0*t**3.
t*(t - 1)**2
Let n = 1 - 0. Let o = n - -2. Factor 0*a**3 + a**2 - 3*a**2 + 2*a**o.
2*a**2*(a - 1)
Factor -4 + c + 22*c**2 + 2 - 21*c**2.
(c - 1)*(c + 2)
Let a(c) = 8*c. Let l be a(2). Suppose 3*d - s = -5*s - 6, 4*s = 2*d - l. Let -2 - 13*x**4 + d*x - 5*x**4 + 2 + 6*x**3 + 10*x**2 = 0. Calculate x.
-1/3, 0, 1
Let b(w) be the first derivative of 5*w**4/6 + 25*w**3/2 - 185*w**2/12 - 10*w - 58. Determine c so that b(c) = 0.
-12, -1/4, 1
Find l, given that 2/3*l - 1 + 5/3*l**2 - 4/3*l**3 = 0.
-3/4, 1
Let b(k) = -k**2 - 3*k - 9. Let y(h) = 1. Let w(p) = 2*b(p) + 14*y(p). Suppose w(o) = 0. What is o?
-2, -1
Suppose -p + 3*o + 6 = 0, -4*p + 5*o + 11 - 1 = 0. Factor p - 2/3*z**2 - 4/3*z + 2/3*z**3.
2*z*(z - 2)*(z + 1)/3
Let d(n) be the second derivative of -n**10/60480 + n**9/30240 + n**8/13440 - n**7/5040 + n**4/4 - 3*n. Let g(c) be the third derivative of d(c). Factor g(s).
-s**2*(s - 1)**2*(s + 1)/2
Suppose y - 20 = -0. Let c = y + 15. Factor -4 - 2*h**4 + 8*h**3 + 13*h - c*h - 28*h**2 + 6*h**5 + 8*h**5 + 34*h**4.
2*(h - 1)*(h + 1)**3*(7*h + 2)
Suppose -5*c + y + y + 16 = 0, -5*c - 3*y + 1 = 0. Suppose c*l - 3*l**3 - 5*l**3 + 9*l**3 - 3*l**3 = 0. What is l?
-1, 0, 1
Let z be 3/(-1)*33/(-33). Let o(g) be the first derivative of 4 + 1/6*g**z - 3/8*g**4 - 1/2*g + 3/4*g**2. Factor o(j).
-(j - 1)*(j + 1)*(3*j - 1)/2
Let v(t) be the second derivative of -1/36*t**4 + 1/60*t**5 + 0*t**2 + 0 + 0*t**3 + 2*t. Factor v(w).
w**2*(w - 1)/3
Suppose -6 = -w + 3*l, -3*w - 2*l = -5*l - 6. Suppose 0 + 2/3*r**2 + w*r = 0. What is r?
0
Factor -77*h**2 + h**4 - 11*h**4 - 45*h**3 - 120 + 187*h**2 + 20*h + 5*h**5.
5*(h - 2)**3*(h + 1)*(h + 3)
Let n(o) be the second derivative of -o**6/660 + o**5/165 - 3*o**2/2 + o. Let w(j) be the first derivative of n(j). Factor w(a).
-2*a**2*(a - 2)/11
Suppose 3*h - 18 = -6. Let g(m) be the first derivative of 1 + 0*m + 7/4*m**h + 3*m**3 + m**2. Factor g(y).
y*(y + 1)*(7*y + 2)
Let h = 493/2 + -242. Factor 1/2*u**2 + 11/2*u**4 + h*u**3 + 2*u**5 + 0 - 1/2*u.
u*(u + 1)**3*(4*u - 1)/2
Factor 5/3*z + 5/6 - 35/6*z**2 + 10/3*z**3.
5*(z - 1)**2*(4*z + 1)/6
Suppose -4*m + 18 = -2. Let a(f) = -f + 7. Let u be a(m). Factor l**2 - l + u*l**2 - 2*l**2.
l*(l - 1)
Let i(t) be the first derivative of -4/9*t**3 + 1/6*t**2 - 1/12*t**4 + 0*t - 2 + 4/15*t**5. Suppose i(y) = 0. Calculate y.
-1, 0, 1/4, 1
Find j such that 2/5*j**2 - 6/5*j + 4/5 = 0.
1, 2
Let j(w) be the second derivative of w**6/900 - w**5/300 + w**3/3 + 3*w. Let b(i) be the second derivative of j(i). Determine r so that b(r) = 0.
0, 1
Let p(r) be the second derivative of -r**4/3 + 4*r**3 + 13*r. What is y in p(y) = 0?
0, 6
Let d(y) be the second derivative of 0 + 6*y - 1/27*y**3 + 1/54*y**4 + 0*y**2. Factor d(u).
