**4 + c.
-2*(c - 2)*(c + 1)**3
Let j = 0 - -2. Let b be -4 + 2 + (12 - j). Solve 3*l**2 + b*l + 2 - 2 - 2*l = 0.
-2, 0
Let i(a) be the second derivative of a**8/168 + 2*a**7/105 - a**6/60 - a**5/15 - a**2/2 + 5*a. Let f(h) be the first derivative of i(h). Factor f(d).
2*d**2*(d - 1)*(d + 1)*(d + 2)
Let d(z) = 2*z**2 - 2*z + 18. Let l(v) = -3*v**2 + 3*v - 18. Let m(b) = 6*d(b) + 5*l(b). Factor m(x).
-3*(x - 3)*(x + 2)
Let n(l) be the third derivative of l**8/20160 - l**7/1680 + l**6/360 + l**5/20 + 2*l**2. Let f(x) be the third derivative of n(x). Find y such that f(y) = 0.
1, 2
Let a(r) be the second derivative of 0 + 0*r**3 + 1/135*r**6 - 1/63*r**7 + 0*r**2 - 4*r + 1/45*r**5 + 0*r**4. Let a(h) = 0. What is h?
-2/3, 0, 1
Let s be (-5 + 6)*(3 - 1). Let g be ((-6)/30)/(s/(-4)). Factor -g - 4/5*t - 2/5*t**2.
-2*(t + 1)**2/5
Factor -9*d**2 + 12*d**4 + 3*d**3 + 12*d**3 + d - 8*d - 3 - 8*d.
3*(d - 1)*(d + 1)**2*(4*d + 1)
Let z(t) be the second derivative of -t**6/10 + 2*t**5/15 + 7*t**4/6 + 4*t**3/3 - t**2 + 8*t. Let v(p) be the first derivative of z(p). Factor v(i).
-4*(i - 2)*(i + 1)*(3*i + 1)
Factor 12*u**4 + 3*u**5 + 2*u**2 + 15*u**4 - 29*u**4 - 2*u**3 - u**5.
2*u**2*(u - 1)**2*(u + 1)
Find q such that 0 + 0*q + 0*q**2 + 0*q**3 + 1/2*q**4 + 1/2*q**5 = 0.
-1, 0
Let c(k) = -4*k**2 - 2*k. Let u(n) = -23*n**2 - 11*n. Let p(f) = -34*c(f) + 6*u(f). Factor p(i).
-2*i*(i - 1)
Suppose 2*t + 3*r + 36 = r, 5*r + 30 = -t. Let f be 4/5*t/(-6). Let 0*c - 2*c + 42*c**4 - 6*c - 24*c**f + 26*c**3 = 0. What is c?
-1, -2/7, 0, 2/3
Let s = 23259/25 - 930. Let f = s + 1/25. Factor 0*p - 2/5*p**2 + f.
-2*(p - 1)*(p + 1)/5
Let -1 - 2 + 4*j**2 - 4*j - 5*j**2 = 0. What is j?
-3, -1
Let x(d) be the third derivative of d**6/480 - d**5/80 + d**4/32 - d**3/24 - 25*d**2. Suppose x(j) = 0. Calculate j.
1
Let q be 17/5 + (-4)/2. Factor -3/5*w**4 - w**2 + q*w**3 + 0 + 1/5*w.
-w*(w - 1)**2*(3*w - 1)/5
Let i(z) be the second derivative of z**8/30240 + z**7/3780 + z**6/1620 + z**4/4 + 4*z. Let w(m) be the third derivative of i(m). Suppose w(f) = 0. What is f?
-2, -1, 0
Let m(f) be the third derivative of f**5/75 + f**4/10 - 8*f**3/15 + 7*f**2. Factor m(p).
4*(p - 1)*(p + 4)/5
Factor -31 - 66*u + 3*u**3 + 7 + 57*u**4 - 42*u**4 + 3*u**5 - 51*u**2.
3*(u - 2)*(u + 1)**3*(u + 4)
Let r be (0/3)/(-3 - -5). Factor 4/3*g**2 - 5/3*g**4 + 0 + r*g + 25/2*g**5 - 14/3*g**3.
g**2*(3*g + 2)*(5*g - 2)**2/6
Let o(p) be the first derivative of 5*p**4/48 + p**3/2 + p**2/2 + 2*p + 3. Let m(f) be the first derivative of o(f). Factor m(c).
(c + 2)*(5*c + 2)/4
Suppose 4*r + t = 6*t + 10, 10 = 5*r - 5*t. Let x(y) be the second derivative of 1/27*y**3 + 1/30*y**5 + r + 0*y**2 - 2*y - 1/135*y**6 - 1/18*y**4. Factor x(l).
