Question

Verify that (x + a)(x+b)(x+c) is factor of f(x)= x³ +(a+b+c)x²+(ab + ac + bc)x + abc.​

Answer 1

Explanation:

Hey there!

Please look explanation in picture. As all the factor gives us "0" while putting them in equation, it is verified that they are the factors of f(x).

Hope it helps!

Answer 2

Explanation:

`LHS = \\\\=(x+a)(x+b)(x+c) \\\\=(x+a)(x^2 + cx + bx + bc)\\\\=x(x^2 +(b+c)x + bc) + a(x^2 + (b+c)x + bc)\\\\=x^3 + (b+c)x^2 + bcx+ ax^2 + (b+c)ax+ abc\\\\=x^3 + ax^2 + (b+c)x^2 + bcx + abx + acx + abc\\\\=x^3 + (a+b+c)x^2 + (ab+ac+bc)x+ abc\\\\= RHS`