 for i.
2/9, 3, 5
Factor 280*t**2 - 3039*t - 3275*t - 4*t**3 + 1414*t.
-4*t*(t - 35)**2
Let c be (-2)/((-26)/30 + 1). Let j be 2/(-3)*(9 + c). Suppose -22*k**3 - 3*k - 10*k**5 + 7*k**5 - 23*k**3 - 9*k**5 - 21*k**2 - 39*k**j = 0. Calculate k.
-1, -1/4, 0
Let z = 116/17 - 6578/969. Let c = z + 161/285. Factor c*j**2 - 3/5*j**4 + 3/5*j**3 - 3/5*j + 0.
-3*j*(j - 1)**2*(j + 1)/5
Let p(q) be the third derivative of q**6/480 + 7*q**5/240 + 11*q**4/96 + 5*q**3/24 - 32*q**2 - q. Factor p(i).
(i + 1)**2*(i + 5)/4
Let u(k) be the first derivative of -k**5/15 + 2*k**4/3 - 22*k**3/9 + 4*k**2 - 3*k + 53. Solve u(m) = 0.
1, 3
Let q(s) = -2*s**3 + 5*s**2 - 2. Let l be q(2). Suppose l*w = -2*w, 0 = 4*j + 4*w. Factor 2/3*h - 10/3*h**2 + j + 8/3*h**3.
2*h*(h - 1)*(4*h - 1)/3
Let t(l) = -9*l**3 + 48*l**2 - 7*l. Let k(s) = s**3 - 7*s**2. Let r(u) = -24*k(u) - 3*t(u). Let r(z) = 0. Calculate z.
-7, -1, 0
Let i(l) = 3*l**2 + 2*l + 4. Let r(t) = -t**2. Suppose 4*n = n - 2*c - 5, c = -n - 3. Let y be 8/((-2)/n) - -3. Let b(s) = y*i(s) - 5*r(s). Factor b(d).
2*(d - 2)*(d + 1)
Suppose 4*x = -2*x. What is k in 2*k**2 + x*k + 2*k**2 + 6*k - 2*k = 0?
-1, 0
Let r be 2 - 0 - (-10)/(-6). Suppose 3*f - 14 = -5*x + f, 0 = x + 3*f - 8. Factor -r*y + 0 + 4/3*y**x.
y*(4*y - 1)/3
Let n(w) be the first derivative of 1/21*w**3 + 1 - 3/7*w + 1/7*w**2. Suppose n(j) = 0. Calculate j.
-3, 1
Let i be (-12257)/(-4017) - (-2)/(-39). Suppose -2*l**i + 1/2*l**4 + 5/2*l**2 + 0 - l = 0. Calculate l.
0, 1, 2
Let w(v) be the second derivative of 5*v**4/72 - 55*v**3/36 - 5*v**2 + 3*v + 23. Let w(f) = 0. What is f?
-1, 12
Let v(b) be the first derivative of -b**4 + 356*b**3/3 - 4048*b**2 + 7744*b + 76. Suppose v(o) = 0. Calculate o.
1, 44
Factor -32/3*n - 16/3*n**3 + 40/3*n**2 + 0 + 2/3*n**4.
2*n*(n - 4)*(n - 2)**2/3
Let q be 3 - (-12)/(-4) - -2. Factor 6*g**2 + g**2 - 8*g**q + 72 + 24*g + 3*g**2.
2*(g + 6)**2
Suppose 0 = -3*f + 2 - 14. Let n be ((-1)/9)/(f/264). Solve 4/3 + 8*k**2 + n*k = 0.
-2/3, -1/4
Let f(v) be the first derivative of -v**6/30 + 14*v**5/25 - 6*v**4/5 + 137. Let f(h) = 0. Calculate h.
0, 2, 12
Let l = 20 - 16. Let s(c) = -c**2 + 5*c - 2. Let x be s(l). Solve -24 - 13*y**x + 36*y + 3*y**3 - y**2 - 4*y**2 = 0.
2
Let i(h) be the first derivative of 5 + 1/6*h**4 + 0*h - 2/9*h**3 + 0*h**2. Factor i(t).
2*t**2*(t - 1)/3
Determine k so that -30*k + 115/4 + 5/4*k**2 = 0.
1, 23
Let b(g) be the third derivative of 7/144*g**4 - 1/240*g**6 + 1/180*g**5 + 0 + 1/18*g**3 + 0*g + 9*g**2. Factor b(v).
-(v - 2)*(v + 1)*(3*v + 1)/6
Suppose 2*f = 5*b - 39, b + 2*f - 19 + 4 = 0. Suppose -2*v + b = j, j + 17 = -5*v + 32. Find m such that 0 - 1/6*m**v + 1/2*m**3 - 1/3*m = 0.
-2/3, 0, 1
Let s(h) be the second derivative of -h**4/27 - 7*h**3/27 - 2*h**2/3 + 55*h. Factor s(q).
