Without actual division, prove that \(2x^4– 5x^3+ 2x^2– x + 2\) is divisible by \(x^2– 3x + 2\).
Proof:
Wa can prove by showing of quadraitc polynomial \(x^2– 3x + 2\) is also the of the polynomial \(2x^4– 5x^3+ 2x^2– x + 2\).
On factoring \(x^2– 3x + 2\) by splitting the middle term.
\(x^2– 3x + 2\) \(=\)
[Note: Let's solve further based on ascending order of the factor value.]
Let \(p(x) = 2x^4 - 5x^3 + 2x^2 - x + 2\) and one of the factor \(q(x) =\) .
We know that \(q(x) = 0\).
Thus, \(x =\)
Substituing the above value \(x\) in the polynomial \(p(x)\),
we have \(p(\)\() = \)
Let \(p(x) = 2x^4 - 5x^3 + 2x^2 - x + 2\) and \(g(x) =\) .
We know that \(g(x) = 0\).
Thus, \(x =\)
Substituing the above value \(x\) in the polynomial \(p(x)\),
we have \(p(\)\() = \)
Answer variants:
\(x-2\)
factors
multiples
\(0\)
\(1\)
\(2\)
\(x-1\)