
-1, -1/4, 0
Let y(t) be the third derivative of -t**6/1020 + t**5/170 - t**4/68 + t**3/51 - 3*t**2. Find v, given that y(v) = 0.
1
Let x(y) be the third derivative of -1/15*y**6 + 1/35*y**7 + 0*y**3 + 2*y**2 + 0 + 1/30*y**5 + 0*y + 0*y**4. Factor x(s).
2*s**2*(s - 1)*(3*s - 1)
Let z(d) be the second derivative of 7*d**5/180 - 5*d**4/108 - 8*d**3/27 - 2*d**2/9 + 5*d. Find i, given that z(i) = 0.
-1, -2/7, 2
Factor -2/9*x**2 + 2/9*x**3 - 8/9*x + 8/9.
2*(x - 2)*(x - 1)*(x + 2)/9
Let f(l) = 8*l**2 + 7*l - 7. Let m(v) = v**2 + v - 1. Let s(x) = 2*f(x) - 14*m(x). Factor s(j).
2*j**2
Factor -21*d + 5*d**2 + 33*d - 32 + 20*d**2 + 19*d**2.
4*(d + 1)*(11*d - 8)
Let w(f) be the second derivative of f**6/40 - 3*f**2/2 + 2*f. Let s(x) be the first derivative of w(x). Factor s(t).
3*t**3
Let u(l) be the first derivative of -l**2 + 2/5*l**5 + 1/3*l**4 + 1/9*l**6 - 4/9*l**3 - 2/3*l + 5. Determine b, given that u(b) = 0.
-1, 1
Suppose 0 = -4*t - 16, -2*d + 0*t = -t - 4. Suppose -2/3*j + 0 + 4/3*j**2 - 4/3*j**4 + 2/3*j**5 + d*j**3 = 0. Calculate j.
-1, 0, 1
Let h(n) be the first derivative of -2*n**5/35 - n**4/7 - 2*n**3/21 + 31. Factor h(z).
-2*z**2*(z + 1)**2/7
Let a = 88 - 83. Let z(l) be the first derivative of 0*l + 2 + 4/21*l**3 - 1/14*l**4 + 0*l**2 - 2/35*l**a. Factor z(k).
-2*k**2*(k - 1)*(k + 2)/7
Let j = -49 - -50. Let h be j - 0 - (-6)/(-54). Factor h*k + 2/9*k**2 - 2/9*k**3 - 8/9.
-2*(k - 2)*(k - 1)*(k + 2)/9
Suppose -60 = 3*l + 3*w, -4*l - 60 = w - 2*w. Let b be (-4)/l - (-30)/8. Factor g**2 + 0*g - 7/2*g**3 + 0 + b*g**4 - 3/2*g**5.
-g**2*(g - 1)**2*(3*g - 2)/2
Let x be 2*(1 + (-10)/(-4)). Let d = x - 5. Factor -2*o**3 + d*o**2 + 3*o - o**2 - 3*o**2 + 2*o**4 - o.
2*o*(o - 1)**2*(o + 1)
Suppose -2*f = -2*c - 2, -c - f - 3*f + 9 = 0. Let d be (2 - 2)/(-3 + c). Suppose 0*h + d + 1/3*h**2 = 0. What is h?
0
Factor -3*s**2 + 5*s + 0*s**2 + 4 + s + 5.
-3*(s - 3)*(s + 1)
Let g be (4 - 4) + (-8)/(-6). Factor 4/3 + 1/3*u**2 + g*u.
(u + 2)**2/3
Let x(p) be the second derivative of p**6/420 + p**5/210 + p**2 + p. Let t(b) be the first derivative of x(b). Determine d so that t(d) = 0.
-1, 0
Let v = 28 - 20. Let i = v + -31/4. Factor -i*s - 1/4 + 1/4*s**3 + 1/4*s**2.
(s - 1)*(s + 1)**2/4
Suppose 3*r + 5*s = 14, -5*s - 1 + 6 = 0. Let o be 14/8 + (-3)/(-12). Suppose -4*y**2 + y**r + 3*y**2 - 3*y + 3*y**o = 0. Calculate y.
-3, 0, 1
Let h(m) be the second derivative of -m**5/25 + 2*m**4/15 - 12*m. Factor h(c).
-4*c**2*(c - 2)/5
Let z(i) be the first derivative of i**7/560 - i**6/48 + i**5/10 - i**4/4 - 2*i**3/3 - 2. Let o(m) be the third derivative of z(m). Suppose o(q) = 0. What is q?
1, 2
Let n = 86 + -772/9. Factor 4/9*h + n*h**2 + 2/9.
