
-1, 3
Let v(l) be the second derivative of -l**5/20 - 2*l**4/9 - 7*l**3/18 - l**2/3 + 15*l. Factor v(u).
-(u + 1)**2*(3*u + 2)/3
Let t be 6/(-4) + 1 - -1. Let b be 0 + 0 + -4 - (-45)/10. Factor b + p**3 - t*p**4 + 0*p**2 - p.
-(p - 1)**3*(p + 1)/2
Let 3/4*x**3 + 3/4*x**2 + 0 - 3/2*x = 0. What is x?
-2, 0, 1
Suppose -g = 5*x + 13, -2*x - 16 = 2*g + 3*x. Let h = 0 - g. Factor -5*z**2 + h*z**2 + z**2.
-z**2
Factor -5/4*r**4 + 5/4*r**5 + 5/4*r - 5/4 + 5/2*r**2 - 5/2*r**3.
5*(r - 1)**3*(r + 1)**2/4
Let c be (2/(-3))/((-392)/168). Factor c*i - 2/7*i**2 + 0.
-2*i*(i - 1)/7
Let j(y) be the third derivative of -y**6/24 - y**5/3 - 25*y**4/24 - 5*y**3/3 + 17*y**2. Suppose j(x) = 0. Calculate x.
-2, -1
Let i(p) = -10*p**3 + 6*p**2 + 16. Let d(m) = -4*m**3 + 6*m**3 - m**2 - 6 + 3. Let g(k) = 16*d(k) + 3*i(k). Solve g(w) = 0.
-1, 0
Let x(t) = -t**3 - 2*t**2 + 2. Let u be x(-2). Suppose 3*a = 0, -u*a = 4*g + 3*a - 16. Factor 2/3*z**3 + 0*z - 2/3*z**5 + 0 + 0*z**2 + 0*z**g.
-2*z**3*(z - 1)*(z + 1)/3
Let q = 29/6 - 307/66. Let -2/11 - 2/11*t + 2/11*t**3 + q*t**2 = 0. Calculate t.
-1, 1
Let o be (-107)/54 - (-1 - 1). Let z(p) be the third derivative of -1/270*p**5 + o*p**4 - 1/27*p**3 - p**2 + 0*p + 0. Let z(x) = 0. What is x?
1
Let v(s) be the first derivative of -2*s**3/3 + 5*s**2 - 8*s - 15. Factor v(w).
-2*(w - 4)*(w - 1)
Let a(r) = -r**3 - 5*r**2 - r - 5. Let p be 15/6*2*-1. Let j be a(p). Suppose -1/2*g + 1/2*g**4 - 1/2*g**2 + j + 1/2*g**3 = 0. What is g?
-1, 0, 1
Let d(k) be the third derivative of -k**8/560 - k**7/175 - k**6/200 - 22*k**2. Factor d(b).
-3*b**3*(b + 1)**2/5
Let s(n) be the third derivative of -1/160*n**6 - 4*n**2 + 0*n + 1/280*n**7 + 0*n**3 + 0*n**4 + 0 + 0*n**5. Let s(x) = 0. What is x?
0, 1
Let h(z) = 8*z**2 + 28*z**4 + 6 - 4 - 2*z**2 - 22*z**3. Let q(u) = 56*u**4 - 44*u**3 + 13*u**2 + 5. Let b(v) = -5*h(v) + 2*q(v). Factor b(r).
-2*r**2*(2*r - 1)*(7*r - 2)
Let w(q) be the second derivative of -5*q**6/6 + 9*q**5/4 - 5*q**4/4 - 5*q**3/6 + 29*q. Let w(i) = 0. Calculate i.
-1/5, 0, 1
Let j(q) = -q**4 - q**2 + q - 1. Let h(s) = 4*s**4 + 8*s**2 - 3*s + 5. Let v(i) = -3*h(i) - 15*j(i). Determine p so that v(p) = 0.
-1, 0, 2
Let q(a) be the third derivative of -32*a**5/45 + 4*a**4/3 - a**3 + 23*a**2. Factor q(v).
-2*(8*v - 3)**2/3
Let d(b) = -b**3 + 8*b**2 - b + 10. Let f be d(8). Determine i so that 0 + 5/4*i**f + 1/2*i = 0.
-2/5, 0
Let u(s) be the first derivative of 4*s**6/3 + 34*s**5/5 + 12*s**4 + 26*s**3/3 + 2*s**2 - 63. Determine o, given that u(o) = 0.
-2, -1, -1/4, 0
Factor 1/2 - 1/4*c**2 + 1/4*c.
-(c - 2)*(c + 1)/4
Let d(j) be the first derivative of -j**6/6 + j**4/4 + 15. Factor d(b).