-2*l*(l - 1)**3/9
Suppose 4*w + 0*w + 20 = 0, w = -5*b + 65. Let -152*l**2 + b*l**4 - 16*l + 686*l**5 - 65*l**4 + 135*l**3 - 555*l**3 - 47*l**4 = 0. What is l?
-2/7, 0, 1
Factor 18*q**3 - 15*q**4 + 6*q**3 - 29*q**2 + 41*q**2.
-3*q**2*(q - 2)*(5*q + 2)
Let g(i) = -1 + i**2 + 1 - 10*i**2 + 5*i**3. Let d be 6/(-4)*2/1. Let u(b) = -2*b**3 + 4*b**2. Let h(p) = d*g(p) - 7*u(p). Let h(r) = 0. What is r?
-1, 0
Let l be 2 + (-84)/45 - (-208)/65. Let f = 0 - -3. Suppose -8/3*a**2 - 4/3 - 2/3*a**f - l*a = 0. Calculate a.
-2, -1
Let i(v) = -3*v**2 - 4*v - 5. Let f be (2 + -1)*(-3 + 4). Let u be ((-2)/3)/(f/6). Let y(p) = 1. Let d(w) = u*y(w) - i(w). Factor d(a).
(a + 1)*(3*a + 1)
Let b(k) be the first derivative of k**4/30 - 3*k + 3. Let r(g) be the first derivative of b(g). Let r(a) = 0. Calculate a.
0
Solve -2/7*d + 4/7*d**2 + 0 - 2/7*d**3 = 0 for d.
0, 1
Factor 2*s**5 - 4*s**4 - 20*s**3 - 17*s**3 + 33*s**3 + 2*s**4.
2*s**3*(s - 2)*(s + 1)
Let r = 172/205 + -8/205. Find t, given that r*t + 2/5*t**2 + 0 = 0.
-2, 0
Suppose 18 = -20*v + 29*v. Find u such that 0 + 0*u + 2/11*u**4 + 2/11*u**3 + 0*u**v = 0.
-1, 0
Determine g, given that 3/4*g**2 + 3*g + 0 = 0.
-4, 0
Solve -6*g**2 + 0 + 9/2*g + 3/2*g**3 = 0 for g.
0, 1, 3
Let m(g) = 13*g**3 + 27*g**2 + 12*g - 2. Let l(b) = -25*b**3 - 55*b**2 - 25*b + 5. Let k(u) = 6*l(u) + 14*m(u). Suppose k(t) = 0. Calculate t.
-1, -1/4
Let d(s) be the first derivative of s**7/84 - s**6/20 + 3*s**5/40 - s**4/24 + 3*s + 2. Let g(f) be the first derivative of d(f). Find a, given that g(a) = 0.
0, 1
Let y(h) = -h**3 - 5*h**2 + 7*h + 8. Let o be y(-6). Factor -4/3*m**o + 4 + 8/3*m.
-4*(m - 3)*(m + 1)/3
Let a(q) be the first derivative of 1/3*q**3 + 1 - 2*q - 1/2*q**2. Factor a(o).
(o - 2)*(o + 1)
Let v(w) = -1. Let s(u) = -u**3 + u**2 + 6*u + 3. Let b(o) = s(o) + 3*v(o). Suppose b(a) = 0. What is a?
-2, 0, 3
Factor 7*m**3 + 4*m**4 + m**3 - 2*m - 4*m**2 - 6*m.
4*m*(m - 1)*(m + 1)*(m + 2)
Let x = -26 - -30. Let b(v) be the second derivative of 0*v**2 + 1/42*v**7 + 2/15*v**6 + 1/3*v**x + 0 + 1/6*v**3 + 3/10*v**5 + v. Determine r so that b(r) = 0.
-1, 0
Solve 8*u**3 - 3*u**5 - u**5 - 700*u + 696*u = 0 for u.
-1, 0, 1
Factor 8*j**3 - 8*j - 5*j**4 + 12*j**2 - 12*j**4 + 5*j**4.
-4*j*(j - 1)*(j + 1)*(3*j - 2)
Let r(s) = s**3 + s**2 - s. Let n(x) = -3*x**2 - 6*x - 1. Suppose 2*v - 6 = 2*u - 14, 4 = -2*v. Let b(m) = u*r(m) - n(m). Factor b(h).
(h + 1)**2*(2*h + 1)
Let d(z) be the second derivative of -3*z**5/40 - z**4/8 + z**3/2 - 4*z. Factor d(f).
-3*f*(f - 1)*(f + 2)/2
Let -5*c**2 - 2 - 10*c + 7 + 10 = 0. What is c?
-3, 1
Let w = 2/53 - -473/106. Let j(g) = -g - 5. Let f be j(-8). Factor 0 + w*a**3 + 1/2*a + f*a**2.
a*(3*a + 1)**2/2
Let -134 - 540*o + 4*o**2 - 45*o**2 - 946 - 49*o**2 - 5*o**3 = 0. What is o?
