16x2 - 25 = (4x + 5) ( 4x - 5)
16x^2 - 25 Recognise that both 16 and 25 are squared numbers, 16 = 4^(2) & 25 = 5^(2) Substituting 4^(2)x^(2) - 5^(2) = > (4x)^(2) - 5^(2) We now have two squared terms with a negative between them. NB two squared terms with positive does NOT factor. Factoring (4x - 5)(4x + 5)
If you mean 5x^2 -125 then it is 5(x^2 -25) when factored
The difference of two squares is quick way to factor polynomials when certain constraints are met: Namely that you have two squares (e.g. 4, 25, 36x2 , 144a6) and one is subtracting from the others (e.g. 25 - 36x2). IF these two constraints are met, then you are able to factor the polynomial by finding the square roots of the squares. sqrt(25)=5 sqrt(36x2) = 6x Therefore 25 - 36x2 = (5+6x)(5-6x) in factored form. In general, given any two squares, a2 and b2, AND they are subtracting, a2 - b2, you can factor them to be (a + b)(a - b).
n + 25 =====
16x2 - 25 = (4x + 5) ( 4x - 5)
Factor the polynomial x2 - 10x + 25. Enter each factor as a polynomial in descending order.
16x2 + 40x + 25 = 16x2 + 20x + 20x + 25 = 4x(4x + 5) + 5(4x + 5) = (4x + 5)(4x + 5) = (4x + 5)2
-23
25(10x2 - 1)
(4x + 5)(4x + 5)
2(2g2 - 25)
4x+516x2 + 40x + 25= (4x + 5) (4x + 5)
(r + 5)(r + 5)
16x2 - 25 is a quadratic polynomial which defines the function f(x) = 16x2 - 25, whose graph is a parabola. Since the x-term is missing, then the y-axis is also the axis of symmetry. When x = 0, then f(x) = -25, so that (0, -25) is the y-intercept point, which also is the vertex of the parabola (the vertex lies on the symmetry line). When f(x) = 0, we have 16x2 - 25 = 0 factor the difference of the two squares (4x - 5)(4x + 5) = 0 let each factor equal to zero 4x - 5 = 0 or 4x + 5 = 0 x = 5/4 or x = -5/4 Thus, (-5/4, 0) and (5/4, 0) are the x-intercepts points. Plot the points on a coordinate system and draw the parabola that passes through them.
(x - 5)(x - 5)
(2x + 5)(2x - 5)