(2x+3)²2 =16 facatorisation method
Answers
Answer:
1.1 Evaluate : (2x-3)2 = 4x2-12x+9
Trying to factor by splitting the middle term
1.2 Factoring 4x2-12x-7
The first term is, 4x2 its coefficient is 4 .
The middle term is, -12x its coefficient is -12 .
The last term, "the constant", is -7
Step-1 : Multiply the coefficient of the first term by the constant 4 • -7 = -28
Step-2 : Find two factors of -28 whose sum equals the coefficient of the middle term, which is -12 .
-28 + 1 = -27
-14 + 2 = -12 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -14 and 2
4x2 - 14x + 2x - 7
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (2x-7)
Add up the last 2 terms, pulling out common factors :
1 • (2x-7)
Step-5 : Add up the four terms of step 4 :
(2x+1) • (2x-7)
Which is the desired factorization
Equation at the end of step
1
:
(2x - 7) • (2x + 1) = 0
STEP
2
:
Theory - Roots of a product
2.1 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.
Solving a Single Variable Equation:
2.2 Solve : 2x-7 = 0
Add 7 to both sides of the equation :
2x = 7
Divide both sides of the equation by 2:
x = 7/2 = 3.500
Solving a Single Variable Equation:
2.3 Solve : 2x+1 = 0
Subtract 1 from both sides of the equation :
2x = -1
Divide both sides of the equation by 2:
x = -1/2 = -0.500
your answer is the above picture
Step-by-step explanation:
I hope you got the best answer ...
