7
Suppose 4*y - 18*a - 7972 = -13*a, 2*y + 5*a - 3956 = 0. Let u be (-4)/22 + (y/110)/7. Find f such that 3/5 - 3/5*f**2 - u*f + 12/5*f**3 = 0.
-1, 1/4, 1
Find n such that n**2 + 43 + 5*n**3 - 16*n**2 - 3*n**3 + 16*n - 11 + n**2 = 0.
-1, 4
Find a, given that -60/7*a**2 - 132/7 + 4/7*a**3 + 188/7*a = 0.
1, 3, 11
Let u(k) be the third derivative of -k**5/170 - 31*k**4/204 - 10*k**3/51 + 62*k**2. Find y, given that u(y) = 0.
-10, -1/3
Let g(h) be the third derivative of -h**5/240 - 5*h**4/24 + 7*h**3/8 - 627*h**2. Determine z, given that g(z) = 0.
-21, 1
Suppose -23*l - 7 = 5*r - 19*l, -7*r + 4 = l. Factor -1/2*d**2 - r - 5/2*d**3 + 3/2*d**4 + 5/2*d.
(d - 1)**2*(d + 1)*(3*d - 2)/2
Factor -88/7*v**2 + 96/7*v - 36/7 - 4/7*v**4 + 32/7*v**3.
-4*(v - 3)**2*(v - 1)**2/7
Find r such that 40*r**2 + 7*r + r + 43*r**3 - 29*r**3 - 4*r**4 - 14*r**4 = 0.
-1, -2/9, 0, 2
Determine z so that 8/5 + 2*z**2 - 16/5*z - 2/5*z**3 = 0.
1, 2
Let k be (1 - (2 + -2)) + 156/39. Let l(u) be the third derivative of 0 + 0*u - u**2 + 0*u**4 - 1/390*u**k + 1/780*u**6 + 0*u**3. Factor l(w).
2*w**2*(w - 1)/13
Let g(a) = a**3 + 4*a**2 - 4*a - 6. Let i be g(-6). Let u be (-10)/(-4)*(2 + i/30). Determine c, given that 0*c**2 + 0 + u*c**3 - 1/2*c = 0.
-1, 0, 1
Let c = 8 - 4. Suppose c*q - 7*f = -5*f + 10, q - 5*f = 25. Suppose 3/2*g**5 + 9/2*g**4 + q*g + 9/2*g**3 + 0 + 3/2*g**2 = 0. What is g?
-1, 0
Find y such that 56/11*y + 16/11*y**4 + 50/11*y**3 + 2/11*y**5 + 16/11 + 76/11*y**2 = 0.
-2, -1
Suppose p - 5*s + 1 = -p, 6 = 2*p + 2*s. Let h(g) be the second derivative of 1/24*g**3 - 5*g + 0*g**p + 1/80*g**5 - 1/24*g**4 + 0. What is u in h(u) = 0?
0, 1
Let v = -563/37 + 9645/629. Determine z so that -v*z**4 + 0*z + 0 + 4/17*z**3 + 0*z**2 = 0.
0, 2
Let t be 19/39 + (-8)/(-12) - 1. Determine n, given that -6/13*n**3 + 0*n**4 + t*n**5 + 0 + 4/13*n**2 + 0*n = 0.
-2, 0, 1
Let t(r) be the third derivative of 2*r**2 + 1/105*r**7 + 1/3*r**6 + 121/3*r**3 - 55/3*r**4 + 2*r + 13/5*r**5 + 0. Factor t(l).
2*(l - 1)**2*(l + 11)**2
Let z = -34104/31 - -1100. Let t = 47/124 + z. Factor 3/2*i**2 + i**3 + 1/4*i**4 + i + t.
(i + 1)**4/4
Let b(w) be the first derivative of -30 - 3/5*w**3 + 3/25*w**5 + 0*w**2 + 3/10*w**4 + 0*w. Factor b(q).
3*q**2*(q - 1)*(q + 3)/5
Let h(g) be the second derivative of -g**9/75600 + g**8/11200 - g**7/6300 + 25*g**4/12 - 10*g. Let l(t) be the third derivative of h(t). Factor l(o).
-o**2*(o - 2)*(o - 1)/5
Suppose 1 + 13 = 7*a. Find p, given that -5*p**3 + p**a - 5*p - 11*p**2 + 0*p**3 = 0.
-1, 0
Suppose 28 = -3*h - 2*r, -29 = 5*h + 5*r + 11. Let i = h + 16. Solve 3*x**3 - 7*x**2 - x - x - 5*x**i - 12*x**3 - x**5 = 0 for x.
-2, -1, 0
What is j in 9*j - 21/2*j**2 + 0*j**3 + 0 + 3/2*j**4 = 0?
