Can I get some exercise on this topic and answer it please

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ScanSolve AI Tutor · Accepted Answer

Here is an exercise on the topic of solving quadratic equations by factoring. Question: Solve the quadratic equation: x² + 5x + 6 = 0 Solution: Step 1: We need to find two numbers that multiply to 6 and add up to 5. These numbers are 2 and 3. Step 2: Rewrite the middle term (5x) using these two numbers: x² + 2x + 3x + 6 = 0. Step 3: Factor by grouping. Group the first two terms and the last two terms: (x² + 2x) + (3x + 6) = 0. Step 4: Factor out the greatest common factor from each group: x(x + 2) + 3(x + 2) = 0. Step 5: Notice that (x + 2) is a common factor. Factor it out: (x + 2)(x + 3) = 0. Step 6: Set each factor equal to zero and solve for x: x + 2 = 0 ⟹ x = −2; x + 3 = 0 ⟹ x = −3; The solutions are x = −2 and x = −3. Final Answer: The solutions to the equation x² + 5x + 6 = 0 are x = −2 and x = −3.

Can I get some exercise on this topic and answer it please

Step-by-step solution

We need to find two numbers that multiply to 6 and add up to 5.

Rewrite the middle term (5x) using these two numbers

Factor by grouping.

Factor out the greatest common factor from each group

Notice that (x + 2) is a common factor.

Set each factor equal to zero and solve for x

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