
Let c(u) be the first derivative of u**6/66 - 3*u**5/55 + u**4/22 + 12. Solve c(p) = 0 for p.
0, 1, 2
Let p(c) = -3*c**5 - c**4 + c**3 + 5*c**2 + 2*c. Suppose -5*q - 2*d = 5, 6*q = q + 3*d + 20. Let a(x) = -x**5 - x**3. Let g(v) = q*p(v) - 2*a(v). Factor g(w).
-w*(w - 2)*(w + 1)**3
Factor 5/4*m**2 + 35/4*m + 25/2.
5*(m + 2)*(m + 5)/4
Suppose -4/3*r - 1/3*r**2 - 4/3 = 0. What is r?
-2
Suppose -21*b - 14*b + 105 = 0. Solve 16/5*w + 2/5*w**b + 8/5 + 2*w**2 = 0.
-2, -1
Suppose 0 = -6*v + 6 + 18. Let l(j) be the third derivative of 0*j + 1/60*j**5 + 0 + 1/12*j**3 - 5/96*j**v - 3*j**2 - 1/480*j**6. Factor l(k).
-(k - 2)*(k - 1)**2/4
Find p such that -2*p**3 - 5*p - 8*p**2 - 12*p**2 - 12 + 42 - 3*p**3 = 0.
-3, -2, 1
Let u(h) = -4*h - 5. Suppose -3*z + 4*g = 22, 0 = -3*z + 3*g - 26 + 8. Let n be u(z). Determine p so that -2/5*p**2 + 3/5*p**n + 2/5 - 3/5*p = 0.
-1, 2/3, 1
Suppose 0 = 4*r + r + 10. Let f be (-9)/(135/(-20)) - r. Solve 6*o**3 - 6*o - f*o**2 - 4/3 + 14/3*o**4 = 0.
-1, -2/7, 1
Let g be -7 - 51/12*-2. Factor -3/2*o**2 - g + 15/4*o.
-3*(o - 2)*(2*o - 1)/4
Let p be (6/(-8))/(9/(-24)). What is i in -3/2*i**2 + 1/2*i**3 + p + 0*i = 0?
-1, 2
Let y(n) be the third derivative of -n**7/420 + n**6/630 - n**3/3 + 2*n**2. Let c(t) be the first derivative of y(t). Find w such that c(w) = 0.
0, 2/7
Let w be (-200)/40 - 1*(-3 + -2). Determine z, given that -2/5*z**5 + 2/5*z - 4/5*z**4 + w*z**3 + 0 + 4/5*z**2 = 0.
-1, 0, 1
Let x(r) be the first derivative of -r**4/42 + r**3/21 - 8*r + 3. Let p(y) be the first derivative of x(y). Solve p(m) = 0.
0, 1
Let k = 32/31 - 33/62. Find o such that k*o**2 + 0 - 3/2*o = 0.
0, 3
Factor 0 - 3*t**3 - 2*t**4 - 1/2*t**5 - 1/2*t - 2*t**2.
-t*(t + 1)**4/2
Let x(j) be the second derivative of j**7/200 + 2*j**6/75 + j**5/50 - j**3/6 + 3*j. Let w(a) be the second derivative of x(a). Factor w(z).
3*z*(z + 2)*(7*z + 2)/5
Let q(x) be the first derivative of x**3/9 + x**2/3 + 1. Factor q(u).
u*(u + 2)/3
Suppose -6*f**5 - 2*f**3 - f**2 + f**2 + f**2 + f**2 - 10*f**4 = 0. Calculate f.
-1, 0, 1/3
Let q be (15/6)/((-3)/38). Let b = q + 32. Determine n, given that -b*n**2 + 1/3 + 0*n = 0.
-1, 1
Let d = -1/6 + 1/2. Let 0*h + d - 1/3*h**2 = 0. What is h?
-1, 1
Let p be 198/(-67) - (-9)/3. Let o = p + 186/335. Factor -21/5*j - 6/5*j**4 + 24/5*j**2 - 6/5*j**3 + o*j**5 + 6/5.
3*(j - 1)**4*(j + 2)/5
Suppose 2*w + 4*i + 0 = -4, -3*i - 14 = -4*w. Determine m, given that 4/3 - w*m + 2/3*m**2 = 0.
1, 2
Let t be 8*(6/2 - 2). Factor 14*n**2 + 0*n**2 - t + 0*n**3 - 6*n**3.
-2*(n - 2)*(n - 1)*(3*n + 2)
Let w be 2*2/24*(-16)/(-2). What is u in 0*u**2 + 2/3*u**3 - w - 2*u = 0?
-1, 2
Let k(q) be the first derivative of 2*q - 1/4*q**4 + 3 + 2/5*q**5 - 1/2*q**2 - 2*q**3. Find z, given that k(z) = 0.