2*(h + 1)**2/9
Let v(s) = 2*s**2 - 9*s + 7. Let r(x) = 2*x**2 - 8*x + 6. Let c(i) = 3*r(i) - 4*v(i). Determine t, given that c(t) = 0.
1, 5
Suppose 0 = -4*w - 12, 0*y + 33 = 3*y - 3*w. Let n = 11 - y. Factor 2*h - h**2 - n + 2 - 4*h.
-(h + 1)**2
Let k(x) be the third derivative of -x**7/63 - x**6/10 - 17*x**5/90 + 4*x**3/9 + 2*x**2. Solve k(q) = 0.
-2, -1, 2/5
Suppose 3*x**2 + 13*x**2 + 1 - 1 + 12*x + 2 = 0. Calculate x.
-1/2, -1/4
Let x(c) be the first derivative of -14/75*c**5 - 1 - 4/45*c**3 + 0*c + 0*c**2 + 3/10*c**4. Factor x(w).
-2*w**2*(w - 1)*(7*w - 2)/15
Factor 2/9*i + 4/9 - 2/9*i**2.
-2*(i - 2)*(i + 1)/9
Let v(i) be the second derivative of i**7/126 + i**6/90 - i**5/30 - i**4/18 + i**3/18 + i**2/6 - 6*i. What is u in v(u) = 0?
-1, 1
Let f(s) be the first derivative of -1/9*s**3 - 1/4*s**4 - 1/15*s**5 + 1/2*s**2 + 3 + 2/3*s. Factor f(n).
-(n - 1)*(n + 1)**2*(n + 2)/3
Let t(y) be the first derivative of y**4 - 4*y**3/3 - 3. Factor t(c).
4*c**2*(c - 1)
Let y(x) be the first derivative of -5*x**3/2 - 9*x**2/4 + 3*x + 6. Let y(d) = 0. Calculate d.
-1, 2/5
Let k be (-14)/196*(-14)/4. Let f(z) be the first derivative of 21/20*z**5 - 3/8*z**2 - 1/2*z**3 + 2 + k*z + 3/8*z**6 + 5/8*z**4. Find n such that f(n) = 0.
-1, 1/3
Let m(y) be the second derivative of -1/20*y**5 + 0*y**3 + 1/12*y**4 + 0 + 0*y**2 - 3*y. Factor m(i).
-i**2*(i - 1)
Let b(c) = -c**2 - 1. Let o(r) = 7*r**2 - 28*r + 31. Let q(v) = 5*b(v) + o(v). Find f such that q(f) = 0.
1, 13
Suppose -3/5*h**4 - 3/5*h + 3/5*h**3 + 0 + 3/5*h**2 = 0. Calculate h.
-1, 0, 1
Suppose -3*y + 2*q = -12 + 4, -4*y + 10 = -2*q. Suppose m - y = -0. Suppose -d - d**2 - d**2 - d - m*d = 0. Calculate d.
-2, 0
Let d = -74 + 78. Let c(p) be the third derivative of 0*p + 0*p**d + 0*p**3 - 1/30*p**5 + 0 - 2*p**2. Factor c(m).
-2*m**2
Let d be (-1)/(-3 + (-10)/(-4)). Suppose d*y - 398 = 610. Factor 343*x**4 - 16 - 150*x + 52*x - 392*x**3 - y*x**2 - 62*x.
(x - 2)*(7*x + 2)**3
Let f be 0/(-4)*5/10. Let o(j) be the first derivative of -2 + 1/7*j**2 + f*j - 1/14*j**4 + 2/21*j**3 - 2/35*j**5. Factor o(c).
-2*c*(c - 1)*(c + 1)**2/7
Suppose -g + 7 - 7 = 0. Suppose -2*y**4 - 2/3*y**5 - 2/3*y**2 + 0*y - 2*y**3 + g = 0. What is y?
-1, 0
Let m(c) be the first derivative of 7*c**3/4 - 45*c**2/4 + 6*c + 47. Factor m(o).
3*(o - 4)*(7*o - 2)/4
Suppose -t - 135 = 8*o - 3*o, -4*t = o + 46. Let c be 1 - (-4 - o/6). Solve 1/3*b**2 - c - 1/3*b = 0.
-1, 2
Let m be ((-3)/6)/(2/32). Let h be ((-1)/m)/((-4)/(-24)). Solve 0 + 1/4*j**4 + h*j**2 - 1/4*j - 3/4*j**3 = 0 for j.
0, 1
Let d(l) be the third derivative of l**5/12 - 5*l**3/6 - 11*l**2. Factor d(n).
5*(n - 1)*(n + 1)
Suppose 3 = 4*t + 3*b, -4*b + 4 = t + 3*t. Let i be (-8)/77 + (-4)/(-14). Factor t*l + 2/11*l**2 - i*l**3 + 0.
