Simplify:
(2a2 + 5) (2a2 + 7) + 5
Answers
Answer:
Given expression is: (a
3
−2a
2
+4a−5)−(−a
3
−8a+2a
2
+5)
=a
3
−2a
2
+4a−5+a
3
+8a−2a
2
−5
=2a
3
−4a
2
+12a−10
Hence simplified form of the given expression is =2a
3
−4a
2
+12a−10
Step-by-step explanation:
×
☰
Logo Icon
Simplification or other simple results
Calculator Icon
Camera Icon
Handwritting Icon
Enter an equation or a problem
We think you wrote:
2a2(5a-6)-5a(a2-3a+4)-7(a-5)
This deals with simplification or other simple results.
Overview
Steps
Topics
1 result(s) found
5a
3
+3a
2
−27a+35
See steps
Step by Step Solution:
More Icon
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "a2" was replaced by "a^2". 1 more similar replacement(s).
STEP
1
:
Equation at the end of step 1
(((2•(a2))•(5a-6))-(5a•(((a2)-3a)+4)))-7•(a-5)
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring a2-3a+4
The first term is, a2 its coefficient is 1 .
The middle term is, -3a its coefficient is -3 .
The last term, "the constant", is +4
Step-1 : Multiply the coefficient of the first term by the constant 1 • 4 = 4
Step-2 : Find two factors of 4 whose sum equals the coefficient of the middle term, which is -3 .
-4 + -1 = -5
-2 + -2 = -4
-1 + -4 = -5
1 + 4 = 5
2 + 2 = 4
4 + 1 = 5
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step
2
:
(((2•(a2))•(5a-6))-5a•(a2-3a+4))-7•(a-5)
STEP
3
:
Equation at the end of step
3
:
((2a2•(5a-6))-5a•(a2-3a+4))-7•(a-5)
STEP
4
:
Equation at the end of step 4
(2a2•(5a-6)-5a•(a2-3a+4))-7•(a-5)
STEP
5
:
Checking for a perfect cube
5.1 5a3+3a2-27a+35 is not a perfect cube
Trying to factor by pulling out :
5.2 Factoring: 5a3+3a2-27a+35
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -27a+35
Group 2: 3a2+5a3
Pull out from each group separately :
Group 1: (-27a+35) • (1) = (27a-35) • (-1)
Group 2: (5a+3) • (a2)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
5.3 Find roots (zeroes) of : F(a) = 5a3+3a2-27a+35
Polynomial Roots Calculator is a set of methods aimed at finding values of a for which F(a)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers a which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 5 and the Trailing Constant is 35.
The factor(s) are:
of the Leading Coefficient : 1,5
of the Trailing Constant : 1 ,5 ,7 ,35
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 60.00
-1 5 -0.20 40.48
-5 1 -5.00 -380.00
-7 1 -7.00 -1344.00
-7 5 -1.40 64.96
-35 1 -35.00 -209720.00
1 1 1.00 16.00
1 5 0.20 29.76
5 1 5.00 600.00
7 1 7.00 1708.00
7 5 1.40 16.80
35 1 35.00 217140.00
Polynomial Roots Calculator found no rational roots
Final result :
5a3 + 3a2 - 27a + 35
Terms and topics
More Icon
Canceling out