Let f(w) = -w**3 - 6*w**2 - w - 1. Let i be f(-6). Factor 3 - 4*t**2 + i*t + 5*t + 6*t**2 + 5.
2*(t + 1)*(t + 4)
Let k(n) be the first derivative of -n**3/6 + 29*n**2/2 - 841*n/2 - 120. Factor k(p).
-(p - 29)**2/2
Factor 0 + 8/9*m**2 + 2/9*m.
2*m*(4*m + 1)/9
Let o = -2378 + 2378. Factor 1/2*j**4 - j**2 + 0 + 1/2*j**3 + o*j.
j**2*(j - 1)*(j + 2)/2
Let y(d) be the third derivative of 0*d + 2*d**2 + 0*d**5 + 0*d**4 + 0*d**3 + 5/336*d**8 + 0*d**6 + 1/42*d**7 + 0. Factor y(j).
5*j**4*(j + 1)
Factor -p**4 + 0 + 0*p + 1/2*p**3 + 1/2*p**2.
-p**2*(p - 1)*(2*p + 1)/2
Suppose -2*h = 2*d - 12, -3*h - 4*d + 15 = -2*h. Factor 4 + 12*r - 28*r**4 + 6*r**3 + 16*r**2 - h*r**2 + 29*r**4.
(r + 1)**2*(r + 2)**2
Let q be 9/21 + -1 + 1. Let d = -6/77 - -39/77. Find r, given that d*r**2 + 0 + q*r = 0.
-1, 0
Let p(z) be the second derivative of z**5/25 + 2*z**4/5 + 6*z**3/5 + 10*z. Suppose p(y) = 0. Calculate y.
-3, 0
Suppose 10*j - 3 = -3 + 20. Suppose 1/6*g + 1/4*g**3 + 0 - 1/3*g**4 + 3/4*g**j = 0. What is g?
-1, -1/4, 0, 2
Let i(q) = q**3 + 3*q**2 - q + 1. Let s be (-6)/(-6)*(-2)/(-1). Let a = -6 + s. Let c(p) = -3*p**3 - 8*p**2 + 3*p - 3. Let o(f) = a*c(f) - 11*i(f). Factor o(r).
(r - 1)**2*(r + 1)
Solve 111/8 + 3/8*b**2 - 57/4*b = 0.
1, 37
Let y(r) be the second derivative of -r**6/70 - 3*r**5/10 - 11*r**4/7 - 20*r**3/7 + 496*r. Factor y(b).
-3*b*(b + 2)**2*(b + 10)/7
Let i(v) be the second derivative of v**8/1344 + v**7/126 + v**6/48 - v**4/4 + 4*v. Let o(h) be the third derivative of i(h). Suppose o(m) = 0. Calculate m.
-3, -1, 0
Let x = 24 + 54. Suppose 4*h + 5*o - 294 = 0, o - x + 4 = -h. Factor -4 + 12*z**2 - h*z**2 - 5*z - 27*z.
-4*(4*z + 1)**2
Let h(l) be the third derivative of -2*l**3 + 0*l + 1/15*l**5 + 0 + 16*l**2 + 1/3*l**4. Factor h(r).
4*(r - 1)*(r + 3)
Let k(h) = -h**3 + 10*h**2 - 15*h - 3. Let g be k(8). Let j(m) be the first derivative of -3/16*m**4 - g - 9/4*m + 15/8*m**2 - 1/4*m**3. Factor j(f).
-3*(f - 1)**2*(f + 3)/4
Let s(v) be the first derivative of -3*v**6/4 - 21*v**5/10 - 15*v**4/8 - v**3/2 + 458. Find n such that s(n) = 0.
-1, -1/3, 0
Let a(c) be the second derivative of c**6/40 - 27*c**5/80 + 21*c**4/16 - 19*c**3/8 + 9*c**2/4 - 37*c. Factor a(x).
3*(x - 6)*(x - 1)**3/4
Let d(i) be the third derivative of -i**5/210 - 19*i**4/42 - 2*i**2 - 245. Suppose d(m) = 0. Calculate m.
-38, 0
Let x(f) = -2*f - 4. Let j be x(-3). Suppose 4*s = o + 4, -4*s - 2 = o + j. Factor -4*d + 6 + s*d**2 + d**2 - 2 - d.
(d - 4)*(d - 1)
Let a = -19 + 27. Find b such that 0*b**2 + 5*b**3 + b**2 - 4*b**4 + a*b**4 = 0.
-1, -1/4, 0
Let c(v) = -v**3 + 12*v + 38. Let h(d) = -d**2 - 2*d - 1. Let w(i) = c(i) + 6*h(i). Factor w(k).
-(k - 2)*(k + 4)**2
Let d be 1*7/(-3)*-3. Determine b, given that -d*b + 5*b - 9*b - 5*b - 2*b**2 - 32 = 0.
