
-1, 0
Let j(s) be the third derivative of s**7/210 + s**6/30 + s**5/20 - s**4/6 - 2*s**3/3 - 10*s**2. Find o such that j(o) = 0.
-2, -1, 1
Suppose -4*u = -p + 24, 4*u - 6 = u. Suppose 5*q + 7 = p. What is f in 7/4*f - 1/4*f**q + 1/2*f**3 + 1/2*f**4 - 2*f**2 - 1/2 = 0?
-2, 1
Let i(v) = -v**4 - 3*v**3 + 4*v**2 - 3. Let q(z) = 3*z**4 + 5*z**3 - 8*z**2 + 5. Let w(o) = 5*i(o) + 3*q(o). Determine l, given that w(l) = 0.
-1, 0, 1
Suppose w + 22 = 12*w. Let 0*v - 2/3*v**4 + 10/9*v**3 - 4/9*v**w + 0 = 0. What is v?
0, 2/3, 1
Let y be (0 + 1 - 0)*1. Determine d so that -4*d**3 + y - 8 + 6*d**2 + 8*d - 2*d**4 - 1 = 0.
-2, 1
Let g(a) be the second derivative of 0*a**2 - 1/25*a**5 + 0*a**3 + 4*a + 0*a**4 + 1/21*a**7 + 1/25*a**6 + 0. Factor g(d).
2*d**3*(d + 1)*(5*d - 2)/5
Let q(y) be the second derivative of 5*y**7/42 - 2*y**6/3 + 3*y**5/4 + 18*y. Factor q(r).
5*r**3*(r - 3)*(r - 1)
Let v(w) = -w**3 - 1. Let d(f) = 2187*f**4 - 2913*f**3 - 2592*f**2 - 624*f - 45. Let h(i) = d(i) + 3*v(i). Let h(n) = 0. What is n?
-2/9, 2
Let b(i) be the first derivative of 4 - 14*i**2 - 8*i + 16/3*i**3. Factor b(g).
4*(g - 2)*(4*g + 1)
Let v(n) = -13*n**3 + 15*n**2 - 2*n. Let k(w) = -w**3 + w**2. Let m(p) = -24*k(p) + 3*v(p). Factor m(s).
-3*s*(s - 1)*(5*s - 2)
Let b(k) = 25*k**4 - 61*k**3 + 47*k**2 - 8*k + 3. Let i(t) = -t**4 + t**3 + t**2 + 1. Let r(o) = b(o) - 3*i(o). Determine j so that r(j) = 0.
0, 2/7, 1
Let z(l) = -l**4 + 2*l**3 + l**2 - 4*l - 2. Let j(t) = -t**4 - t**3 - t**2 + 1. Let y(v) = 2*j(v) - z(v). Suppose y(s) = 0. Calculate s.
-2, -1, 1
Let q(w) be the third derivative of w**5/360 - w**3/36 - 7*w**2. Factor q(n).
(n - 1)*(n + 1)/6
Let f(i) = 5*i - 7. Let y be f(2). Solve -6*x**4 + 134*x**2 + y*x**5 + 3*x**3 - 134*x**2 = 0 for x.
0, 1
Let f be (6/(-360))/(1/(-1)). Let y(m) be the third derivative of -2*m**2 + f*m**4 + 1/30*m**3 + 0 + 0*m + 1/300*m**5. Determine v so that y(v) = 0.
-1
Factor -21*b - 7 - 27*b**2 + 7 + 6.
-3*(b + 1)*(9*b - 2)
Let i(j) be the second derivative of 2*j + 0*j**2 + 1/30*j**4 + 0 + 0*j**3. Suppose i(a) = 0. What is a?
0
Let w(k) be the second derivative of 0 - k**2 - 2*k - 1/3*k**3 - 1/24*k**4. Solve w(y) = 0 for y.
-2
Suppose 2*k + 0*k = 6. Factor -l**k + 50*l**4 - 3*l**3 - 22*l**2 - 6*l**3 - 10*l**2 - 8*l.
2*l*(l - 1)*(5*l + 2)**2
Let u(g) be the first derivative of -2 - 16/5*g**2 + 14/15*g**3 + 8/5*g. Factor u(x).
2*(x - 2)*(7*x - 2)/5
Let z(t) be the second derivative of -1/5*t**2 - 1/20*t**4 - t + 1/6*t**3 + 0. Solve z(g) = 0 for g.
2/3, 1
Let p be ((-7)/14)/((-5)/((-320)/(-52))). Factor 2/13*w**2 - 8/13*w + p.
2*(w - 2)**2/13
Let n(x) be the second derivative of -x**8/168 + x**6/60 - 2*x**2 + x. Let m(a) be the first derivative of n(a). Determine i so that m(i) = 0.
