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

Question

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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Tryphena 4 weeks 2021-08-18T10:56:01+00:00 2 Answers 1 views 0

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    0
    2021-08-18T10:57:25+00:00

    Answer:

    Step-by-step 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

    0
    2021-08-18T10:58:00+00:00

    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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