Answer:
Roots of the cubic equation.
Explanation:
Factoring: 16x3+80x2-9x-45
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -9x-45
Group 2: 16x3+80x2
Pull out from each group separately :
Group 1: (x+5) • (-9)
Group 2: (x+5) • (16x2)
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Add up the two groups :
(x+5) • (16x2-9)
3.3 Factoring: 16x2-9
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 16 is the square of 4
Check : 9 is the square of 3
Check : x2 is the square of x1
Factorization is : (4x + 3) • (4x - 3)
Final result :
(4x + 3) • (4x - 3) • (x + 5)
Terms and topics
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hence, answer is (4x+3)