 - 5*n**4.
2*n*(n - 1)**3*(n + 1)
Let i(t) be the second derivative of 0 + 0*t**2 - 1/15*t**3 - 12*t + 1/30*t**4. What is w in i(w) = 0?
0, 1
Suppose 3*o = 5*y + 113 - 122, 0 = -5*y - 3*o - 9. Factor y - 1/5*b**5 - 1/5*b**2 + 1/5*b**4 + 1/5*b**3 + 0*b.
-b**2*(b - 1)**2*(b + 1)/5
Find y, given that 2/3*y**4 - 46/9*y**2 - 88/9*y - 8/3 + 8/9*y**3 = 0.
-2, -1/3, 3
Let v(y) be the third derivative of 83*y**5/30 - 41*y**4/6 - y**3/3 + 282*y**2. Factor v(b).
2*(b - 1)*(83*b + 1)
Let a be 0/(-7*(2 + 96/(-42))). Factor a + 1/6*r + 0*r**2 - 1/6*r**3.
-r*(r - 1)*(r + 1)/6
Let a(k) be the third derivative of k**9/7560 + k**8/1680 - k**7/1260 - k**6/180 + 25*k**4/24 + 31*k**2. Let r(p) be the second derivative of a(p). Factor r(x).
2*x*(x - 1)*(x + 1)*(x + 2)
Let d(k) be the third derivative of k**5/60 - 11*k**4/12 - 23*k**3/6 - 65*k**2. Let d(w) = 0. What is w?
-1, 23
Let z = 550/9 + -61. Suppose -13 = -2*a - 5. Factor 0 + 0*u**2 - z*u**3 + 1/9*u**a + 0*u.
u**3*(u - 1)/9
Let t(o) be the first derivative of o**3/4 + 9*o**2/4 + 6*o + 41. Factor t(m).
3*(m + 2)*(m + 4)/4
Let y(o) = -o**3 - 8*o**2 - 7*o - 11. Let d be y(-7). Let s be ((-35 - 5)/4)/d. Factor -2/11*v**3 - s*v**2 - 8/11 - 16/11*v.
-2*(v + 1)*(v + 2)**2/11
Let q = 697/1068 - -26/267. Factor -21/2*f**3 - 12*f**2 - 9/2*f**4 - 27/4*f - q*f**5 - 3/2.
-3*(f + 1)**4*(f + 2)/4
Let c(z) be the first derivative of z**6/21 - 2*z**5/35 - 3*z**4/14 + 2*z**3/21 + 2*z**2/7 + 81. Determine x, given that c(x) = 0.
-1, 0, 1, 2
Find w such that -214/3*w - 74/9*w**3 + 440/9*w**2 - 4 = 0.
-2/37, 3
Let y(u) be the third derivative of u**6/40 + 81*u**5/10 - u**4/8 - 81*u**3 + 163*u**2 + 3. Factor y(p).
3*(p - 1)*(p + 1)*(p + 162)
Let s be 66/(-165) - (-1)/5*2. Suppose 29*y - 28*y = s. Find l, given that 4/9*l**4 + 0 + 0*l**2 - 2/9*l**3 + y*l - 2/9*l**5 = 0.
0, 1
Suppose 3*a = 4*x - 22, 465*x = 3*a + 467*x - 20. Determine z, given that 12/13*z**3 + 0 + 18/13*z**a + 8/13*z + 2/13*z**4 = 0.
-4, -1, 0
Let y(m) be the first derivative of 8 + 3/14*m**4 + 1/7*m**2 + 2/35*m**5 + 0*m + 2/7*m**3. Factor y(j).
2*j*(j + 1)**3/7
Let g(v) = v**3 - 11*v**2 - 12*v + 2. Let k be g(12). Factor -3 - k*h**2 + 4 + 1.
-2*(h - 1)*(h + 1)
Let c(k) be the second derivative of 11*k + 0*k**2 + 0 - 1/2160*k**6 + 1/72*k**4 - 1/720*k**5 + k**3. Let p(n) be the second derivative of c(n). Factor p(t).
-(t - 1)*(t + 2)/6
Let b(q) be the first derivative of 24*q + 34*q**2 + 20/3*q**3 - 3. Factor b(s).
4*(s + 3)*(5*s + 2)
Let l be (-6)/14 + (-72720)/(-11900). Let j = 29/5 - l. Solve 12/17*a**2 - j - 18/17*a**5 - 42/17*a**4 - 20/17*a**3 + 6/17*a = 0 for a.
-1, 1/3
Let m be -7 + 1/(-10)*2 + 2392/260. What is i in 1/8*i + 1/8*i**m - 1/8*i**3 - 1/8 = 0?
-1, 1
Let u = 2941 + -2937. Let f(n) be the third derivative of 0 - 1/84*n**8 - 2/105*n**7 + 0*n**u + 0*n**3 + 1/15*n**5 + 1/30*n**6 + 0*n - 3*n**2. Factor f(b).