-4
Let y(n) = -n**2 + 20*n + 20. Let m be y(21). Let v be (m - -2)/((-21)/(-5) - 4). Suppose 3/2*h**2 - h + 1/2*h**3 + 0 + 1/2*h**v - 3/2*h**4 = 0. What is h?
-1, 0, 1, 2
Factor 0 - 5/2*m**2 - 35/2*m.
-5*m*(m + 7)/2
Let i be 3 - 17/5 - 753/(-20). Let k = -673/20 + i. Factor -3/5*s**3 - 12/5 - k*s**2 - 27/5*s.
-3*(s + 1)**2*(s + 4)/5
Let d = -13856/3 + 4619. Factor 0 - d*a - 1/3*a**2.
-a*(a + 1)/3
Determine h, given that 46/11*h + 2/11*h**2 - 48/11 = 0.
-24, 1
Suppose 0 = 2*d - 3*d + 5. Suppose 0 = -d*u + 30. Solve w**2 + 5*w**2 - 4*w - 4*w**2 - u*w**2 = 0.
-1, 0
Solve 25*q**2 + 55*q - 7*q**4 - 55*q**3 - 3*q**4 - 60 + 40*q**2 + 5*q**4 = 0.
-12, -1, 1
Solve 14*h**4 + h**4 - 5*h**5 - 15*h**3 + 5*h**3 = 0.
0, 1, 2
Let s(m) = m**3 + m**2 + 4*m + 4. Let j(n) = -5*n**3 - 3*n**2 - 19*n - 22. Let k(q) = 4*j(q) + 22*s(q). Suppose k(c) = 0. What is c?
-3, -2, 0
Factor -11/4*g**2 + 0 + 7/2*g.
-g*(11*g - 14)/4
Let l(a) be the third derivative of 0*a - 12*a**2 + 1/84*a**4 + 0*a**3 + 0 - 1/420*a**5. Factor l(j).
-j*(j - 2)/7
Suppose 0 = -10*i + 14*i - 12. Suppose -i = 4*r - 5*p - 11, -3*r + 2*p = -6. Factor 4/3*t + 2/3 + 8/3*t**3 - 14/3*t**r.
2*(t - 1)**2*(4*t + 1)/3
Let s(o) be the second derivative of 0*o**3 - 1/60*o**5 + 1/90*o**6 - 17*o + 0*o**4 + 0*o**2 + 0. Factor s(y).
y**3*(y - 1)/3
Let f(j) be the second derivative of 3*j**5/140 - 15*j**4/28 + 24*j**3/7 + 96*j**2/7 - 2*j - 26. Solve f(t) = 0.
-1, 8
Suppose 2*t - 10 = -3*t. Suppose 0*l - t*l + 5*p + 21 = 0, -2*l = 2*p. Let 3*g**3 - l*g - g**3 - 5*g = 0. What is g?
-2, 0, 2
Let n(x) = -7*x**3 - 4*x**2 + 33*x - 22. Let w(d) = -69*d**3 - 39*d**2 + 327*d - 219. Let c(k) = 21*n(k) - 2*w(k). Solve c(p) = 0.
-8/3, 1
Let s(n) = -n**2 - n + 1. Let c(u) = -3*u**3 - 23*u**2 - 44*u - 11. Let b(v) = 2*c(v) - 2*s(v). Factor b(j).
-2*(j + 3)*(j + 4)*(3*j + 1)
Factor 20/9*u**2 + 0 - 16/9*u - 2/9*u**4 - 2/9*u**3.
-2*u*(u - 2)*(u - 1)*(u + 4)/9
Let x(i) be the third derivative of 2/5*i**6 + 0*i**3 + 1/168*i**8 - 22*i**2 + 8/105*i**7 + 16/15*i**5 + 0 + 4/3*i**4 + i. Factor x(v).
2*v*(v + 2)**4
Let r(t) be the third derivative of t**5/450 + t**4/60 - 26*t**2 + 2. Let r(l) = 0. Calculate l.
-3, 0
Find g such that 2/11*g**2 + 28/11*g + 48/11 = 0.
-12, -2
Find z, given that -274/7*z**2 - 368/7*z - 10/7*z**3 - 104/7 = 0.
-26, -1, -2/5
Let t(b) be the first derivative of b**6/6 + b**5/5 - 5*b**4/4 + b**3 - 87. Determine c so that t(c) = 0.
-3, 0, 1
Suppose 3*i - 3 + 0 = 2*z, -4*z = 5*i - 27. Suppose -i*p = -7*p. Factor 3/2*m**2 + p - m - 1/2*m**3.
-m*(m - 2)*(m - 1)/2
Let w(i) be the first derivative of 17*i**7/420 + i**6/90 + 40*i**3/3 + 18. Let o(m) be the third derivative of w(m). Factor o(a).
