1
Let f(a) be the third derivative of a**7/1155 - a**6/132 + a**5/110 + 5*a**4/132 - 4*a**3/33 - 24*a**2. Suppose f(s) = 0. What is s?
-1, 1, 4
Let r(t) be the second derivative of -t - 1/72*t**4 + 0 - 1/12*t**2 - 1/18*t**3. Factor r(w).
-(w + 1)**2/6
Let m = 17 + -11. Let o(n) be the first derivative of -2 + 1/12*n**3 + 0*n**2 + 1/4*n**4 - 1/6*n**m + 0*n - 1/20*n**5. Let o(q) = 0. Calculate q.
-1, -1/4, 0, 1
Let w(n) = 12*n**4 - 8*n**3 + 8*n - 4. Let m(s) = -s**4 + s**3 - s**2 - s + 1. Let g(u) = 8*m(u) + w(u). Let g(l) = 0. Calculate l.
-1, 1
Factor -2*i**4 + 3 - 3 - 38*i**2 + 46*i**2 + 6*i**3.
-2*i**2*(i - 4)*(i + 1)
Let s(d) be the first derivative of d**4/4 - d**3/3 - d**2/2 + 1. Let w(h) = 6*h**3 - 14*h**2 + 7*h - 2. Let i(f) = -2*s(f) + w(f). Factor i(y).
(y - 2)*(2*y - 1)**2
Determine x, given that 11*x**2 + 10*x**2 - x + 9*x**3 - 9*x + 3 - 7*x = 0.
-3, 1/3
Let o(w) = w**2 - 7*w + 6. Let v be o(6). Find x such that -x**3 + x**3 + 2*x**3 + v*x**3 = 0.
0
Let d(i) be the first derivative of i**7/525 + i**6/300 + i**2/2 + 2. Let l(j) be the second derivative of d(j). Factor l(n).
2*n**3*(n + 1)/5
Let r(l) be the second derivative of l**7/21 + l**6/5 - 2*l**4/3 - 37*l. Factor r(i).
2*i**2*(i - 1)*(i + 2)**2
Let r(g) be the third derivative of -g**7/280 + g**6/80 + g**5/80 - g**4/16 + g**2 + 22*g. Factor r(h).
-3*h*(h - 2)*(h - 1)*(h + 1)/4
Let p(r) = -3*r**2 - 2*r - 3. Let m(d) = -d**2 - 1. Let q = 2 + -3. Let f(u) = q*p(u) + 4*m(u). Factor f(a).
-(a - 1)**2
Let b = 256/13 + -1228/65. Determine l, given that b*l**3 - 2/5*l + 0*l**4 + 0*l**2 - 2/5*l**5 + 0 = 0.
-1, 0, 1
Let i(k) be the third derivative of -k**7/630 + k**6/180 - k**4/36 + k**3/18 - 6*k**2. Solve i(r) = 0 for r.
-1, 1
Let n be (-12)/(-8)*8/6. Let r(t) be the first derivative of 1/4*t**4 + 2 - 1/2*t**n - 1/3*t**3 + t. Suppose r(c) = 0. Calculate c.
-1, 1
Let d = 12/11 - 13/22. Factor 0 - d*s - 4*s**3 - 7/2*s**2 + 8*s**4.
s*(s - 1)*(4*s + 1)**2/2
Let x(m) be the second derivative of 0 - 7/30*m**6 + 1/14*m**7 + 1/4*m**4 + 0*m**2 + m - 1/3*m**3 + 3/20*m**5. Find p, given that x(p) = 0.
-2/3, 0, 1
Let l(z) be the third derivative of -z**8/10080 + z**7/1260 - z**5/15 - 7*z**2. Let j(r) be the third derivative of l(r). Factor j(d).
-2*d*(d - 2)
Let v(y) be the first derivative of 1/7*y**3 - 2/7*y**2 + 1/21*y**4 + 2 - y. Let t(l) be the first derivative of v(l). Solve t(n) = 0.
-2, 1/2
Let w(b) = b**2 - b - 3. Let f be w(3). Let v be 3*(-2 + f)*1. Factor -d**v + 0*d**2 + 4 - d**2 - 3 + d.
-(d - 1)*(d + 1)**2
Let o(i) be the first derivative of i**4/10 + 2*i**3/3 + 7*i**2/5 + 6*i/5 + 2. Find g such that o(g) = 0.
-3, -1
Let p(t) be the first derivative of -2*t**6 - 16*t**5/5 + t**4 + 8*t**3/3 + 10. Factor p(k).
-4*k**2*(k + 1)**2*(3*k - 2)
Let w be 114/(-38)*(-9)/6. Factor -3/2 - w*z - 9/2*z**2 - 3/2*z**3.
