Factorise a² + 5 ab – 104 b².
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Answer:
Solution
Step-by-step explanation:
In the given polynomial a
In the given polynomial a 2
In the given polynomial a 2 +5a−104,
In the given polynomial a 2 +5a−104,The first term is a
In the given polynomial a 2 +5a−104,The first term is a 2
In the given polynomial a 2 +5a−104,The first term is a 2 and its coefficient is 1.
In the given polynomial a 2 +5a−104,The first term is a 2 and its coefficient is 1.The middle term is 5a and its coefficient is 5.
In the given polynomial a 2 +5a−104,The first term is a 2 and its coefficient is 1.The middle term is 5a and its coefficient is 5.The last term is a constant term −104.
In the given polynomial a 2 +5a−104,The first term is a 2 and its coefficient is 1.The middle term is 5a and its coefficient is 5.The last term is a constant term −104.Multiply the coefficient of the first term by the constant 1×−104=−104.
In the given polynomial a 2 +5a−104,The first term is a 2 and its coefficient is 1.The middle term is 5a and its coefficient is 5.The last term is a constant term −104.Multiply the coefficient of the first term by the constant 1×−104=−104.We now find the factor of −104 whose sum equals the coefficient of the middle term, which is 5 and then factorize the polynomial a
2
2 +5a−104 as shown below:
2 +5a−104 as shown below:
2 +5a−104 as shown below: a
2 +5a−104 as shown below: a 2
2 +5a−104 as shown below: a 2 +5a−104
2 +5a−104 as shown below: a 2 +5a−104=a
2 +5a−104 as shown below: a 2 +5a−104=a 2
2 +5a−104 as shown below: a 2 +5a−104=a 2 +13a−8a−104
2 +5a−104 as shown below: a 2 +5a−104=a 2 +13a−8a−104=a(a+13)−8(a+13)
2 +5a−104 as shown below: a 2 +5a−104=a 2 +13a−8a−104=a(a+13)−8(a+13)=(a−8)(a+13)
2 +5a−104 as shown below: a 2 +5a−104=a 2 +13a−8a−104=a(a+13)−8(a+13)=(a−8)(a+13)Hence, a
2 +5a−104 as shown below: a 2 +5a−104=a 2 +13a−8a−104=a(a+13)−8(a+13)=(a−8)(a+13)Hence, a 2
2 +5a−104 as shown below: a 2 +5a−104=a 2 +13a−8a−104=a(a+13)−8(a+13)=(a−8)(a+13)Hence, a 2 +5a−104=(a−8)(a+13).
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