Rewrite x2 + 5x + 6 as an equivalent expression in the form x2 + rx + sx + 6, then factorize.

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3.1.3 Rewrite x² + 5x + 6 as an equivalent expression in the form x² + rx + sx + 6. Step 1: Identify the values for r and s. From the previous activity (question 2.5, which was part of 3.1), the two integers that multiply to 6 and add to 5 are 2 and 3. So, r=2 and s=3. Step 2: Substitute r and s into the expression. x² + 2x + 3x + 6 The equivalent expression is x² + 2x + 3x + 6. 3.1.4 Use the knowledge obtained from activity 2 on grouping and the distributive property to factorize the expression. Step 1: Group the terms from the expression in 3.1.3. (x² + 2x) + (3x + 6) Step 2: Factor out the common factor from the first group. x(x + 2) Step 3: Factor out the common factor from the second group. 3(x + 2) Step 4: Combine the factored groups. x(x + 2) + 3(x + 2) Step 5: Factor out the common binomial factor (x + 2). (x + 2)(x + 3) The factorized expression is (x + 2)(x + 3).

Rewrite x2 + 5x + 6 as an equivalent expression in the form x2 + rx + sx + 6, then factorize.

Answer

Step-by-step solution

Identify the values for $r$ and $s$ .

Substitute $r$ and $s$ into the expression.

Group the terms from the expression in 3.1.3.

Factor out the common factor from the first group.

Factor out the common factor from the second group.

Combine the factored groups.

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

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Rewrite x2 + 5x + 6 as an equivalent expression in the form x2 + rx + sx + 6, then factorize.

Answer

Step-by-step solution

Identify the values for rrr and sss.

Substitute rrr and sss into the expression.

Group the terms from the expression in 3.1.3.

Factor out the common factor from the first group.

Factor out the common factor from the second group.

Combine the factored groups.

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

Try one yourself

Still stuck on this one?

More Mathematics Questions

Identify the values for $r$ and $s$ .

Substitute $r$ and $s$ into the expression.

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