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Question
How to expand the middle term in quadratic polynomial
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Solution
The middle term of a quadratic equation is the term that has an 'x' in it but not the one that has 'x2' in it. For example, the middle term of the following quadratic equation.
2x2−4x−6=0 is −4x
Remember to take the sign at the left of the middle term as well.
Now to split the middle term, you have to find two numbers (negative or positive) that add up to give the number in the middle term. For example, the following pairs of numbers add up to give the number - 4 of the middle term:
1) -2 + - 2 = - 4
2) -3 + - 1 = - 4
3) - 5 + 1 = - 4
4) - 6 + 2 = - 4 Which of the above pairs of numbers should be taken. There is another rule to determine that: The product of the two parts of the middle term should be equal to the product of the first and last terms in the quadratic equation/expression. The first and last terms in the quadratic equation.
2x2−−4x−6=0
are 2x2 and −6. Their product is 2x2×−6=−12x2
So if you split the number of the middle term into two parts 'a' and 'b', then their product should be -12. Which of the pairs of numbers mentioned above multiply to give -12.
−6×2=−12
There fore these two numbers -6 and 2 will form the correct two parts of the middle term -4x of the quadratic equation 2x2−4x−6=0 Since -4x = -6x + 2x,
we can write -6x + 2x in place of -4x in the quadratic equation. That is, 2x2−4x−6=0 is same as
2x2−6x+2x−6=0
Similarly you will split the middle term of all other quadratic equations.
2x2−4x−6=0 is −4x
Remember to take the sign at the left of the middle term as well.
Now to split the middle term, you have to find two numbers (negative or positive) that add up to give the number in the middle term. For example, the following pairs of numbers add up to give the number - 4 of the middle term:
1) -2 + - 2 = - 4
2) -3 + - 1 = - 4
3) - 5 + 1 = - 4
4) - 6 + 2 = - 4
Which of the above pairs of numbers should be taken. There is another rule to determine that:
The product of the two parts of the middle term should be equal to the product of the first and last terms in the quadratic equation/expression.
The first and last terms in the quadratic equation.
2x2−−4x−6=0
are 2x2 and −6. Their product is 2x2×−6=−12x2
So if you split the number of the middle term into two parts 'a' and 'b', then their product should be -12. Which of the pairs of numbers mentioned above multiply to give -12.
−6×2=−12
There fore these two numbers -6 and 2 will form the correct two parts of the middle term -4x of the quadratic equation 2x2−4x−6=0
2x2−−4x−6=0
are 2x2 and −6. Their product is 2x2×−6=−12x2
So if you split the number of the middle term into two parts 'a' and 'b', then their product should be -12. Which of the pairs of numbers mentioned above multiply to give -12.
−6×2=−12
There fore these two numbers -6 and 2 will form the correct two parts of the middle term -4x of the quadratic equation 2x2−4x−6=0
Since -4x = -6x + 2x,
we can write -6x + 2x in place of -4x in the quadratic equation. That is, 2x2−4x−6=0 is same as
2x2−6x+2x−6=0
Similarly you will split the middle term of all other quadratic equations.
we can write -6x + 2x in place of -4x in the quadratic equation. That is, 2x2−4x−6=0 is same as
2x2−6x+2x−6=0
Similarly you will split the middle term of all other quadratic equations.
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