Method 2 4g2 + 11g + 6 Use number sense and reasoning, with mental math. The factors of 4g2 are 4g and 1g, or 2g and 2g. The factors of 6 are 6 and 1, or 3 and 2. Arrange the factor combinations vertically. 4g 6 2g 6 Form the products, then add. 1g 1 2g 1 4g + 6g = 10g 2g + 12g = 14g These combinations don’t work. Try a different combination. 4g 3 Form the products, then add. 1g 2 8g + 3g = 11g This is the correct combination of factors. So, 4g2 + 11g + 6 = (4g + 3)(g + 2) b) Method 1 6m2 7m 10 – – Find the factors of the form (am + + b)(cm d). The coefficient of is 6, so the coefficients of the 1st terms in the binomial are m2 factors of 6, which are 1 and 6, or 2 and 3. The constant term in the trinomial is so the 2nd in the binomial are factors –10, of which are 1 and or and 10, or and 5, or 2 and –10, –10, –1 –2 –5. The coefficient of the middle term of the trinomial, is between the coefficients of –7, the other two terms, so try combinations of the lesser factors first; that is, try combinations of 1 and 6 with combinations of ±2 and ±5. So, the binomials could be: (m + 2)(6m 5) or (m 5)(6m + 2) or – – (m 2)(6m + 5) or (m + 5)(6m 2) – – Check if any of the 4 binomial products above has its equal to m-term –7m. (m + 2)(6m 5) = 6m2 + 7m 10 – – (m 5)(6m + 2) = 6m2 28m 10 – – – (m 2)(6m + 5) = 6m2 7m 10 – – – This is the correct trinomial so we need not any further. 6m2 7m 10 = (m 2)(6m + 5) – – – (Solution continues.)
Method 2 4g2 + 11g + 6 Use number sense and reasoning, with mental math. The factors of 4g2 are 4g and 1g, or 2g and 2g. The factors of 6 are 6 and 1, or 3 and 2. Arrange the factor combinations vertically. 4g 6 2g 6 Form the products, then add. 1g 1 2g 1 4g + 6g = 10g 2g + 12g = 14g These combinations don’t work. Try a different combination. 4g 3 Form the products, then add. 1g 2 8g + 3g = 11g This is the correct combination of factors. So, 4g2 + 11g + 6 = (4g + 3)(g + 2) b) Method 1 6m2 – 7m – 10 Find the factors of the form (am + b)(cm + d). The coefficient of m2 is 6, so the coefficients of the 1st terms in the binomial are factors of 6, which are 1 and 6, or 2 and 3. The constant term in the trinomial is –10, so the 2nd in the binomial are factors of –10, which are 1 and –10, or –1 and 10, or –2 and 5, or 2 and –5. The coefficient of the middle term of the trinomial, –7, is between the coefficients of the other two terms, so try combinations of the lesser factors first; that is, try combinations of 1 and 6 with combinations of ±2 and ±5. So, the binomials could be: (m + 2)(6m – 5) or (m – 5)(6m + 2) or (m – 2)(6m + 5) or (m + 5)(6m – 2) Check if any of the 4 binomial products above has its m-term equal to –7m. (m + 2)(6m – 5) = 6m2 + 7m – 10 (m – 5)(6m + 2) = 6m2 – 28m – 10 (m – 2)(6m + 5) = 6m2 – 7m – 10 This is the correct trinomial so we need not any further. 6m2 – 7m – 10 = (m – 2)(6m + 5) (Solution continues.)
miap_ch3_notes.docx