-1, 0, 1
Let q = 297 + -294. Factor 0 - 9/4*i**2 - 3/4*i**q - 3/2*i.
-3*i*(i + 1)*(i + 2)/4
Let h(u) be the first derivative of u**4/18 - 2*u**3/9 + 2*u**2/9 - 4. Factor h(r).
2*r*(r - 2)*(r - 1)/9
Let v(t) be the second derivative of 27*t**7/7 - 93*t**6/5 + 71*t**5/2 - 67*t**4/2 + 16*t**3 - 4*t**2 + 4*t. Factor v(z).
2*(z - 1)**3*(9*z - 2)**2
Let z(y) be the third derivative of -y**5/90 + 2*y**4/9 - 16*y**3/9 + 5*y**2. Suppose z(f) = 0. What is f?
4
Let s(l) be the second derivative of l**7/105 + l**6/25 + l**5/25 - l**4/15 - l**3/5 - l**2/5 + 12*l. Factor s(j).
2*(j - 1)*(j + 1)**4/5
Let c(r) be the third derivative of -r**7/120 + 19*r**6/480 - r**5/30 - r**4/24 - 9*r**2. Suppose c(z) = 0. What is z?
-2/7, 0, 1, 2
Suppose 9*p - 4*p - 2*y - 16 = 0, 0 = 4*p - 3*y - 10. Factor 8*b**3 + b + 5*b**2 + 0*b**3 + 3*b**p + 2*b**4 - b**4.
b*(b + 1)*(2*b + 1)**2
Let s(k) be the first derivative of -k**6/6 + k**5/5 + k**4/4 - k**3/3 + 26. Factor s(p).
-p**2*(p - 1)**2*(p + 1)
Let b = 145 + -143. Let -2/3*x**b + 16/3*x - 8/3 + 2/3*x**5 - 10/3*x**3 + 2/3*x**4 = 0. What is x?
-2, 1
Let z = 12/23 - 3337/6440. Let j(q) be the third derivative of 3*q**2 - 1/240*q**5 + 0*q + 0 + z*q**7 + 0*q**4 + 0*q**3 - 1/240*q**6. Factor j(n).
n**2*(n - 1)*(3*n + 1)/4
Let y(s) be the first derivative of -2*s**3/15 + 11. Determine o so that y(o) = 0.
0
Let l(h) = -7*h**2 - 11*h + 4*h - 5 + 5. Let o(s) = -3*s**2 - 3*s. Let c(n) = -4*l(n) + 9*o(n). Suppose c(k) = 0. Calculate k.
-1, 0
Let h = 29 + -18. Let c(z) = z - 11. Let u be c(h). Suppose 0 + 2/7*f**3 + u*f - 2/7*f**2 = 0. What is f?
0, 1
Suppose 0 = 2*p + p + 6. Let j = 0 - p. Factor -5*v + 5*v - 1 - v**j + 2*v.
-(v - 1)**2
Factor 4 - 27*w**2 + 2*w + 29*w**2 + 4*w.
2*(w + 1)*(w + 2)
Let r(s) = s**3 + 16*s**2 - 17*s + 9. Let b(y) = 8*y**2 - 8*y + 4. Let w(k) = -9*b(k) + 4*r(k). Solve w(z) = 0 for z.
0, 1
Let l(g) = g - 4. Let v be l(9). Suppose -13 - v = -6*f. Factor -16/3*c**2 + 14/3*c**f - 2/3 + 1/3*c**5 + 3*c - 2*c**4.
(c - 2)*(c - 1)**4/3
Let s(g) be the second derivative of -g**4/12 - 5*g**3/6 - 2*g**2 - 10*g + 1. Factor s(c).
-(c + 1)*(c + 4)
Let g(r) be the third derivative of r**8/2240 - r**7/1120 - r**6/480 + r**5/160 - 3*r**3/2 - 7*r**2. Let x(h) be the first derivative of g(h). Factor x(p).
3*p*(p - 1)**2*(p + 1)/4
Let r(z) be the third derivative of z**7/175 - 7*z**6/200 + 9*z**5/100 - z**4/8 + z**3/10 - z**2. Find n such that r(n) = 0.
1/2, 1
Solve 3 + 2*n**3 - 4*n + 0*n + 1 + 2*n - 4*n**2 = 0 for n.
-1, 1, 2
Let m(s) = s**5 - 5*s**4 + 7*s**3 + s**2 - 13*s + 4. Let y(q) = -q. Let i(v) = 4*m(v) - 20*y(v). Solve i(g) = 0.
-1, 1, 2
Let y = -151/4 + 15859/420. Let l(u) be the second derivative of y*u**7 + 1/15*u**3 + 1/5*u**2 - 1/15*u**4 - 1/25*u**5 + 0 - 2*u + 1/75*u**6. Factor l(f).
