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Factor x 2 – 7 x – 18.

–18 can be factored in the following ways:

(1)(–18), (–1)(18), (2)(–9), (–2)(9), (3)(–6), (–3)(6)

The only combination whose sum is also –7 is (2)(–9), so

x 2 – 7 x + 18 = ( x + 2)( x – 9)

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Example: Find the GCF of 198 and 360 using the division method.

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Example: Find the GCF of 198 and 360 using the division method.

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Among the given two numbers, 360 is the larger number and 198 is the smaller number.

Step 1 - Divide the larger number by the smaller number using long division.

Step 2 - If the remainder is 0, then the divisor is the GCF. If the remainder is not 0, then make the remainder of the above step as the divisor and the divisor of the above step as the dividend and perform long division again.

Step 3 - If the remainder is 0, then the divisor of the last division is the GCF. If the remainder is not 0, then we have to repeat step 2 until we get the remainder 0.

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Let's take two binomials (x + 2) and (x + 3) and multiply them with the help of the following steps.

Step 1: To multiply (x + 2)(x + 3), we will take the first term of the first binomial and multiply it with the second binomial, i.e., x(x + 3)

Step 2: Now, we will take the second term of the first binomial and multiply it with the second binomial, i.e., 2(x + 3)

Step 3: We will combine the results of Step 1 and Step 2 and add them, i.e., x(x + 3) + 2(x + 3)

Step 4: Now we will apply the distributive property to x(x + 3) and 2(x + 3) and individually expand them, i.e., x(x + 3) = x² + 3x and 2(x + 3) = 2x + 6

Step 5: We will now add the results obtained in Step 4 by combining the like terms, i.e., x² + 3x + 2x + 6 = x² + 5x + 6

Thus, the product of (x + 2)(x + 3) = x² + 5x + 6. Let us understand this with the help of the calculation shown below.