Which expressions are factors of this polynomial? 2x^4 + x^3 - 29x^2 - 34x + 24

By Rational Root Theorem, all rational roots of a polynomial are in the form p/q, where p divides the constant term 24 and q divides the leading coefficient 2. One such root is 4. Factor the polynomial by dividing it by x-4.

Consider 2x³+9x²+7x-6. By Rational Root Theorem, all rational roots of a polynomial are in the form p/q, where p divides the constant term -6 and q divides the leading coefficient 2. One such root is -3. Factor the polynomial by dividing it by x+3.

Consider 2x²+3x-2. Factor the expression by grouping. First, the expression needs to be rewritten as 2x²+ax+bx-2. To find a and b, set up a system to be solved.

As ab is negative, a and b have the opposite signs. As a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -4.

Calculate the sum for each pair.

The solution is the pair that gives sum 3.

Rewrite as .

Exclude x in the first group and 2 in the second group.

Factor out common term 2x-1 by using distributive property.

Rewrite the complete factored expression.

step-by-step explanation:

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