2*u*(u - 1)/9
Let m(f) be the first derivative of -8 + 0*f - 1/12*f**3 + 1/24*f**6 + 1/20*f**5 + 1/4*f**2 - 3/16*f**4. Factor m(d).
d*(d - 1)**2*(d + 1)*(d + 2)/4
Let c be (6/(-21))/((-15)/7). Let q(v) be the third derivative of 0*v - v**2 - 1/20*v**4 + c*v**3 - 1/30*v**5 + 0. Factor q(t).
-2*(t + 1)*(5*t - 2)/5
Let a = -473/18 - -79/3. Let h(k) be the second derivative of -1/12*k**4 - k - 1/90*k**6 + 0 - 1/20*k**5 + 0*k**2 - a*k**3. What is x in h(x) = 0?
-1, 0
Let h(m) = -2*m + 14. Let y be h(7). Let c be (-9)/(-4) + -2 + 0. Factor -1/4*k**3 + 0 + c*k**5 + y*k + 1/4*k**2 - 1/4*k**4.
k**2*(k - 1)**2*(k + 1)/4
Let r(g) be the second derivative of g**6/90 - g**4/36 - g + 21. Factor r(s).
s**2*(s - 1)*(s + 1)/3
Let j(t) be the first derivative of 1/8*t**4 - 5/24*t**6 + 2 + 0*t**3 + 0*t + 0*t**2 - 3/20*t**5. Let j(f) = 0. Calculate f.
-1, 0, 2/5
Let u(z) be the second derivative of z**5/10 - z**4/6 - 2*z**3/3 + 11*z. Factor u(v).
2*v*(v - 2)*(v + 1)
Let d(b) = -b**3 + 3*b**2 + 5*b. Let h be d(4). Find m, given that -m**2 - h*m**2 - m**4 - 5*m + 7*m + 0*m**3 + 4*m**3 = 0.
0, 1, 2
Let g(n) be the first derivative of -n**5 + 5*n**4 - 5*n**3 - 38. Solve g(t) = 0.
0, 1, 3
Let z = -15/4 + 23/6. Let g(f) be the third derivative of 0 - 1/12*f**4 + 0*f + 1/420*f**7 - 1/60*f**6 + 2*f**2 + z*f**3 + 1/20*f**5. Factor g(s).
(s - 1)**4/2
Let t(n) be the third derivative of 2*n**7/35 + n**6/15 - 3*n**5/5 - 2*n**4 - 8*n**3/3 + 61*n**2. Factor t(b).
4*(b - 2)*(b + 1)**2*(3*b + 2)
Let h be 7/2 + 4/(-8). Find t such that -2*t + 4*t - h*t - t**2 = 0.
-1, 0
Factor 0 + 0*f - 1/2*f**2.
-f**2/2
Let u(b) = b**2 - b. Let g be u(1). Suppose g = -3*q + 2 + 4. Factor 1/4 - 5/4*t + t**q.
(t - 1)*(4*t - 1)/4
Factor 9/2*n - 3/2*n**2 + 1/6*n**3 - 9/2.
(n - 3)**3/6
Factor 0 + 0*y + 4/9*y**2 + 0*y**4 + 2/3*y**3 - 2/9*y**5.
-2*y**2*(y - 2)*(y + 1)**2/9
Let w be (-4)/(-24)*14/2. Let j = w + -2/3. Factor 0 + 1/2*x + j*x**2.
x*(x + 1)/2
Let u(b) be the first derivative of b**4 - 4*b**3 + 9*b**2/2 - 2*b - 17. Let u(t) = 0. Calculate t.
1/2, 2
Let p be 21/14*(-8)/(-6). Let j(m) = -m + 4. Let n be j(p). Factor -3*k**3 + 0 - 2 + 2*k**2 + 2*k + n*k**3 - k**3.
-2*(k - 1)**2*(k + 1)
Suppose 16 + 20 = 3*y + r, -y + 5*r - 4 = 0. Find a such that 6*a + y*a - 2*a + 3*a**3 + 12*a**2 + 6 = 0.
-2, -1
Let t = 5 + -3. Let a(d) be the third derivative of t*d**2 + 0 - 1/150*d**5 + 0*d - 1/30*d**4 - 1/15*d**3. Let a(w) = 0. What is w?
-1
What is r in 16/5*r**3 + 2/5*r**4 + 0*r + 8/5*r**2 - 6/5*r**5 + 0 = 0?
-1, -2/3, 0, 2
Let q(p) be the third derivative of -p**7/105 + p**6/120 + p**5/30 - p**4/24 + 6*p**2. Factor q(g).
-g*(g - 1)*(g + 1)*(2*g - 1)
Let s(x) be the third derivative of -1/50*x**5 + 0*x**3 + 0*x - 6*x**2 + 1/30*x**4 + 0 + 1/300*x**6. Factor s(f).
