cdot(2a-3b)\\\rm 4)\\\tt a)~\sf x^2+12x+64\\\sf\sqrt{x^2}=x~~\sqrt{64}=8~~~~2\cdot x\cdot8=16x\ne12x\\\sf n\tilde ao~\acute e~trin\hat omio~quadrado~perfeito\\\tt b)~\sf a^2-22a+121\\\sf \sqrt{a^2}=a~~\sqrt{121}=11~~~2\cdot a\cdot11=22a\\\sf \acute e~trin\hat omio~quadrado~perfeito\end{array}}$

$\large\boxed{\begin{array}{l}\tt c)~\sf 4b^2+10b+25\\\sf\sqrt{4b^2}=2b~~\sqrt{25}=5~~~2\cdot2b\cdot5=20b\ne10b\\\sf n\tilde ao~\acute e~trin\hat omio~quadrado~perfeito\\\tt d)~\sf a^2x^2+2ax+1\\\sf \sqrt{a^2x^2}=ax~~\sqrt{1}=1~~2\cdot ax\cdot1=2ax\\\sf \acute e~trin\hat omio~quadrado~perfeito\\\tt e)~\sf y^2-2y+4\\\sf\sqrt{y^2}=y~~\sqrt{4}=2~~~2\cdot y\cdot2=4y\ne2y\\\sf n\tilde ao~\acute e~trin\hat omio~quadrado~perfeito\end{array}}$

$\large\boxed{\begin{array}{l}\tt f)~\sf x^2+5x+16\\\sf\sqrt{x^2}=x~~\sqrt{16}=4~~~2\cdot x\cdot4=8x\ne5x\\\sf n\tilde ao~\acute e~trin\hat omio~quadrado~perfeito\end{array}}$