-1, 1/2, 2
Let c be -1 - (-20)/16 - (-115)/20. Let y(d) be the first derivative of 0*d**2 + 0*d**3 + 0*d + 2/35*d**5 + 0*d**4 - 1/21*d**c + 3. Factor y(t).
-2*t**4*(t - 1)/7
Let c be -1 + 0 + 10 + 2. Let r = c - 8. Factor 1 + r*k**2 + 12*k + 3 + 2*k**2.
(k + 2)*(5*k + 2)
Let n(l) = -l**2 + 3*l. Suppose -4*y = -9*y - 10, -4*y = 3*k - 1. Let h be n(k). Factor r**5 + 5*r**3 - 3*r**4 - 3*r**3 + 0*r**5 + h*r**4.
r**3*(r - 2)*(r - 1)
Let v(x) be the first derivative of -2*x**3/3 - 3*x**2 - 4*x - 2. Find p such that v(p) = 0.
-2, -1
Let r = 33 + -33. Let a(b) be the second derivative of 0*b**2 + 1/30*b**3 - 3*b + r - 1/60*b**4. Factor a(v).
-v*(v - 1)/5
Solve -11 - 11*n**3 + 23 - 3*n**3 - 10*n**2 - 2*n**4 + 14*n = 0 for n.
-6, -1, 1
Let v(t) be the first derivative of 5*t**2 + 4*t + 1 + 2*t**3 - 2/5*t**5 - 1/2*t**4. Find f such that v(f) = 0.
-1, 2
Determine x so that 0 + 0*x**3 + 2/3*x**4 - 2*x**2 - 4/3*x = 0.
-1, 0, 2
Determine b so that -51/5*b + 6/5 + 108/5*b**2 = 0.
2/9, 1/4
Factor -5 + 5*b - 10*b - 3 + 12*b**2 - 15*b.
4*(b - 2)*(3*b + 1)
Suppose -4*g - 5 = -5*g. Suppose -5*d + 5*o + g = 0, -5*d + d + o = -1. Let 1/2*w**2 - 1/2*w + d = 0. What is w?
0, 1
Let g = 8 + -5. Suppose g*c + 0 = w + 13, -2*w = -2*c + 6. Factor 3 + d**w + 2*d**2 - 6*d**2.
-3*(d - 1)*(d + 1)
Let o(w) be the second derivative of w**6/165 - w**5/55 - 2*w**4/33 + 8*w**3/33 - 17*w. Solve o(h) = 0.
-2, 0, 2
Let h = 0 + 2. Determine l, given that -l**3 + l**h + 3*l**2 - 3*l**2 = 0.
0, 1
Let a(m) = 8*m**2 + 2*m + 14. Let g(b) = -10*b**2 - 3*b - 15. Let y(c) = -7*a(c) - 6*g(c). Factor y(t).
4*(t - 1)*(t + 2)
Let k(b) be the third derivative of -b**6/180 - b**5/30 - b**4/12 - 2*b**3/3 + b**2. Let p(y) be the first derivative of k(y). Find s such that p(s) = 0.
-1
Let k(b) be the second derivative of -b**4/12 + 5*b**3/6 + 7*b**2 - 7*b - 2. Determine q so that k(q) = 0.
-2, 7
Let p(a) = 6*a. Let v be p(1). Find n, given that -n**4 + v*n**2 - 3*n**2 - 3*n**2 = 0.
0
Let a be -8 - -13 - -1*1. Let t be 4/(-4) + 10/a. Factor -4/3*m - t - 2/3*m**2.
-2*(m + 1)**2/3
Let k(m) be the second derivative of -2*m**5/5 + 3*m**4 + 10*m**3/3 - 8*m. Factor k(o).
-4*o*(o - 5)*(2*o + 1)
Suppose -4*g + 7*g - 4*h + 176 = 0, 172 = -3*g + 5*h. Let l = 194/3 + g. Factor 1/3*t**4 - l + t + 1/3*t**2 - t**3.
(t - 2)*(t - 1)**2*(t + 1)/3
Suppose -2*i + 2/3*i**3 + 0*i**2 - 4/3 = 0. What is i?
-1, 2
Let a(l) = -l**3 + 5*l**2 + 5*l - 21. Let u be a(5). Factor 2/11*d**2 + 2/11*d**5 + 6/11*d**u + 0*d + 0 + 6/11*d**3.
2*d**2*(d + 1)**3/11
Let h = -158 + 161. Factor -2*v - 5/2*v**4 + 4*v**2 + 7/2*v**h + 0.
-v*(v - 2)*(v + 1)*(5*v - 2)/2
Let y(r) be the third derivative of 0*r - 4*r**2 + 0*r**3 + 1/60*r**6 + 0 + 1/12*r**4 - 1/15*r**5. Factor y(a).