-3*(z + 1)**3/2
Let z = 11/7 - 41/35. Solve -7/5*v**3 - 9/5*v**2 + 0 - z*v = 0 for v.
-1, -2/7, 0
Let l = -125 + 127. Factor -1/3*a**l + 0 + a.
-a*(a - 3)/3
Let f(a) = -a**3 - a + 1. Let g(o) = o**4 + 10*o**3 + 24*o**2 + 34*o + 14. Let b(h) = 4*f(h) + 2*g(h). Solve b(v) = 0.
-2
Let r(d) be the second derivative of 3/4*d**2 + 0 - 1/20*d**6 - 5*d + 3/20*d**5 + 0*d**4 - 1/2*d**3. Factor r(t).
-3*(t - 1)**3*(t + 1)/2
Let o(l) = -l**2 - 13*l + 2. Let i be o(-13). Factor -3*z**4 + z**2 + 2*z**3 - i*z**5 + z**5 - z**3 + 2*z**4.
-z**2*(z - 1)*(z + 1)**2
Let j = 3/55 - -431/165. Factor -j - 40/3*v - 14*v**2.
-2*(3*v + 2)*(7*v + 2)/3
Factor 3/5*s**5 + 0 + 3/5*s**4 - 6/5*s**3 + 0*s + 0*s**2.
3*s**3*(s - 1)*(s + 2)/5
Let l(q) be the first derivative of -q**4/7 + 19*q**3/21 - 11*q**2/14 - 4*q/7 - 30. Factor l(x).
-(x - 4)*(x - 1)*(4*x + 1)/7
Let v(b) be the first derivative of -b**7/140 + b**6/80 + 2*b**2 - 3. Let t(u) be the second derivative of v(u). Let t(d) = 0. Calculate d.
0, 1
Let s(d) be the third derivative of -d**8/1176 + d**7/245 + d**6/42 + d**5/105 - 3*d**4/28 - 5*d**3/21 + 12*d**2. Suppose s(o) = 0. Calculate o.
-1, 1, 5
Suppose -4*k + 10 = -w, -3*k - 3*w + 9 + 6 = 0. Suppose -3*u = -2 - 4. Factor 4*z - k - 9*z**2 - z**u + 3.
-2*z*(5*z - 2)
Let r(l) = -l**3 + 6*l**2 + 8*l - 4. Let w be r(7). Suppose w*x = 2*t - 14, -5*t = -4*x + x - 26. Factor -2/7*g**2 + 2/7*g**t + 2/7*g**5 - 2/7*g**3 + 0*g + 0.
2*g**2*(g - 1)*(g + 1)**2/7
Let h(g) be the second derivative of -g**9/13608 + g**7/1890 - g**5/540 - g**3/2 - 3*g. Let o(a) be the second derivative of h(a). Suppose o(u) = 0. What is u?
-1, 0, 1
Let m(d) be the first derivative of 6*d**2 + 4*d**3 + 0*d + 3/4*d**4 - 6. Factor m(z).
3*z*(z + 2)**2
Let k(b) be the first derivative of 0*b - 3 - 3/4*b**4 + 1/2*b**6 + 0*b**3 + 0*b**5 + 0*b**2. Let k(d) = 0. What is d?
-1, 0, 1
Let y(d) be the second derivative of -1/120*d**6 + 0*d**3 + 1/60*d**5 - 2*d + 0*d**4 + 0 + d**2. Let r(h) be the first derivative of y(h). Solve r(c) = 0 for c.
0, 1
Let i(n) = -6*n**2 - 6*n. Let q be ((-6)/4)/((-7)/14). Let x(b) = 5*b**2 + 5*b - 1. Let w(l) = q*i(l) + 4*x(l). What is k in w(k) = 0?
-2, 1
Let d = 24 + -95/4. Let 0*u**2 - 1/4*u**5 + 0 + 0*u + d*u**3 + 0*u**4 = 0. What is u?
-1, 0, 1
Let k(f) be the second derivative of 6*f + 0*f**2 + 1/28*f**4 + 0 + 1/210*f**6 - 1/42*f**3 - 3/140*f**5. Suppose k(o) = 0. Calculate o.
0, 1
Let v(u) be the third derivative of -2*u**7/105 - u**6/30 + 2*u**5/5 + 2*u**4/3 - 16*u**3/3 - 9*u**2. Suppose v(m) = 0. Calculate m.
-2, 1, 2
Let q(h) = 12*h - 201. Let n be q(17). Solve -2/5*y**5 - 4/5*y + 6/5*y**n + 2/5*y**4 + 0 - 2/5*y**2 = 0.
-1, 0, 1, 2
Let t = 5 - 1. Determine m so that 2*m**3 + t*m**3 - 3*m - 8*m**5 + 5*m**5 = 0.
