Factor completely and then place the factors in the proper location on the grid.
4n2 + 28n + 49
Recognize the perfect square form, a^2+2ab+b^2 = (a + b)^2
4n^2 + 28n + 49
(2n + 7)^2
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wolfram alpha
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Wolfram Alpha: Computation Knowledge Engine
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4n^2+28n+49
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To factor the quadratic expression 4n^2 + 28n + 49, we need to look for two binomial factors that, when multiplied together, give us the given expression.
Step 1: Determine the factors of the product of the coefficient of the squared term (4) and the constant term (49). In this case, the product is 4 * 49 = 196.
The factors of 196 are:
1, 196
2, 98
4, 49
7, 28
14, 14
Step 2: Look for a pair of factors that can be combined in such a way that their sum equals the coefficient of the linear term (28). In this case, the pair is 7 and 28.
Step 3: Rewrite the original quadratic expression by splitting the linear term (28n) into two terms, using the pair of factors found in Step 2.
4n^2 + 7n + 21n + 49
Step 4: Group the terms and factor out the greatest common factor (GCF) from each group.
(4n^2 + 7n) + (21n + 49)
GCF of the first group: n
GCF of the second group: 7
n(4n + 7) + 7(3n + 7)
Step 5: Factor out the GCF (4n + 7) from both terms.
(n + 7)(4n + 7)
The completely factored form of the given quadratic expression 4n^2 + 28n + 49 is (n + 7)(4n + 7).