Common Core: High School - Algebra : Rewriting Expressions Using its Structure: CCSS.Math.Content.HSA-SSE.A.2
Study concepts, example questions & explanations for Common Core: High School - Algebra
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Example Questions
Example Question #11 : Rewriting Expressions Using Its Structure: Ccss.Math.Content.Hsa Sse.A.2
Factor the quadratic expression.
To factor the quadratic expression
set up the expression in factored form, leaving blanks for the numbers that are not yet known.
At this point, you need to find two numbers - one for each blank. By looking at the original expression, a few clues can be gathered that will help find the two numbers. The product of these two numbers will be equal to the last term of the original expression (-9, or c in the standard quadratic formula), and their sum will be equal to the coefficient of the second term of the original expression (0, or b in the standard quadratic formula). Because their product is negative (-9) and the sum is zero, that must mean that they have different signs but the same absolute value.
Now, at this point, test a few different possibilities using the clues gathered from the original expression. In the end, it's found that the only numbers that work are 3 and -3, as the product of 3 and -3 is -9, and sum of 3 and -3 is 0. So, this results in the expression's factored form looking like...
This is known as a difference of squares.
Example Question #32 : Seeing Structure In Expressions
Factor the quadratic expression.
To factor the quadratic expression
set up the expression in factored form, leaving blanks for the numbers that are not yet known.
At this point, you need to find two numbers - one for each blank. By looking at the original expression, a few clues can be gathered that will help find the two numbers. The product of these two numbers will be equal to the last term of the original expression (-16, or c in the standard quadratic formula), and their sum will be equal to the coefficient of the second term of the original expression (0, or b in the standard quadratic formula). Because their product is negative (-16) and the sum is zero, that must mean that they have different signs but the same absolute value.
Now, at this point, test a few different possibilities using the clues gathered from the original expression. In the end, it's found that the only numbers that work are 4 and -4, as the product of 4 and -4 is -16, and sum of 4 and -4 is 0. So, this results in the expression's factored form looking like...
This is known as a difference of squares.
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