-2*l**2*(l - 1)/11
Let b(v) = v**2 + 4*v + 1. Let t be b(-3). Let g = 0 - t. Find a such that 2*a**2 + 4*a**5 - a - g*a**5 + 3*a**3 + 5*a**4 - 3*a**2 = 0.
-1, 0, 1/2
Let c be 10/(-12) + (-2)/12. Let f(n) = n**3 + n + 1. Let x(t) = -2*t**3 - 3*t**2 + t + 1. Let j(a) = c*f(a) + x(a). Suppose j(o) = 0. What is o?
-1, 0
Suppose 27*c + 36*c**2 + 1/3*c**5 + 0 + 18*c**3 + 4*c**4 = 0. Calculate c.
-3, 0
Let a(g) be the first derivative of -g**5/240 + g**4/24 - g**3/6 - 3*g**2/2 - 1. Let h(m) be the second derivative of a(m). Suppose h(z) = 0. What is z?
2
Let y(f) be the first derivative of 5*f**3/3 - 15*f**2 + 25*f + 53. Factor y(v).
5*(v - 5)*(v - 1)
Let l(x) be the third derivative of x**6/240 + 7*x**5/120 + 5*x**4/16 + 3*x**3/4 + x**2. Find u, given that l(u) = 0.
-3, -1
Let q = 63/265 + -2/53. Let m = 7/10 - q. Solve 0 + 1/2*n**2 + m*n**3 - n = 0.
-2, 0, 1
Let p(v) = -v**3 + 4*v**2 + 2*v - 6. Let k be p(4). Factor -4*w**2 - 2*w**k + 6 - 4 - 6*w**2 - 6*w**4 - 16*w**3.
-2*(w + 1)**3*(3*w - 1)
Suppose 3*g - 12 = 2*i + 3*i, 0 = g + 2*i - 4. Let c = 4 - g. Determine z so that 2/9*z**2 + 4/9*z**3 + 2/9*z**4 + 0 + c*z = 0.
-1, 0
Let t = -148 + 4441/30. Let x(y) be the second derivative of 0 + 2*y - t*y**4 - 1/15*y**3 + 0*y**2. Determine p so that x(p) = 0.
-1, 0
Let t(c) be the first derivative of -1/3*c**3 + 0*c + c**2 + 4. Factor t(v).
-v*(v - 2)
What is n in -2*n**3 + 5*n**4 + 8*n**3 + 3*n**4 - 6*n**4 = 0?
-3, 0
Let g(o) = -17*o**2 - 22*o - 5. Let v(u) = 120*u**2 + 155*u + 35. Let t(j) = -15*g(j) - 2*v(j). Find s such that t(s) = 0.
-1, -1/3
Let z(j) = -3*j - 17. Let g be z(-7). Find x such that -2/3*x**g + 0*x + 2*x**3 + 0 - 4/3*x**2 = 0.
0, 1, 2
Let r(t) be the third derivative of t**5/20 - t**4/4 - 3*t**3/2 - 15*t**2. Factor r(w).
3*(w - 3)*(w + 1)
Suppose 2/9*s**2 + 14/9*s + 4/9 - 14/9*s**3 - 2/3*s**4 = 0. Calculate s.
-2, -1, -1/3, 1
Let n(r) be the third derivative of 0 + 1/420*r**6 + 0*r**4 + 2*r**2 + 1/147*r**7 + 0*r**3 + 1/392*r**8 + 0*r - 1/210*r**5. Suppose n(g) = 0. Calculate g.
-1, 0, 1/3
Let i(l) be the first derivative of l**3/3 + 3*l**2/2 + 20. Determine w, given that i(w) = 0.
-3, 0
Let l(b) be the third derivative of 0*b**5 + 0 - 1/24*b**4 + 0*b**3 + b**2 + 1/120*b**6 + 0*b. Solve l(h) = 0 for h.
-1, 0, 1
Let a(c) = -c**2. Let l(h) = 5*h**2 + 28*h + 98. Let o(g) = 6*a(g) + 2*l(g). Find z such that o(z) = 0.
-7
Let j(t) be the third derivative of 0 + 1/210*t**5 + 0*t**4 + 0*t - t**2 + 0*t**3 + 1/420*t**6. Let j(n) = 0. What is n?
-1, 0
Let b(n) be the first derivative of -n**7/20 + n**6/9 - n**5/15 - n**3 + 4. Let r(j) be the third derivative of b(j). Factor r(x).
-2*x*(3*x - 2)*(7*x - 2)
Let p(d) be the second derivative of 0 + 4/3*d**2 - d + 20/9*d**3 + 25/18*d**4. What is f in p(f) = 0?
-2/5
Let x(u) be the second derivative 