-3, 0, 1, 2
Let a(v) be the second derivative of v**6/6 + 13*v**5/5 + 145*v**4/12 + 25*v**3/3 - 122*v. Let a(n) = 0. Calculate n.
-5, -2/5, 0
Let l(j) be the first derivative of 2*j**3/15 - 18*j/5 + 104. Factor l(a).
2*(a - 3)*(a + 3)/5
Let h = -52 - -31. Let v = h + 26. Factor -r**v + 2*r**2 - 5*r**2 + 4*r**3 + r**4 - r**2.
-r**2*(r - 2)*(r - 1)*(r + 2)
Let g be (72/(-60))/(63/(-30)). Let w(i) be the first derivative of 1/7*i**2 - 1/14*i**4 - 2/7*i**3 + 2/35*i**5 - 6 + g*i. Factor w(n).
2*(n - 2)*(n - 1)*(n + 1)**2/7
Factor -19 + v**2 + 49 + 31*v + 186 - 3*v - 20.
(v + 14)**2
Let d(a) = a**2 - 3. Let f(o) = -6*o**2 - o + 16. Suppose -5*j - 3 + 13 = 0. Let c be (-9)/6*(-44)/6. Let k(s) = c*d(s) + j*f(s). Find m, given that k(m) = 0.
-1
Let g(v) = -14*v + 227. Let f be g(16). Let r(u) be the first derivative of -2/3*u**2 + 11 + 0*u**5 + 0*u + 2/3*u**4 - 2/9*u**6 + 0*u**f. Solve r(d) = 0.
-1, 0, 1
Let f(x) be the first derivative of -x**5/15 + x**4/24 + x**3/9 - x**2/12 + 454. Factor f(p).
-p*(p - 1)*(p + 1)*(2*p - 1)/6
Suppose 7*g - 149 = -128. Factor 20/3*q + 4/3*q**g - 8*q**2 + 0.
4*q*(q - 5)*(q - 1)/3
Let j(y) be the first derivative of y**4/20 - 22*y**3/15 + 38*y**2/5 - 72*y/5 - 166. Let j(g) = 0. Calculate g.
2, 18
Let o(t) be the first derivative of t**5/70 - 2*t**4/21 + 5*t + 5. Let n(u) be the first derivative of o(u). Determine f so that n(f) = 0.
0, 4
Suppose -4*w - 10 = -2*z, -w + 19 = 3*z + 4. Determine b so that -1/2*b**4 - 3/2*b**2 + w - 3/2*b**3 - 1/2*b = 0.
-1, 0
Let v(i) be the second derivative of -21*i**5/40 - 5*i**4 + 61*i**3/4 - 21*i**2/2 - 98*i. Find t, given that v(t) = 0.
-7, 2/7, 1
Let n(g) be the third derivative of g**6/1620 - g**5/270 - 5*g**3/2 - 32*g**2. Let u(w) be the first derivative of n(w). Factor u(s).
2*s*(s - 2)/9
Let n(v) be the second derivative of 0 + 3*v**4 + 3/5*v**6 - 39/20*v**5 - 1/14*v**7 + 31*v + 0*v**2 - 2*v**3. Factor n(q).
-3*q*(q - 2)**2*(q - 1)**2
Factor 30*y**2 - 25*y**3 + 810*y**4 + 805*y**4 - 1610*y**4.
5*y**2*(y - 3)*(y - 2)
Let h = -124 + 124. Let a(r) be the third derivative of 0 - 5/6*r**4 - 12*r**2 + 10/3*r**3 + 1/12*r**5 + h*r. Let a(s) = 0. Calculate s.
2
Let u be 162/(-4) - (-17)/34. Let s be (1/(-4))/(((-35)/u)/(-7)). Suppose 6*r + 0 - 3/2*r**3 - 6*r**s + 3/2*r**4 = 0. Calculate r.
-2, 0, 1, 2
Let m(t) be the second derivative of 5*t**6/216 + 7*t**5/72 + 5*t**4/36 + 41*t**3/6 + 31*t. Let f(z) be the second derivative of m(z). Factor f(y).
5*(y + 1)*(5*y + 2)/3
Let a(v) be the second derivative of -v**5/35 - 3*v**4/7 - 10*v**3/7 - 2*v**2 + 97*v. Factor a(i).
-4*(i + 1)**2*(i + 7)/7
Let d(v) be the second derivative of v**5/15 + 10*v**4/9 + 56*v**3/9 + 16*v**2 + 22*v - 1. Factor d(n).
4*(n + 2)**2*(n + 6)/3
Suppose -3*v - 14 = -68. Suppose -b = b - 30. Solve -2*t**3 - 6*t - v*t + 0 + b*t**2 + 12 - t**3 = 0 for t.
