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Q- 49x square + 7x - 12
MATHEMATICS CLASS 8 FACTORISATION
Answers
Answer:
Step 1 :
Equation at the end of step 1 :
(72x2 - 7x) - 12 = 0
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 49x2-7x-12
The first term is, 49x2 its coefficient is 49 .
The middle term is, -7x its coefficient is -7 .
The last term, "the constant", is -12
Step-1 : Multiply the coefficient of the first term by the constant 49 • -12 = -588
Step-2 : Find two factors of -588 whose sum equals the coefficient of the middle term, which is -7 .
-588 + 1 = -587
-294 + 2 = -292
-196 + 3 = -193
-147 + 4 = -143
-98 + 6 = -92
-84 + 7 = -77
-49 + 12 = -37
-42 + 14 = -28
-28 + 21 = -7
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -28 and 21
49x2 - 28x + 21x - 12
Step-4 : Add up the first 2 terms, pulling out like factors :
7x • (7x-4)
Add up the last 2 terms, pulling out common factors :
3 • (7x-4)
Step-5 : Add up the four terms of step 4 :
(7x+3) • (7x-4)
Which is the desired factorization
Equation at the end of step 2 :
(7x - 4) • (7x + 3) = 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 : 7x-4 = 0
Add 4 to both sides of the equation :
7x = 4
Divide both sides of the equation by 7:
x = 4/7 = 0.571
Solving a Single Variable Equation :
3.3 Solve : 7x+3 = 0
Subtract 3 from both sides of the equation :
7x = -3
Divide both sides of the equation by 7:
x = -3/7 = -0.429