Let x = theta. Substitute x into the expression to form a quadratic equation.

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To resolve the expression 2 cos² θ + 13 cos θ + 15 into factors. Step 1: Let x = cos θ. Substitute x into the expression to form a quadratic equation. 2x² + 13x + 15 Step 2: Factor the quadratic expression by splitting the middle term. We need two numbers that multiply to 2 × 15 = 30 and add up to 13. These numbers are 3 and 10. 2x² + 3x + 10x + 15 Step 3: Group the terms and factor out common factors from each group. (2x² + 3x) + (10x + 15) x(2x + 3) + 5(2x + 3) Step 4: Factor out the common binomial factor (2x + 3). (2x + 3)(x + 5) Step 5: Substitute back cos θ for x. (2 cos θ + 3)(cos θ + 5) The factored expression is: (2 cos θ + 3)(cos θ + 5)

Let x = theta. Substitute x into the expression to form a quadratic equation.

Answer

Step-by-step solution

Let $x = \cos \theta$ .

Factor the quadratic expression by splitting the middle term.

Group the terms and factor out common factors from each group.

Factor out the common binomial factor $(2x + 3)$ .

Substitute back $\cos \theta$ for $x$ .

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Let x = theta. Substitute x into the expression to form a quadratic equation.

Answer

Step-by-step solution

Let x=cos⁡θx = \cos \thetax=cosθ.

Factor the quadratic expression by splitting the middle term.

Group the terms and factor out common factors from each group.

Factor out the common binomial factor (2x+3)(2x + 3)(2x+3).

Substitute back cos⁡θ\cos \thetacosθ for xxx.

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More Mathematics Questions

Let $x = \cos \theta$ .

Factor out the common binomial factor $(2x + 3)$ .

Substitute back $\cos \theta$ for $x$ .