2*(f - 1)**2*(f + 1)**3/5
Let v = -16 - -26. Suppose -q + 4 = -2*b, 5*b + v = -0*q - 2*q. Suppose -3*g - 2 - 2*g**2 + 4*g**4 - 3*g**2 + q*g + 3 + 3*g**3 = 0. Calculate g.
-1, 1/4, 1
Let p(w) be the third derivative of -w**9/151200 + w**8/50400 + w**7/6300 + w**5/20 + w**2. Let t(q) be the third derivative of p(q). Factor t(y).
-2*y*(y - 2)*(y + 1)/5
Let z(d) = -2*d**2 - d + 1. Let k(t) = -44*t**2 + 4*t - 16. Let n(q) = k(q) - 20*z(q). Determine m so that n(m) = 0.
3
Let p be -4 - ((-72)/54)/((-2)/(-7)). Determine r so that -2/3*r - 2/3*r**2 + p*r**3 + 2/3 = 0.
-1, 1
Let s(a) be the first derivative of 0*a - 3 - 2*a**3 + 3/2*a**4 - 2/5*a**5 + a**2. Factor s(p).
-2*p*(p - 1)**3
Solve -36/13*a**2 - 216/13*a - 2/13*a**3 - 432/13 = 0 for a.
-6
Let r(z) be the first derivative of 1/8*z**2 - 1/40*z**5 - 2*z + 0*z**4 + 1/12*z**3 + 2 - 1/120*z**6. Let j(q) be the first derivative of r(q). Factor j(n).
-(n - 1)*(n + 1)**3/4
Let u be (-4)/(12/(-15)) + -1. Suppose 0*x + x - 5 = -u*j, 11 = 4*j - x. Suppose 2 - 5 - j*t**3 + 1 + 2*t + 2*t**2 = 0. Calculate t.
-1, 1
Let c = 5 + -3. Let i(x) be the third derivative of 1/120*x**6 + 2*x**c + 0 + 0*x + 0*x**3 - 1/18*x**4 - 1/45*x**5. Solve i(t) = 0.
-2/3, 0, 2
Let f(j) be the third derivative of -2*j**7/105 + j**6/15 - j**5/15 - 2*j**2. Factor f(s).
-4*s**2*(s - 1)**2
Let n(j) = j**4 - j. Let l = 8 - 10. Let f(m) = 3*m**4 + 4*m**3 + 5*m**2. Let b(i) = l*n(i) + f(i). Let b(t) = 0. What is t?
-2, -1, 0
Let q(l) be the second derivative of 1/28*l**7 + 0*l**2 - l - 7/60*l**6 + 3/40*l**5 + 0 - 1/6*l**3 + 1/8*l**4. Factor q(a).
a*(a - 1)**3*(3*a + 2)/2
Let m be (9/(-5) + 1)*-5. Let r be (-20)/(-45)*9/6. Factor -2/9*x**m - 2/3*x**2 + 0 + 2/9*x + r*x**3.
-2*x*(x - 1)**3/9
Let y be (-1 + -10)*(4 - 1). Let o be 0 + 3 + y/12. Factor -1/4 + o*f**2 - 1/4*f**3 + 1/4*f.
-(f - 1)**2*(f + 1)/4
Let g be (-6)/26*(2 - 32/12). Suppose g*w**4 - 4/13 - 6/13*w**3 + 6/13*w + 2/13*w**2 = 0. Calculate w.
-1, 1, 2
Let q(j) be the second derivative of j**6/180 + j**5/60 + j**3/3 - 2*j. Let o(l) be the second derivative of q(l). Let o(x) = 0. What is x?
-1, 0
Let v(f) be the first derivative of -f**4/20 - 10. Find q such that v(q) = 0.
0
Suppose 3*k = -5 + 17. Suppose k*h + 5*s = 31, -1 = -3*h + 2*h + s. Factor 1/2*o**2 - 3/4*o**h + 0*o + 0 - 1/4*o**3.
-o**2*(o + 1)*(3*o - 2)/4
Let h(p) be the third derivative of 1/1440*p**6 + 1/3*p**3 + 0*p**4 + p**2 + 0 - 1/480*p**5 + 0*p. Let u(w) be the first derivative of h(w). Factor u(y).
y*(y - 1)/4
Let a be 1/3 - (-35)/21. Suppose k - 13 = -4*q, 2*q + a*q + 5*k = 17. Factor 7*c - c**3 - 8*c + 2*c**q.
c*(c - 1)*(c + 1)
Let i(u) = u**5 - u**3 + u**2 - 1. Let a(y) = 6*y**5 + 5*y**4 - 7*y**3 + 9*y**2 - 9. Let 