-4*b**2*(b - 1)*(b + 1)**2
Let t(w) be the third derivative of -w**5/20 + 7*w**4 - 55*w**3/2 - 78*w**2 + 3*w. Factor t(b).
-3*(b - 55)*(b - 1)
Let 70/3*f + 2/3*f**3 + 22/3*f**2 + 50/3 = 0. Calculate f.
-5, -1
Suppose -v + 2 = v. Suppose -v - 5 = -3*j. Factor -2*l - 3*l**4 + l**3 + 0*l + l**j + l + 2*l**2.
-l*(l - 1)*(l + 1)*(3*l - 1)
Let d(r) be the second derivative of -6/13*r**2 - 1/3*r**3 - 1/130*r**5 - 4/39*r**4 - 7*r + 0. What is q in d(q) = 0?
-6, -1
Let x = 2157 + -6467/3. Factor 0 + 16/3*p + x*p**3 - 16/3*p**2.
4*p*(p - 2)**2/3
Let h(r) be the second derivative of r**4/3 - 8*r**3 - 26*r**2 - 366*r. Determine k, given that h(k) = 0.
-1, 13
Let w(n) be the third derivative of 1/80*n**5 - 1/80*n**6 - 1/140*n**7 + 1/8*n**3 - 1/896*n**8 - 6*n**2 + 5/64*n**4 + 0*n + 0. Find g such that w(g) = 0.
-2, -1, 1
Suppose 0 = 277*p + 88 - 649 + 7. Determine m so that p - 8/5*m - 2/5*m**2 = 0.
-5, 1
Let a be 2/6*(-63)/28*2/(-3). Solve 3/2*z**3 + 0 + 3/2*z**2 + 1/2*z**4 + a*z = 0.
-1, 0
Factor 37*u + 20 - 3*u**4 - 11*u**2 - 25*u**3 - 4*u**2 - 12*u + u**4 - 3*u**4.
-5*(u - 1)*(u + 1)**2*(u + 4)
Let y(k) be the second derivative of 0 - 1/200*k**6 - 9/40*k**4 + k**2 + 3/50*k**5 + 0*k**3 + 4*k. Let a(o) be the first derivative of y(o). Factor a(i).
-3*i*(i - 3)**2/5
Let j = -10599 + 10601. Factor 6/11*i + 4/11*i**j - 10/11*i**3 + 0.
-2*i*(i - 1)*(5*i + 3)/11
Let a(c) = c**3 + 6*c**2 + 111*c - 94. Let s(f) = f**3 + f**2 + f + 1. Let k(y) = -a(y) + 6*s(y). Suppose k(j) = 0. What is j?
-5, 1, 4
Suppose 2*x - 6 = h - 0*x, 3*h + 10 = 4*x. Suppose 4*f = 2*f + 4. Factor -3*g**2 + 0*g**h - 2*g + 5*g**2 - 4*g**f.
-2*g*(g + 1)
Let h(w) be the second derivative of -w**8/16800 - w**7/1680 - w**6/450 - w**5/300 - w**3/3 + 15*w. Let f(c) be the second derivative of h(c). Factor f(k).
-k*(k + 1)*(k + 2)**2/10
Let v(n) = 5*n**4 - 20*n**3 + 15*n - 30. Let x(j) = -j**2 + j - 2. Let i(h) = v(h) - 15*x(h). Factor i(p).
5*p**2*(p - 3)*(p - 1)
Let j = 28009767482/15611865 + -6/1040791. Let z = j + -1792. Factor 0*s**4 + 2/15*s**5 + 0 - 16/15*s**3 + z*s + 0*s**2.
2*s*(s - 2)**2*(s + 2)**2/15
Suppose y - 8 = -4*p, 3*p - 2*y + 8 = 7*p. Let s be (-2)/2*(-10 - p). Factor 3*i**4 - 12*i + 12*i**2 + 4 - s*i**3 + 1 + 6*i**2 - 2.
3*(i - 1)**4
Suppose -4*n = -i - 0*i - 10, 3*i - 2*n - 10 = 0. Factor -20*g - 4*g**3 - 1 + 8 - 21 + i - 16*g**2.
-4*(g + 1)**2*(g + 2)
Let n(o) = -5*o - 3. Let g be n(-4). Suppose 5*i + 5*p = -20, g = -3*i - p - 3*p. Factor 2 - 5*t - 3 + 5 + t**2 - i + t**3.
(t - 1)**2*(t + 3)
Let m = 6 + -2. Let p be (-2)/4*(-1)/(12/(-6))*0. Solve p*d + 0 - 8/5*d**5 - 16/5*d**3 - 16/5*d**2 + 28/5*d**m = 0 for d.
