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

[tex]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[/tex]

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Sueraiuka Sueraiuka · Answer 2 · 2021-06-25T16:24:40+02:00

Sueraiuka Sueraiuka

25-06-2021

Answer:

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!

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

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