2*a**2*(17*a + 2)
Let h(i) be the first derivative of -4*i**6/3 - 2*i**5 + 27*i**4/2 + 22*i**3/3 - 23*i**2 - 12*i - 200. Solve h(g) = 0 for g.
-3, -1, -1/4, 1, 2
Let v(g) be the second derivative of -g**6/6 - g**5/2 + 5*g**4/12 + 5*g**3/3 - 11*g. Determine a, given that v(a) = 0.
-2, -1, 0, 1
Suppose -14 = -2*k - 10. Let h(p) be the first derivative of -2/3*p**3 + 0*p - 1 - p**k. Suppose h(f) = 0. Calculate f.
-1, 0
Let k(s) = s**3 + 38*s**2 + 220*s + 23. Let v be k(-7). Factor -4/3 - v*n - 2/3*n**2.
-2*(n + 1)*(n + 2)/3
Let d = -3041 - -3044. Determine m so that -8/5*m**2 + 4/5*m**d - 16/5*m + 0 + 2/5*m**4 = 0.
-2, 0, 2
Let u(x) be the second derivative of -x**5/80 - 5*x**4/48 - 7*x**3/24 - 3*x**2/8 - 325*x. Factor u(v).
-(v + 1)**2*(v + 3)/4
Let p(c) be the third derivative of -c**6/180 - c**5/18 + 2*c**2 - 51. Solve p(r) = 0 for r.
-5, 0
Suppose 4/7*o**2 + 20/7*o + 16/7 = 0. Calculate o.
-4, -1
Suppose -1 = 6*j - 37. Find u, given that -12*u + 20*u - j*u**5 - 7*u**3 + u**3 + 20*u**4 - 24*u**2 = 0.
-1, 0, 1/3, 2
Let x(c) be the second derivative of 2*c**7/21 + 2*c**6/15 - c**5 + c**4 - 72*c. Factor x(r).
4*r**2*(r - 1)**2*(r + 3)
Let k(l) = l**3 + l**2 + 3*l - 1. Let c(d) = d**4 - 7*d**3 - d**2 - 5*d. Let o(a) = -2*c(a) - 6*k(a). Factor o(r).
-2*(r - 3)*(r - 1)**2*(r + 1)
Let n(g) be the first derivative of -5/9*g**3 + 8 - 15*g + 5*g**2. Factor n(q).
-5*(q - 3)**2/3
Let a(n) = -n - 6*n**2 + 7*n**2 - 13 - 6*n. Let x be a(10). Factor -s + x + 3*s**2 - 17.
s*(3*s - 1)
Let o(b) = b**2 + 4*b - 4. Let f be o(-5). Let y = f + -1. Suppose -1/4*h + 1/4*h**3 + 0*h**2 + y = 0. What is h?
-1, 0, 1
Let c = 139/288 - -5/288. Factor -1/3*t + c*t**4 - 5/6*t**2 + 2/3*t**3 + 0.
t*(t - 1)*(t + 2)*(3*t + 1)/6
Suppose -15*f = -7*f - 104. Suppose 2*z - f*a = -14*a + 2, 2*a = -5*z + 6. Factor -7/8*s**2 + s + 1/8*s**3 + z.
(s - 4)**2*(s + 1)/8
Factor 0 - 128/7*v + 48/7*v**2 - 4/7*v**3.
-4*v*(v - 8)*(v - 4)/7
Let -636*n + 288 - 21/8*n**3 - 663/8*n**2 = 0. Calculate n.
-16, 3/7
Suppose -7*a + 31 = 3. What is t in -1 + 4*t - 3 - a + 4*t**2 = 0?
-2, 1
Let o be 3/(-15) + (-1870)/(-3850). Determine q so that -4*q**2 + 0 + o*q**3 + 14*q = 0.
0, 7
Let v = -40 - -96. Solve 12*q**3 + 8*q**2 + v*q - 4 - 118*q - 6*q**5 + 56*q - 4*q**4 = 0 for q.
-1, -2/3, 1
Let n(t) be the first derivative of t**4/8 + 9*t**3/2 + 135*t**2/4 - 675*t/2 + 347. Factor n(x).
(x - 3)*(x + 15)**2/2
Let y be (3/6 + (-66)/22)*(3 - 4). Determine x so that 23/8*x**4 + 7/8*x**5 - 19/8*x**2 - 1/2 + 13/8*x**3 - y*x = 0.
-2, -1, -2/7, 1
Let k = 128669/17156 + 1/17156. Let 5/4*h**2 + 5/4*h - k = 0. Calculate h.
-3, 2
Let f(r) = r**3 - 2*r**2 + r - 2. Let i(m) = 3*m**3 - 5*m**2 + 2*m - 5. Suppose 2*z - 1 = -11. Let d(k) = z*f(k) + 2*i(k). Factor d(x).
x*(x - 1)*(x + 1)
Let q be -4 + (-544)