factorise by using factor theoram 21x^2-x-2
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Answer:
Step by Step Solution:
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Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
Step by step solution :
STEP
1
:
Equation at the end of step 1
((3•7x2) - x) - 2 = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 21x2-x-2
The first term is, 21x2 its coefficient is 21 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -2
Step-1 : Multiply the coefficient of the first term by the constant 21 • -2 = -42
Step-2 : Find two factors of -42 whose sum equals the coefficient of the middle term, which is -1 .
-42 + 1 = -41
-21 + 2 = -19
-14 + 3 = -11
-7 + 6 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and 6
21x2 - 7x + 6x - 2
Step-4 : Add up the first 2 terms, pulling out like factors :
7x • (3x-1)
Add up the last 2 terms, pulling out common factors :
2 • (3x-1)
Step-5 : Add up the four terms of step 4 :
(7x+2) • (3x-1)
Which is the desired factorization
Equation at the end of step
2
:
(3x - 1) • (7x + 2) = 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.
Solving a Single Variable Equation:
3.2 Solve : 3x-1 = 0
Add 1 to both sides of the equation :
3x = 1
Divide both sides of the equation by 3:
x = 1/3 = 0.333
Solving a Single Variable Equation:
3.3 Solve : 7x+2 = 0
Subtract 2 from both sides of the equation :
7x = -2
Divide both sides of the equation by 7:
x = -2/7 = -0.286
Supplement : Solving Quadratic Equation Directly
Solving 21x2-x-2 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Answer:
21x^2-x-2
= 21x^2-7x+6x-2
= 7x(3x-1)-2(3x-1)
= (7x-2) (3x-1)
I hope that this answer is useful for you