-b**3*(b - 1)*(b + 1)
Suppose 17 = -4*j + 5*i, -5*j + j - 3*i + 23 = 0. Factor -4*y**5 + 2*y**4 + 3*y**3 + y**j + y**4 + 5*y**5.
y**2*(y + 1)**3
Let j = -71 + 74. Let x(d) be the second derivative of j*d - 1/30*d**6 + 0 + 3/20*d**5 - 1/4*d**4 + 1/6*d**3 + 0*d**2. Factor x(i).
-i*(i - 1)**3
Suppose 5*s - s = -32. Let a(r) = -2*r**4 + 2*r**3 + 6*r**2 - 10*r - 12. Let q(u) = -u - 1. Let j(y) = s*q(y) + a(y). Find i, given that j(i) = 0.
-1, 1, 2
Let i be -4 + 258/78 + 2 + -1. Determine y so that -2/13*y**4 - 4/13*y**3 + i*y**2 - 2/13 + 2/13*y + 2/13*y**5 = 0.
-1, 1
Let i(r) be the first derivative of 7*r**6/180 + 11*r**5/120 + r**4/12 - r**3/3 - 3. Let f(w) be the third derivative of i(w). Factor f(k).
(2*k + 1)*(7*k + 2)
Let k(a) be the second derivative of a**7/231 + 4*a**6/165 + a**5/22 + a**4/33 + 14*a. Suppose k(r) = 0. What is r?
-2, -1, 0
Let j(b) be the second derivative of b**2 + 1/20*b**5 + 2*b + 5/6*b**3 + 1/3*b**4 + 0. What is m in j(m) = 0?
-2, -1
Let l(v) = 15*v**2 + 36*v + 45. Let f(u) = -8*u**2 - 18*u - 22. Let x(d) = -9*f(d) - 5*l(d). Factor x(t).
-3*(t + 3)**2
Let l(b) be the third derivative of 0*b - 2*b**2 + 0*b**3 - 1/70*b**7 + 0*b**5 + 0 + 0*b**4 - 1/40*b**6. Factor l(g).
-3*g**3*(g + 1)
Factor 4*t**2 - 21 - 4*t**3 - 5*t + 40 + 3*t**3 - 17.
-(t - 2)*(t - 1)**2
Let a(w) be the first derivative of -1/6*w**4 + 1/3*w**2 - 2/9*w**3 + 0*w - 4 + 2/15*w**5. Factor a(d).
2*d*(d - 1)**2*(d + 1)/3
Let b = 574/3 - 190. Factor -4/3*a**3 + 4/3*a - a**2 - 1/3*a**4 + b.
-(a - 1)*(a + 1)*(a + 2)**2/3
Let i(k) be the third derivative of k**8/1848 + 4*k**7/1155 + k**6/220 - 16*k**2. What is d in i(d) = 0?
-3, -1, 0
Factor 5*f**3 - 2*f**4 + 6*f**4 + 8 - 4*f - 6*f**3 + 5*f**3 - 12*f**2.
4*(f - 1)**2*(f + 1)*(f + 2)
Let m(i) be the second derivative of i**6/240 - 3*i**5/160 + i**4/32 - i**3/48 - 11*i. Suppose m(q) = 0. What is q?
0, 1
Let h(p) = 55*p**3 - 210*p**2 - 35*p + 85. Let t(r) = 9*r**3 - 35*r**2 - 6*r + 14. Let v(m) = 6*h(m) - 35*t(m). Factor v(s).
5*(s - 2)*(s - 1)*(3*s + 2)
Suppose p + 2*p + 4*o = 64, p - o = 26. Let j be ((-18)/p)/(45/(-24)). Solve -2/5*w**2 + 0 - j*w = 0.
-1, 0
Let -1/5*m**3 + m**2 + 1/5*m - 2/5*m**4 - 3/5 = 0. What is m?
-3/2, -1, 1
Let p(i) be the third derivative of -i**7/350 - 3*i**6/200 - 3*i**5/100 - i**4/40 - 2*i**2. Factor p(s).
-3*s*(s + 1)**3/5
Let h(c) be the third derivative of -c**6/96 + 5*c**5/48 - 5*c**4/12 + 5*c**3/6 - 39*c**2. Factor h(x).
-5*(x - 2)**2*(x - 1)/4
Let t be ((-22)/4)/(9/(-18)). Let z = t - 7. Factor -4/7*u**2 + 0 + 0*u**3 + 2/7*u**5 - 2/7*u + 4/7*u**z.
2*u*(u - 1)*(u + 1)**3/7
Let h(b) be the third derivative of b**6/600 + b**5/200 - b**4/20 + b**3/6 - 7*b**2. Let i(l) be the first derivative of h(l). Factor i(m).
3*(m - 1)*(m + 2)/5
Let y(r) be the second derivative of r**2 - 2/3*r**3 + 0 - 4*r - 1/15*r**6 + 0*r**4 + 1/5*r**5. Factor y(v).
