Factor. 16j^2 - 8j + 1 ______

Question

Bytelearn · Accepted Answer

Check Perfect Square Trinomial: Determine if the quadratic can be factored as a perfect square trinomial. A perfect square trinomial is in the form (aj + b)^2 = a^2j^2 + 2abj + b^2. We need to check if 16j^2 - 8j + 1 fits this pattern. 16j^2 is a perfect square, as (4j)^2 = 16j^2. 1 is a perfect square, as (1)^2 = 1. The middle term, -8j, should be equal to 2 * (4j) * (1) = 8j for a perfect square trinomial, but we have -8j. Since the middle term is negative and the signs of the terms in a perfect square trinomial are the same, this is not a perfect square trinomial.Explore Other Factoring Techniques: Look for other factoring techniques since it is not a perfect square trinomial. We can try to factor by grouping or use the quadratic formula to see if the trinomial can be factored. The quadratic formula is not necessary for factoring, so we will attempt to factor by grouping.Factor by Grouping: Attempt to factor by grouping. To factor by grouping, we need to find two numbers that multiply to the product of the coefficient of j^2 (16) and the constant term (1), which is 16 * 1 = 16, and add up to the coefficient of j (-8). The numbers that satisfy these conditions are -4 and -4, since (-4) * (-4) = 16 and (-4) + (-4) = -8.Rewrite Middle Term: Rewrite the middle term using the numbers found in Step 3. 16j^2 - 8j + 1 can be rewritten as 16j^2 - 4j - 4j + 1. Now we can group the terms: (16j^2 - 4j) + (-4j + 1).Factor Each Group: Factor each group separately. From the first group (16j^2 - 4j), we can factor out 4j: 4j(4j - 1). From the second group (-4j + 1), we can factor out -1: -1(4j - 1). Now we have: 4j(4j - 1) - 1(4j - 1).Factor Out Common Binomial Factor: Factor out the common binomial factor. Both groups contain the common binomial factor (4j - 1). We can factor this out to get: (4j - 1)(4j - 1) or (4j - 1)^2.

Factor. $\newline$ $16j^2 - 8j + 1$

Full solution

More problems from Factor quadratics: special cases

Related topics

Factor.\newline16j2−8j+116j^2 - 8j + 116j2−8j+1

Factor. $\newline$ $16j^2 - 8j + 1$