2*f*(f - 2)*(f - 1)/5
Let w(u) be the third derivative of u**5/180 + u**4/18 + 2*u**3/9 + 9*u**2. Factor w(j).
(j + 2)**2/3
Let n(o) = -o**4 - o**3 + 3*o**2 - 3*o + 3. Let y be (2/4)/(1/10). Let m(j) = -2*j**4 - 2*j**3 + 5*j**2 - 5*j + 5. Let b(f) = y*n(f) - 3*m(f). Factor b(i).
i**3*(i + 1)
Let w(b) be the second derivative of 243*b**7/56 - 81*b**6/5 + 27*b**5/2 - 14*b**4/3 + 2*b**3/3 + 6*b. Find d such that w(d) = 0.
0, 2/9, 2
Let n = 536 + -536. Factor 1/6*g + 1/6*g**2 + n.
g*(g + 1)/6
Factor -3*w**3 + w - 4*w**4 + w - 8 + 2*w - w**3 + 12*w**2.
-4*(w - 1)**2*(w + 1)*(w + 2)
Let c(l) = -l**2 + 8*l + 3. Let v be c(8). Factor -6*n - 8*n**v - 4*n**3 + 11*n**2 + 9*n**2 - 5*n**2 + 3*n**4.
3*n*(n - 2)*(n - 1)**2
Let w(n) be the third derivative of n**6/480 + n**5/48 + n**4/12 + n**3/6 + 9*n**2. Factor w(z).
(z + 1)*(z + 2)**2/4
Let d(g) be the second derivative of g**5/200 - g**3/60 + 29*g + 1. Let d(b) = 0. Calculate b.
-1, 0, 1
Let y(d) be the first derivative of 5*d**3/12 - 10*d**2 + 80*d + 65. Determine h so that y(h) = 0.
8
Let k(n) be the second derivative of 0*n**2 - n - 1/147*n**7 + 0 + 0*n**3 + 0*n**6 + 1/70*n**5 + 0*n**4. Let k(z) = 0. Calculate z.
-1, 0, 1
Let m(h) = h**2 - 5*h - 2. Let n be m(6). Factor -3*q**2 - q**4 - 3*q**n - q**2 - 6*q**3 + 2*q**4.
-2*q**2*(q + 1)*(q + 2)
Let p be (6 - (-475)/(-55)) + 3. Factor -2/11*d - p*d**2 + 2/11.
-2*(d + 1)*(2*d - 1)/11
Let p(t) = -4*t**2 + 3*t - 3. Let w be 1/(-4) - (-123)/12. Let b(i) = 6*i - w*i + 5*i**2 + 8 - 4. Let g(y) = 3*b(y) + 4*p(y). Factor g(h).
-h**2
Let c(a) be the second derivative of 0*a**2 + 0 + 2/27*a**3 + 6*a + 5/54*a**4. Factor c(t).
2*t*(5*t + 2)/9
Let c(y) = -4*y**3 + 3*y + 5. Let g(p) = p**3 - 1. Let s(a) = -c(a) - 3*g(a). Factor s(n).
(n - 2)*(n + 1)**2
Factor 5*i**3 + 43 + 65*i**2 + 62*i + 53*i + 12.
5*(i + 1)**2*(i + 11)
Let w be (-40)/(-6)*9/6. Let r be (-4 - -6) + 21/2. Factor -2 - r*s**2 + w*s.
-(5*s - 2)**2/2
Let n(t) be the third derivative of -t**7/315 - 2*t**6/45 - 11*t**5/45 - 2*t**4/3 - t**3 + 11*t**2. Factor n(k).
-2*(k + 1)**2*(k + 3)**2/3
Factor -135*j**4 - 72*j**3 - 53*j**5 - 26*j**5 - 12*j**2 - 2*j**5.
-3*j**2*(3*j + 1)*(3*j + 2)**2
Let r(z) be the second derivative of -1/3*z**3 + 1/3*z**4 + z + 0*z**2 + 0 - 1/10*z**5. Let r(u) = 0. What is u?
0, 1
Let f(s) be the third derivative of -s**5/80 + s**4/6 - 5*s**3/24 - 46*s**2. Find q, given that f(q) = 0.
1/3, 5
Suppose 2*x + 2 + x**2 - 2 + x**2 = 0. Calculate x.
-1, 0
Suppose 0 = -10*d - 17 + 57. Suppose -3*a**2 + 0*a + 3*a**3 + 0 - 3/4*a**d = 0. Calculate a.
0, 2
Let s(c) be the second derivative of c**7/315 + c**6/60 + c**5/45 - c**2/2 - 3*c. Let a(u) be the first derivative of s(u). Factor a(r).
2*r**2*(r + 1)*(r + 2)/3
Let c be (