-1/2, 0, 2
Suppose -74 = -6*h - 20. Let w = 3 - h. Let b(y) = -3*y**2 - 9*y + 12. Let v(u) = -u + 1. Let c(r) = w*v(r) + b(r). Suppose c(q) = 0. What is q?
-2, 1
Factor 2*r**2 + 24 + r**2 - 5*r**2 + r - 7*r - 2*r.
-2*(r - 2)*(r + 6)
Let u(a) = 6*a**2 - 4*a + 3. Let q be u(1). Determine k, given that 2*k**3 + 0*k**3 + 2*k**3 + 3*k**q - k**3 - 6*k**4 = 0.
0, 1
Suppose -13*g + 157 = -740. Let v = g - 69. Let v - 2/7*z + 5/7*z**3 - 4/7*z**4 + z**2 = 0. What is z?
-1, 0, 1/4, 2
Let s(o) be the third derivative of -o**6/300 - o**5/25 - 3*o**4/20 - 4*o**3/15 - 2*o**2 - 8*o. Let s(v) = 0. Calculate v.
-4, -1
Suppose 1 + 8 = 3*d. Let c = 304/51 - 90/17. Factor -4/3*w**2 + c*w - 2/3*w**d + 4/3.
-2*(w - 1)*(w + 1)*(w + 2)/3
Let j(z) = -21*z**3 + 99*z**2 - 47*z + 17. Let o(m) = -15*m**3 + 66*m**2 - 32*m + 11. Let g(b) = -5*j(b) + 8*o(b). Factor g(q).
-3*(q - 1)**2*(5*q - 1)
Suppose -126 = -10*w + 7*w. Suppose -21*v = -0*v - w. Factor 0*t - 4/7*t**v - 2/7*t**3 + 0.
-2*t**2*(t + 2)/7
Suppose 2714*u + 129 = 2757*u. Factor 0 + 4/3*s**u + 40/3*s**2 + 100/3*s.
4*s*(s + 5)**2/3
Let g = 7370/16461 - 6/1829. Factor -1/9*z**3 + g + 1/9*z - 4/9*z**2.
-(z - 1)*(z + 1)*(z + 4)/9
Suppose -23*u + 28*u = 15. Let g be (2 + (-9)/6)/(30/128). Determine w, given that -4/15 - g*w**5 + 16/3*w**4 - 2/15*w**u + 34/15*w - 76/15*w**2 = 0.
-1, 1/4, 1, 2
Let r = 2311/9436 + 12/2359. Factor 1/4*w**3 - 1 + w**2 - r*w.
(w - 1)*(w + 1)*(w + 4)/4
Let n = 1/589 + 2353/1767. Factor n*x**3 + 4/3*x**2 - 8/3*x + 0.
4*x*(x - 1)*(x + 2)/3
What is j in -2*j**2 + 24*j**3 - 96*j + 34*j**4 - 6*j**2 - 32*j**4 = 0?
-12, -2, 0, 2
Let i = -12 - -7. Let j(t) = -t**3 - 5*t**2 + 2. Let l be j(i). Factor 15*w - 11*w**2 + 19*w + 8 + 253*w**l + 54*w.
2*(11*w + 2)**2
Let c(t) = t**4 - 1. Let h be ((-6)/9)/(4/150). Let v = h + 26. Let i(l) = -3*l**4 - 3*l**3 + 6. Let q(z) = v*i(z) + 6*c(z). What is a in q(a) = 0?
0, 1
Let y(u) be the first derivative of 21*u**3 + 24*u**2 + 9*u + 111. Let y(p) = 0. What is p?
-3/7, -1/3
Let l(v) = -v**2 - v + 1. Let n(h) = -2*h**3 + 4*h. Let p be ((-2)/(-4))/(6/24). Let k(z) = p*l(z) + n(z). Factor k(y).
-2*(y - 1)*(y + 1)**2
Let g be (3 + -9)/(21/(-372)). Let j = g - 106. Factor 0 + j*l**2 + 0*l.
2*l**2/7
Factor 2/11*r**3 + 96/11*r**2 + 1152/11*r + 0.
2*r*(r + 24)**2/11
Let t(g) be the second derivative of 1/3*g**3 + 1/3*g**4 + 0*g**2 - g + 3/40*g**5 - 1/30*g**6 + 0 - 1/84*g**7. Find m, given that t(m) = 0.
-2, -1, 0, 2
Suppose -b + 32 = 2*p + 3*b, 4*b = 16. Factor -p*w**3 + 12*w + 3 + 2*w**3 - 6*w - 3*w**2.
-3*(w - 1)*(w + 1)*(2*w + 1)
Let k = -17818/33 + 540. Let j(f) be the first derivative of -2/11*f**2 + 0*f + k*f**3 + 1/22*f**4 - 4. Factor j(b).
2*b*(b - 1)*(b + 2)/11
Let p(x) be the first derivat