-6
Find z such that 0 - 1/2*z**3 + 3/2*z**2 + 2*z = 0.
-1, 0, 4
Let w = -2/223 - 6463/446. Let m = 15 + w. Determine c so that -9/4*c**2 + m - 7/4*c = 0.
-1, 2/9
Let r = 308 - 308. Determine l, given that r - 3/4*l**3 + 0*l**4 + 0*l + 3/4*l**5 + 0*l**2 = 0.
-1, 0, 1
Let p(r) be the first derivative of -4*r**3/3 - 4*r**2 + 11. Factor p(j).
-4*j*(j + 2)
Let v(r) be the third derivative of r**7/840 - r**6/80 + 3*r**5/80 + 50*r**2. Determine u, given that v(u) = 0.
0, 3
Suppose 9*u**4 + 4*u**3 - 3*u**4 + 0*u**5 + 2*u**5 = 0. Calculate u.
-2, -1, 0
Let l be 2 + (-2 + -1)*-1. Suppose 0*g + 20 = l*g. Solve 2*a**3 + g*a - 4*a + 0*a**3 - 2*a**5 = 0.
-1, 0, 1
Suppose -2*j - 2*j + i = 0, 0 = -2*i. Let m(t) be the second derivative of 1/12*t**4 + j - 2*t + 1/3*t**3 + 1/2*t**2. What is y in m(y) = 0?
-1
Factor -1/2*c**3 + 0 + 2/3*c - 1/6*c**4 + 0*c**2.
-c*(c - 1)*(c + 2)**2/6
Suppose -a - 2 = -4. Let x be (a/(-16))/((-1)/2). Factor -x*j - 1/4*j**2 + 0.
-j*(j + 1)/4
Let f(r) be the third derivative of -r**5/15 - 5*r**4/24 - r**2. Let v(a) = 2*a**2 + 3*a. Suppose 0 = 4*n - 6*n - 10. Let p(t) = n*v(t) - 3*f(t). Factor p(y).
2*y**2
Let n(y) be the third derivative of -1/66*y**4 + 0*y**3 + 0*y + 0 - 5*y**2 + 1/330*y**5. Find t, given that n(t) = 0.
0, 2
Let s(o) = 8*o**2 + 4*o - 20. Let r(f) = -f**2 - f + 1. Let t = -12 + 11. Let z(i) = t*s(i) - 4*r(i). Factor z(n).
-4*(n - 2)*(n + 2)
Factor 4*y**3 + 3*y**4 - 2*y**2 + 2*y**2 - 3*y**2 - 3*y - y**3.
3*y*(y - 1)*(y + 1)**2
Let m(s) be the first derivative of -2*s**3/27 - s**2/9 - 4. Factor m(z).
-2*z*(z + 1)/9
Suppose -p = -5*p + 20. Let m(k) be the first derivative of -2/7*k + 1/7*k**4 + 1 - 2/7*k**2 + 2/35*k**p + 0*k**3. Factor m(z).
2*(z - 1)*(z + 1)**3/7
Let k(l) = l**4 - l**2 - l + 1. Let t(q) = 5*q**4 - 5*q**2 - q + 1. Let n(y) = k(y) - t(y). Determine v, given that n(v) = 0.
-1, 0, 1
Let r(y) be the second derivative of y**6/135 + y**5/90 + 6*y. Factor r(f).
2*f**3*(f + 1)/9
Let t(q) = -246*q**3 + 582*q**2 + 300*q + 42. Let p(l) = -35*l**3 + 83*l**2 + 43*l + 6. Let x(r) = 44*p(r) - 6*t(r). Solve x(h) = 0 for h.
-1/4, 3
Factor -3*m**5 - 2*m - 3*m**2 + m**5 + 4*m**3 + 3*m**2.
-2*m*(m - 1)**2*(m + 1)**2
Find x such that -64 - 1/4*x**4 + 64*x + 4*x**3 - 24*x**2 = 0.
4
Let o be 1/(-4) - 25/(-4). Let i be 3/9*o/4. Solve -q**3 + i*q**4 + 3/2*q**5 + 0*q**2 + 0 + 0*q = 0 for q.
-1, 0, 2/3
Let m(r) be the third derivative of r**6/300 - r**5/150 - r**4/60 + r**3/15 + 6*r**2. Suppose m(f) = 0. Calculate f.
-1, 1
Let z(y) be the third derivative of y**8/4200 - y**7/1050 + y**5/150 - y**4/60 - y**3/3 - 3*y**2. Let g(a) be the first derivative of z(a). Factor g(h).
2*(h - 1)**3*(h + 1)/5
Suppose 0 = -w - 22 + 23. Let i be (w + 20/(-24))*2. Factor i*x + 0