Answer: Step by step solution : STEP 1 : Equation at the end of step 1 ((22•3×2) – 13x) – 35 = 0 STEP 2 : Trying to factor by splitting the middle term 2.1 Factoring 12×2-13x-35 The first term is, 12×2 its coefficient is 12 . The middle term is, -13x its coefficient is -13 . The last term, “the constant”, is -35 Step-1 : Multiply the coefficient of the first term by the constant 12 • -35 = -420 Step-2 : Find two factors of -420 whose sum equals the coefficient of the middle term, which is -13 . -420 + 1 = -419 -210 + 2 = -208 -140 + 3 = -137 -105 + 4 = -101 -84 + 5 = -79 -70 + 6 = -64 -60 + 7 = -53 -42 + 10 = -32 -35 + 12 = -23 -30 + 14 = -16 -28 + 15 = -13 That’s it Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -28 and 15 12×2 – 28x + 15x – 35 Step-4 : Add up the first 2 terms, pulling out like factors : 4x • (3x-7) Add up the last 2 terms, pulling out common factors : 5 • (3x-7) Step-5 : Add up the four terms of step 4 : (4x+5) • (3x-7) Which is the desired factorization Equation at the end of step 2 : (3x – 7) • (4x + 5) = 0 STEP 3 : Theory – Roots of a product 3.1 A product of several terms equals zero. When a product of two or more terms equals zero, then at least one of the terms must be zero. We shall now solve each term = 0 separately In other words, we are going to solve as many equations as there are terms in the product Any solution of term = 0 solves product = 0 as well Step-by-step explanation: I HOPE THAT IT’S HELPFUL FOR YOU. Reply
Step-by-step explanation: [tex]\huge\color{yellow}\boxed{\colorbox{black}{♡Answer♡}}[/tex] The natural environment or natural world encompasses all living and non-living things occurring naturally, meaning in this case not artificial. The term is most often applied to the Earth or some parts of Earth Reply
Answer:
Step by step solution :
STEP
1
:
Equation at the end of step 1
((22•3×2) – 13x) – 35 = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 12×2-13x-35
The first term is, 12×2 its coefficient is 12 .
The middle term is, -13x its coefficient is -13 .
The last term, “the constant”, is -35
Step-1 : Multiply the coefficient of the first term by the constant 12 • -35 = -420
Step-2 : Find two factors of -420 whose sum equals the coefficient of the middle term, which is -13 .
-420 + 1 = -419
-210 + 2 = -208
-140 + 3 = -137
-105 + 4 = -101
-84 + 5 = -79
-70 + 6 = -64
-60 + 7 = -53
-42 + 10 = -32
-35 + 12 = -23
-30 + 14 = -16
-28 + 15 = -13 That’s it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -28 and 15
12×2 – 28x + 15x – 35
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (3x-7)
Add up the last 2 terms, pulling out common factors :
5 • (3x-7)
Step-5 : Add up the four terms of step 4 :
(4x+5) • (3x-7)
Which is the desired factorization
Equation at the end of step
2
:
(3x – 7) • (4x + 5) = 0
STEP
3
:
Theory – Roots of a product
3.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well
Step-by-step explanation:
I HOPE THAT IT’S HELPFUL FOR YOU.
Step-by-step explanation:
[tex]\huge\color{yellow}\boxed{\colorbox{black}{♡Answer♡}}[/tex]
The natural environment or natural world encompasses all living and non-living things occurring naturally, meaning in this case not artificial. The term is most often applied to the Earth or some parts of Earth