-2*(v - 1)**3*(v + 1)
Let s(w) be the third derivative of 0*w**4 + 0 + 1/360*w**6 + 0*w + 0*w**3 - 4*w**2 + 1/180*w**5 - 1/315*w**7. Suppose s(h) = 0. Calculate h.
-1/2, 0, 1
Find c such that -8*c + 1/2*c**2 + 10 + 1/2*c**3 = 0.
-5, 2
Let i = -2 + 5. Let x(d) be the second derivative of -1/42*d**7 - 3/10*d**5 + 2/15*d**6 + 1/3*d**4 - 2*d + 0 - 1/6*d**i + 0*d**2. Factor x(u).
-u*(u - 1)**4
Suppose 8 = -d - d. Let r = -2 - d. Factor 1/2*f**r + 0*f + 0.
f**2/2
Let w be 2/(-3)*3/(-7). Factor 0*z**2 + 0*z + 2/7*z**5 + 0 - w*z**4 + 0*z**3.
2*z**4*(z - 1)/7
Suppose 0 = -4*x + 5*q + 94, -4*q = 2 - 10. Let u(k) = 4*k**2 - 13*k. Let l(r) = -r**2 + 3*r. Let m(c) = x*l(c) + 6*u(c). Find n such that m(n) = 0.
0
Let c(h) be the third derivative of -h**9/1008 + 3*h**7/280 - h**6/60 + h**3/2 - 8*h**2. Let t(w) be the first derivative of c(w). Solve t(y) = 0 for y.
-2, 0, 1
Suppose -5*y = -i + 15 - 12, 4*i = -2*y + 12. Suppose -20 = -k + 4*a, 3*a + 20 = 5*k - a. Factor 1/3*p**4 + p**i + 1/3*p + k + p**2.
p*(p + 1)**3/3
Let k(u) be the second derivative of -u**5/4 + 5*u**4/12 + u. Factor k(m).
-5*m**2*(m - 1)
Suppose 4*o - 2*o = -5*l + 745, 0 = -4*l - 3*o + 603. Find a such that -27*a**2 + 72*a**2 + 27*a**2 + 5*a - 63*a**3 - l*a**4 - 17*a = 0.
-1, 0, 2/7
Suppose 0 = -3*p + 7*p - 5*c + 13, 4*p - 32 = -4*c. Solve 0 - p*r + 9/2*r**3 + 3/2*r**2 = 0 for r.
-1, 0, 2/3
Let w be 2 - 6 - (-194)/48. Let x(y) be the second derivative of -3*y - 1/6*y**3 + 0 - 1/4*y**2 - w*y**4. What is f in x(f) = 0?
-1
Suppose 2*g = -r, -r + 3*g = -g. Let v = 0 + 0. Factor 1/6*k**4 + r*k + 0*k**2 + v + 1/3*k**3.
k**3*(k + 2)/6
Let m(r) be the third derivative of -r**5/40 - 9*r**4/64 - r**3/8 - 9*r**2. Factor m(z).
-3*(z + 2)*(4*z + 1)/8
Let s(r) be the second derivative of r**7/112 + 5*r. Factor s(f).
3*f**5/8
Let m = 1165 + -44259/38. Let a = m + 4/19. Solve -a*c**3 - 1/6*c + 1/2*c**2 + 1/6*c**4 + 0 = 0.
0, 1
Let r(p) be the second derivative of p**7/10080 - p**6/1440 + p**5/480 - p**4/6 - 3*p. Let w(s) be the third derivative of r(s). Suppose w(a) = 0. Calculate a.
1
Factor 0 + 2/17*w**4 - 8/17*w**3 + 10/17*w**2 - 4/17*w.
2*w*(w - 2)*(w - 1)**2/17
Let o = -179/4 - -45. Let g be ((-6)/(-18))/(2/6). Solve -s + o*s**2 + g = 0.
2
Factor 14/9*q**2 + 16/9*q**3 + 0 + 2/3*q**4 + 4/9*q.
2*q*(q + 1)**2*(3*q + 2)/9
Let q(b) be the third derivative of -b**6/420 + b**5/14 - 25*b**4/28 + 125*b**3/21 - b**2. Solve q(u) = 0 for u.
5
Let j(s) be the third derivative of -6/5*s**5 + 2/5*s**6 + 0*s - s**3 + 0 - 4*s**2 - 15/8*s**4. Factor j(x).
3*(x - 2)*(4*x + 1)**2
Let w(c) be the first derivative of -1/8*c**4 - 2/3*c**3 - c - 5/4*c**2 + 3. Factor w(j).
-(j + 1)**2*(j + 2)/2
Let h(l) be the first derivative of 0*l