Question

mat1033-2257-7474tr@7amintermediate algebra
question 2, 6.4.9 part 1 of 3
score: 11.11%, 1 of 9 points
points: 0 of 1
factor the trinomial by grouping. 8x² + 14x + 3
a. find two numbers whose product is 8·3 = 24 and whose sum is 14.
b. write 14x using the factors from part (a).
c. factor by grouping.
a. the two numbers with a product of 24 and a sum of 14 are (use a comma to separate answers as needed.)

Explanation:

Step1: Find two - factor numbers

We need two numbers \(m\) and \(n\) such that \(m\times n=24\) and \(m + n=14\). By listing the factor - pairs of 24: \((1,24)\), \((2,12)\), \((3,8)\), \((4,6)\). The pair \((2,12)\) satisfies \(2 + 12=14\).

Step2: Rewrite the middle term

Rewrite \(14x\) as \(2x+12x\). So the trinomial \(8x^{2}+14x + 3\) becomes \(8x^{2}+2x+12x + 3\).

Step3: Factor by grouping

Group the terms: \((8x^{2}+2x)+(12x + 3)\). Factor out the greatest common factor from each group. From \(8x^{2}+2x\), we get \(2x(4x + 1)\), and from \(12x+3\), we get \(3(4x + 1)\). Then, \((8x^{2}+2x)+(12x + 3)=(4x + 1)(2x+3)\).

For part (a) of the original question:

Answer:

2,12