Simplify : 12a² + 3(a? – a) – 4a (5 + a)
Answers
Answer:
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Answer:
Changes made to your input should not affect the solution:
(1): "a2" was replaced by "a^2".
Step by step solution :
STEP
1
:
Equation at the end of step 1
((22•3a2) + 19a) + 5 = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 12a2+19a+5
The first term is, 12a2 its coefficient is 12 .
The middle term is, +19a its coefficient is 19 .
The last term, "the constant", is +5
Step-1 : Multiply the coefficient of the first term by the constant 12 • 5 = 60
Step-2 : Find two factors of 60 whose sum equals the coefficient of the middle term, which is 19 .
-60 + -1 = -61
-30 + -2 = -32
-20 + -3 = -23
-15 + -4 = -19
-12 + -5 = -17
-10 + -6 = -16
-6 + -10 = -16
-5 + -12 = -17
-4 + -15 = -19
-3 + -20 = -23
-2 + -30 = -32
-1 + -60 = -61
1 + 60 = 61
2 + 30 = 32
3 + 20 = 23
4 + 15 = 19 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 4 and 15
12a2 + 4a + 15a + 5
Step-4 : Add up the first 2 terms, pulling out like factors :
4a • (3a+1)
Add up the last 2 terms, pulling out common factors :
5 • (3a+1)
Step-5 : Add up the four terms of step 4 :
(4a+5) • (3a+1)
Which is the desired factorization
Equation at the end of step
2
:
(3a + 1) • (4a + 5) = 0
STEP
3
:
Theory - Roots of a product
3.1 A product of several terms equals zero.