Help! I've been having troubles on these questions and really need some help. 1. A strategy got factoring trinomials of the form x^2+bx+c was developed by exploring the product of binomials (x+p) and (x+q).
a) Explain how the development of this factoring strategy is an example of working backwards to solve a problem
b) Explain why px+qx=(9+q)x
c) Explain why the expression x^2+(p+q)x+pq leads to the need to determine integers that add to b and have a product of c when factoring a trinomial of the form x^2+bx+c.

2. Juan is trying to factor x^2+7x+3 and makes the following table (in photo)
Juan concluded that x^2+7x+3 cannot be factored using integers.
a) Is Juan Correct?
b) Comment on Juan's strategy and improve it if possible.

3. Factor each of the following expressions.
a) x^2+9x+20 (My answer I got was (x+5)(x+4))
b) 10n^2+n-3 (For this, I think I got (2n-1)(5n+3)
c) 2(d^2-4de+3e^2 (My answer was 2(d^2-4de+3e^2))

a

step-by-step explanation:

u take $30 minus $24. the answer/original($30)

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.