Factor: 3y2 – 7y – 6.We will assume that 3y2 – 7y – 6 is the product of two binomials and we will use a systematic method to find their terms.Since the terms of 3y2 – 7y – 6 do not have a common factor (other than 1), the only option available is to try to factor it as the product of two binomials.Since the first term is 3y², the first terms of the binomial factors must be 3y and y.ЗуD)Because 3y · y will give 3y2.The second terms of the binomials must be two integers whose product is -6. There are four such pairs: 1(-6), –1(6), 2(-3), and -2(3). When these pairs are entered,and then reversed, as second terms of the binomials, there are eight possibilities to consider. Four of them can be discarded because they include a binomial whose termshave a common factor. If 3y2 – 7y – 6 does not have a common factor (other than 1), neither can any of its binomial factors.Outer: 18yFor the factors –1 and 6: (3y – 1)(y + 6)(Зу + 6)orWe cross this possibility out.A common factor of 3Inner: -y18у — у %3D 17уOuter: -18y(3y + 1)(y -O)For the factors 1 and -6:or(Зу — 6)(у + 1)Inner: yWe cross this possibility out.A common factor of 3-18y + y = -17yOuter: 9y(3y + 3)(y -D)For the factors –2 and 3: (3y – 2)(y + 3)or(Зу + 3)Inner: -2yWe cross this possibility out.A common factor of 39y – 2y = 7yOuter: -9yFor the factors 2 and –3: (3y + 2)(y – 3)(3y-v + 2)orInner: 2yWe cross this possibility out.A common factor of 3-9y + 2y-7yOnly the possibility shown in blue gives the correct middle term of -7y. Thus, Only the possibility shown in blue gives the correct middle term of –7y. Thus,3y2 – 7y – 6 = (3y + 2)(y – 3).Check the factorization by multiplication.Factor: 5t29t – 18.-

Question

Accepted Answer

Quadratic equation 5t2 -9t- 18
To factorize the equation

Factor: 5t2 – 9t – 18.