Answer:
(3x+4)(5x+7)
Step-by-step explanation:
15x^2
+41x+28
Factor the expression by grouping. First, the expression needs to be rewritten as 15x^2
+ax+bx+28. To find a and b, set up a system to be solved.
a+b=41
ab=15×28=420
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 420.
1,420
2,210
3,140
4,105
5,84
6,70
7,60
10,42
12,35
14,30
15,28
20,21
Calculate the sum for each pair.
1+420=421
2+210=212
3+140=143
4+105=109
5+84=89
6+70=76
7+60=67
10+42=52
12+35=47
14+30=44
15+28=43
20+21=41
The solution is the pair that gives sum 41.
a=20
b=21
Rewrite 15x^2
+41x+28 as (15x^2
+20x)+(21x+28).
(15x^2
+20x)+(21x+28)
Factor out 5x in the first and 7 in the second group.
5x(3x+4)+7(3x+4)
Factor out common term 3x+4 by using distributive property.
(3x+4)(5x+7)
Answer:
The answer is A
Step-by-step explanation:
Step-by-step explanation:
Since, x=8 and x=-5 are the roots.
Therefore, (x - 8) & (x - 5) will be factors.
Hence, required quadratic equation can be given as:
Mid point of the points PQ is (₋0.3 , 3.25)
Given points are:
P(₋2 , 2.5)
Q(1.4 , 4)
midpoint of PQ = ?
A location in the middle of a line connecting two points is referred to as the midpoint. The midpoint of a line is located between the two reference points, which are its endpoints. The line that connects these two places is split in half equally at the halfway.
The midpoint calculation is the same as averaging two numbers. As a result, by adding any two integers together and dividing by two, you may find the midpoint between them.
Midpoint formula (x,y) = (x₁ ₊ x₂/2 , y₁ ₊ y₂/2)
we have two points:
P(₋2,2.5) = (x₁,y₁)
Q(1.4,4) = (x₂,y₂)
Midpoint = (₋2 ₊ 1.4/2 , 2.5₊4/2)
= (₋0.6/2 , 6.5/2)
= (₋0.3 , 3.25)
Hence we determined the midpoint of PQ as (₋0.3 , 3.25)
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