2*a*(a - 1)**2
Let y(i) be the third derivative of 0*i**3 + 0*i + 1/42*i**4 + 3*i**2 + 0 - 1/210*i**5. Let y(z) = 0. What is z?
0, 2
Let b(l) be the first derivative of -l**6/6 + 13*l**5/5 - 29*l**4/2 + 106*l**3/3 - 85*l**2/2 + 25*l + 53. Determine n so that b(n) = 0.
1, 5
Let s(q) = -q**3 + 27*q**2 + 58*q + 3. Let a be s(29). Determine o, given that 0 + 1/3*o**a - 2/3*o + 1/3*o**2 = 0.
-2, 0, 1
Let v(w) be the first derivative of w**3/8 - 3*w/2 + 16. What is h in v(h) = 0?
-2, 2
Let p(x) be the third derivative of x**6/30 + 2*x**5/15 + x**4/6 - 5*x**2. Solve p(t) = 0.
-1, 0
Let w be (2/(-20) - 0) + (-5)/(-10). Factor 0 - w*m + 0*m**3 + 2/5*m**5 + 4/5*m**2 - 4/5*m**4.
2*m*(m - 1)**3*(m + 1)/5
Let f = 10/459 - 3569/2295. Let a = -6/5 - f. Let 4/3 + 4/3*w + a*w**2 = 0. Calculate w.
-2
Let h = 14869999/420 + -70809/2. Let n = h - 1/105. Determine y, given that 0 + n*y**4 - 1/4*y**3 - 1/4*y**2 + 0*y + 1/4*y**5 = 0.
-1, 0, 1
Let b = -37 + 37. Let k(i) be the second derivative of 0*i**3 + 1/110*i**5 - 1/66*i**4 + b + 2*i + 0*i**2. Find r such that k(r) = 0.
0, 1
Factor -2/9*z**2 - 8/9 + 8/9*z.
-2*(z - 2)**2/9
Let g(m) = -3*m**5 + m**4 + m**3 - m**2 + 2*m - 2. Let j(r) = r**5 - r + 1. Let w(k) = -5*g(k) - 10*j(k). Suppose w(c) = 0. Calculate c.
-1, 0, 1
Let o be 13/6 + (-4)/24 + 4. Let m(c) be the second derivative of -1/18*c**4 + c + 0 - 1/10*c**5 + 0*c**2 - 2/45*c**o + 0*c**3. Determine r so that m(r) = 0.
-1, -1/2, 0
Let c = 130/33 + -36/11. Let s = 37 - 34. Find b, given that -b**5 - 1/3*b**4 - 1/3 - b + c*b**2 + 2*b**s = 0.
-1, -1/3, 1
Suppose 0 - 1/6*i + 1/3*i**2 - 1/6*i**3 = 0. Calculate i.
0, 1
Let y be ((-2 - -2) + 149)/(-2). Let m = y + 76. Factor 1 + 1/2*x**3 - m*x + 0*x**2.
(x - 1)**2*(x + 2)/2
Let d = 57/7 - 201/35. Let 2/5 + 18/5*c**2 + d*c = 0. Calculate c.
-1/3
Let h(c) = -c**3 + 2*c**2 + 4*c - 3. Let a be h(3). Suppose -5*j + v + 16 + 1 = 0, a = 3*v - 9. Factor -3*m**3 + m**j + m**2 - 3*m**2 + 4*m**3.
m**2*(m - 1)*(m + 2)
Let b(s) be the first derivative of -1/14*s**4 - 3 + 4/21*s**3 + 0*s - 1/7*s**2. Solve b(l) = 0.
0, 1
Let w(v) = 42*v**4 - 12*v**3 - 47*v**2 + 12*v. Let p(h) = -21*h**4 + 6*h**3 + 24*h**2 - 6*h. Let m(d) = 5*p(d) + 3*w(d). Find x such that m(x) = 0.
-1, 0, 2/7, 1
Suppose -6*w + 5*w + 15 = 0. Suppose -22 + 7 = y + 3*g, -4*y - 3*g - w = 0. Let -14/9*s**5 - 26/9*s**2 - 4/9*s + y - 6*s**3 - 46/9*s**4 = 0. What is s?
-1, -2/7, 0
Factor 3/4*f - 3/4*f**2 + 3/2.
-3*(f - 2)*(f + 1)/4
Let t = 224/3 + -74. Factor t*j**2 - 2*j + 4/3.
2*(j - 2)*(j - 1)/3
Let t(s) be the second derivative of s**4/60 + 9*s. Determine m so that t(m) = 0.
0
Let d be 4 + 2 - (3 - (2 + -1)). Let b(h) be the first derivative of 3 + 0*h + d*h**4 + 2*h**2 + 14/3*h**3 + 6/5*h**5. Factor b(n).
2*n