Presentation on theme: "There is a pattern for factoring trinomials of this form, when c"— Presentation transcript:
1There is a pattern for factoring trinomials of this form, when c Factoring PatternsThere is a pattern for factoring trinomials of this form, when cis positivex² + bx + c
2Trinomials have 3 terms x² + 9x +8 The first term is of degree two and so the term is called a quadratic termThe second term is called the linear termThe last term is called the constant(it has no variable factor)The trinomial itself is called a quadratic polynomial
3Examples of trinomials in this form x² + 9x + 8r² + 10 r + 24y² - 14y + 13m² - 10m + 16NOTE: coefficient of quadratic term is 1constant term is positiveNotice that in each case the coefficient of the quadratic term is 1 and the constant term is positive.
4To factor trinomials like x² + 8x + 16 List pairs of factors whose product equal the constant term4 4Find the pair of factors whose sum equals the coefficient of the linear term.4 + 4 = 8
6y² + 20y + 36 Factors of 36 1 36 6 6 9 4 12 3 18 2 Sum of factors 37 Sum of factors3712131520
7So factor y² + 20y + 36 (y + 18) ( y + 2) Check by multiplying the binomials using FOILy² + 2y + 18y + 36y² + 20y + 36
8Factor x² - 12x + 20Since the linear term is negative and the constant term is positive we must list the negative factors of 20.
9So factor x² - 12x + 20We know the only possible factors are –2 and –10 so we write(x – 2)(x – 10)Check by applying FOILx² -10x –2x + 20x² - 12x + 20
10Another Factoring Pattern x² - ax – cThere is also a pattern for factoring trinomials of this form when c is negative
11Trinomials with three terms x² + 29x – 30m² + 12m – 36k² - 25 k – 54g² -g – 2Note: coefficient of quadratic term is 1constant term is negative
12To factor trinomials like x² + 7x - 18 List pairs of factors of -18Sum of factors3-3-7717-17
13So factor x² + 7x - 18Since the linear term is positive select factors which give a positive result when added. But remember, because the constant term is negative, one factor must be negative. Using the preceding factor list we can write(x + 9) (x – 2)Check using FOIL x² - 2x + 9x – 18x² + 7x - 18