-1, 0, 1
Let y(p) be the third derivative of 0*p + 1/10*p**5 + 2*p**2 + 1/60*p**6 + 0 + 0*p**3 + 1/6*p**4. Find l such that y(l) = 0.
-2, -1, 0
Let f(l) be the third derivative of 2*l**7/735 + l**6/70 - l**5/15 - 5*l**4/14 + 12*l**3/7 - 38*l**2. Suppose f(d) = 0. Calculate d.
-3, 1, 2
Suppose -k - 16 = -3*k + 3*f, 3*k - 24 = -3*f. Suppose -k = 5*b - 18. Suppose 64/5 + 2/5*n**5 + 4*n**4 + 32*n + 16*n**3 + 32*n**b = 0. What is n?
-2
Let j = 869/12 - 283/4. Find q such that j*q**2 - 5/3*q**3 + 0*q + 0 = 0.
0, 1
Let j = -168 - -168. Factor j - 1/3*u**5 + 0*u - u**4 - 1/3*u**2 - u**3.
-u**2*(u + 1)**3/3
Factor 1/4*c**2 + 0 - 1/4*c**3 + 1/4*c**5 - 1/4*c**4 + 0*c.
c**2*(c - 1)**2*(c + 1)/4
Factor 0*z + 0*z**2 - 4/7*z**4 + 0 + 4/7*z**5 + 0*z**3.
4*z**4*(z - 1)/7
Let h(t) be the first derivative of -2/9*t**3 - 1 + 1/3*t**2 + 2/15*t**5 + 0*t - 1/6*t**4. Factor h(r).
2*r*(r - 1)**2*(r + 1)/3
Let c(w) be the second derivative of w**4/42 + 2*w**3/21 + w**2/7 - 15*w. Factor c(v).
2*(v + 1)**2/7
Let s be (32/(-90))/(1*(-4)/10). Find c such that 0*c**2 - 2/9*c**3 + 0*c + 0 + s*c**4 = 0.
0, 1/4
Factor -2*h**3 - 7*h + 6*h + 4*h**2 + 7*h.
-2*h*(h - 3)*(h + 1)
Factor -8*j**4 - 13*j**4 + 22*j**4 - 4*j**4 + 3*j**3.
-3*j**3*(j - 1)
Let k = 14 + -3. Factor 2*a**4 - 28*a**3 - k*a**4 - 32*a**2 - 2*a**5 - 18*a - 4 - 3*a**4.
-2*(a + 1)**4*(a + 2)
Let r = 591 - 588. Find p such that 0 + p - 9/2*p**r + 1/2*p**4 + 3/2*p**2 + 3/2*p**5 = 0.
-2, -1/3, 0, 1
Let j be (5 - (-2)/(-1)) + -1. Let i = -1 - -3. Factor -14*z**3 - 1 - 10*z**i - 3*z - 5*z**4 - z**5 - j*z + 4*z**3.
-(z + 1)**5
Let c(i) be the third derivative of 0*i**6 + 1/48*i**4 + 0 + 2*i**2 + 1/60*i**5 - 1/672*i**8 + 0*i**3 + 0*i - 1/210*i**7. Find r, given that c(r) = 0.
-1, 0, 1
Suppose -g - 29*g**2 - 28*g**2 + 77*g**2 - 3*g**3 - 24*g**2 = 0. What is g?
-1, -1/3, 0
Factor 1/2*g**3 - 3/2 - 1/2*g**2 - 5/2*g.
(g - 3)*(g + 1)**2/2
Let p(w) be the first derivative of -2*w**5/25 - 7*w**4/30 - 2*w**3/15 + w**2/5 + 4*w/15 - 51. Factor p(r).
-2*(r + 1)**3*(3*r - 2)/15
Let l(y) = y**3 - 2*y**2 - 3*y - 2. Let k be l(3). Let z be k/(-9) + 48/270. Factor -z*x**4 - 2/5*x**3 + 2/5*x**5 + 0*x + 2/5*x**2 + 0.
2*x**2*(x - 1)**2*(x + 1)/5
Let q(b) = -b**2 + 6*b + 8. Let i be q(7). Let k be i/(-4) + 39/12. Factor 0*j**3 + j**k + 4*j - 3*j + 2*j**2.
j*(j + 1)**2
Let k(c) be the first derivative of -c**8/168 + 2*c**7/105 - c**5/15 + c**4/12 - 3*c**2/2 - 2. Let f(n) be the second derivative of k(n). Factor f(r).
-2*r*(r - 1)**3*(r + 1)
Let h(n) be the third derivative of 0 - 1/12*n**4 - 1/20*n**5 - 3*n**2 - 1/120*n**6 + 0*n + 0*n**3. Factor h(l).
-l*(l + 1)*(l + 2)
Let c(v) be the third derivative 