1, 2
Let b(j) be the second derivative of 2*j**7/35 - 11*j**6/75 + 11*j**5/150 + j**4/18 - j**3/45 + 66*j. Suppose b(r) = 0. Calculate r.
-1/3, 0, 1/6, 1
Suppose -2*l + 47 = 5*p, -5 - 22 = -2*l - p. Let c(n) = n - 7. Let f be c(l). Suppose 0*v**4 + 7*v**4 - 3*v**3 + 19*v**3 + f*v**2 = 0. What is v?
-2, -2/7, 0
Solve 7*c**3 + 189*c**2 + 2*c**4 - 5*c**4 + 8*c**3 - 397*c**2 + 190*c**2 = 0 for c.
0, 2, 3
Determine r so that -41/9*r - 1/9*r**3 + 14/3 + 4/3*r**2 = 0.
2, 3, 7
Let y = 26 - 27. Let g be (-12)/(-6)*-1*1. Let a(p) = p**3 + p + 1. Let q(u) = -14*u**3 + 3*u**2 + 10*u - 5. Let c(l) = g*a(l) + y*q(l). Factor c(t).
3*(t - 1)*(t + 1)*(4*t - 1)
Factor 21*z**4 + 21*z**3 + 24*z**3 - 24 + 3964*z - 4009*z + 3*z**2.
3*(z - 1)*(z + 1)**2*(7*z + 8)
Factor -105/2 - 111/4*z + 51/2*z**2 + 3/4*z**3.
3*(z - 2)*(z + 1)*(z + 35)/4
Let i(s) be the third derivative of s**5/90 + 29*s**4/36 + 28*s**3/9 + 2*s**2 + 92*s. Solve i(w) = 0 for w.
-28, -1
Factor 4/3*m + 0 - 14/9*m**2 + 2/9*m**3.
2*m*(m - 6)*(m - 1)/9
Let y(l) = 19*l - 145. Let d(m) = -9*m + 73. Let j(i) = -13*d(i) - 6*y(i). Let h be j(27). Solve -2/3*n**3 + 4/3 - 2/3*n**4 + h*n**2 + 10/3*n = 0.
-1, 2
Suppose -3*c + 4*c = 5. Factor 15*n**3 - 6 - 3*n**4 + 5*n + 11*n - 27*n**2 + c*n.
-3*(n - 2)*(n - 1)**3
Let z(b) = 9*b - 37. Let o be z(5). Factor -4*m**2 - 7 + 15 - o + 8*m.
-4*m*(m - 2)
Suppose 5*v + 2 = n + n, 4*v - 2*n = 0. Let p be v*-3*2/3. Factor 18*b**p + 4*b**2 + 17*b**3 - 5*b**3 + 10*b**3.
2*b**2*(b + 1)*(9*b + 2)
What is i in -129*i**5 - 13*i**4 + 124*i**5 - 35*i**2 + 48*i**4 + 5*i**3 = 0?
-1, 0, 1, 7
Let t(k) be the third derivative of k**8/2240 + k**7/280 - k**5/10 - k**4/12 + 12*k**2. Let r(n) be the second derivative of t(n). Factor r(c).
3*(c - 1)*(c + 2)**2
Let h(m) be the first derivative of 27/8*m**4 + 0*m**2 + m**3 + 0*m - 17 + 21/10*m**5. What is j in h(j) = 0?
-1, -2/7, 0
Suppose -5*t - 3*i - 2*i = -25, -4*i = 5*t - 26. Find l, given that -14*l + 3*l**4 + 4 - t*l**3 + 18*l**2 - 5*l**3 + l**3 - l**4 = 0.
1, 2
Let c(h) be the third derivative of -h**8/168 + h**7/35 - h**6/30 - 334*h**2. Determine i, given that c(i) = 0.
0, 1, 2
Let t(a) be the second derivative of 0 - 2/15*a**6 - 49*a - 8*a**2 + 0*a**5 + 5/3*a**4 + 0*a**3. Determine d so that t(d) = 0.
-2, -1, 1, 2
Let v(w) be the second derivative of w**7/168 + w**6/30 + 3*w**5/80 - 3*w + 32. Determine j, given that v(j) = 0.
-3, -1, 0
Let x(p) be the third derivative of p**9/7560 - p**8/1680 + p**6/180 - p**5/60 - 11*p**4/24 - 23*p**2. Let w(g) be the second derivative of x(g). Factor w(v).
2*(v - 1)**3*(v + 1)
Let m be (4/10)/(2/20). Factor 77*o**4 - 68*o**m - 6*o**3 - 5*o**5 + 2*o**5.
-3*o**3*(o - 2)*(o - 