-2*(q + 2)*(2*q + 3)/9
Let u be 4*(((-522)/(-36))/(-29))/(2/(-2)). Suppose -20/3*k + 4/3*k**u + 16/3 = 0. Calculate k.
1, 4
Let s(j) be the third derivative of -j**6/900 + 7*j**3/3 - 13*j**2. Let l(y) be the first derivative of s(y). Solve l(t) = 0 for t.
0
Let h(m) be the second derivative of m**6/30 + 2*m**5/15 - m**4/6 - 4*m**3/3 - 6*m**2 + m. Let z(j) be the first derivative of h(j). Factor z(b).
4*(b - 1)*(b + 1)*(b + 2)
Let g = 92 + 67. Factor 82 + 3*a**3 - 6*a**2 - 3*a + 83 - g.
3*(a - 2)*(a - 1)*(a + 1)
Suppose -3*w - 2 = 3*l - 8, -5*w - 4*l = -7. Let f be (-1)/(-2) + (-1)/w. Determine c so that 9/4 + f*c + 1/4*c**2 = 0.
-3
Suppose 696 = -7*d - 1369. Let u = d + 2659/9. Factor 2/9*o**3 + 8/9*o**2 + u + 10/9*o.
2*(o + 1)**2*(o + 2)/9
Let s(v) = 14*v**2 + 2260*v + 642. Let n(u) = 14*u**2 + 2261*u + 641. Let m(y) = 2*n(y) - 3*s(y). Suppose m(d) = 0. What is d?
-161, -2/7
Let r = -5 + 5. Suppose r = 4*o - 13 - 3. Find z such that -3 + 0*z**2 - o*z**2 + 4*z**2 + 3*z**2 = 0.
-1, 1
Suppose -3*f + 0*f - 18 = 3*r, 4*f - 30 = 5*r. Let c be 13/r + (-18)/12*-2. What is m in 1/6 + 1/2*m**2 - 2/3*m**4 - 5/6*m + c*m**3 = 0?
-1, 1/4, 1
Let j(h) = h**2 - 5*h + 3. Let a be j(5). Let k(i) be the first derivative of -2 - 6*i**3 - 1 + 3*i**2 + 5*i**a + 1. Let k(c) = 0. What is c?
0, 2
Suppose -4*a + 5*s + 35 = 0, 4*s = 2*a - a - 17. Let l(c) = 3*c - 13. Let w be l(a). Find b, given that -7/3*b**w - 5/3*b + 2/3 = 0.
-1, 2/7
Let b(z) = 15*z**5 - 53*z**3 + 38*z**2 - 8*z - 8. Let y(g) = -5*g**5 + 18*g**3 - 13*g**2 + 3*g + 3. Let u(t) = 3*b(t) + 8*y(t). What is v in u(v) = 0?
-2, 0, 1
Let h(o) be the second derivative of o**5/40 - 5*o**4/4 - 31*o**3/12 + 336*o + 2. Let h(i) = 0. What is i?
-1, 0, 31
Let s(n) = n**3 - n**2 - 6*n - 2. Let v(g) = 6*g**3 - 6*g**2 - 36*g - 13. Let t(i) = -39*s(i) + 6*v(i). What is j in t(j) = 0?
-2, 0, 3
Let i be 9/(-110)*(2 - 2 - -6). Let a = -1/11 - i. Find l, given that a + l**2 - 7/5*l = 0.
2/5, 1
Let d(m) be the first derivative of -m**3/3 - 7*m**2/2 - 6*m + 31. Let x be d(-6). Suppose 0 + 0*j**2 - 1/4*j**5 + 1/4*j**3 + 0*j**4 + x*j = 0. What is j?
-1, 0, 1
Solve -96/5*r**3 + 3*r**4 - 156/5*r + 201/5*r**2 + 36/5 = 0.
2/5, 1, 2, 3
Factor -31/6*p**2 - 5/3*p - 13/6*p**4 + 0 - 11/2*p**3 - 1/6*p**5.
-p*(p + 1)**3*(p + 10)/6
Suppose 0 = 12*x - 10*x - 16. Suppose -30 - x*h**2 + 24 - 8*h - 5*h - h**3 = 0. Calculate h.
-6, -1
Let z(q) be the first derivative of -2*q**5/75 + 11*q**4/30 - 38*q**3/45 + 3*q**2/5 + 60. Factor z(g).
-2*g*(g - 9)*(g - 1)**2/15
Suppose -7*q + 11*q - 24 = 0. Suppose q*o + 20*o = 0. Let o + 1/3*y**2 - 1/3*y**4 + 1/6*y - 1/6*y**5 + 0*y**3 = 0. What is y?
-1, 0, 1
Let m be (18/480)/(126/8). Let q(t) be the third derivative of 0*t + 2/105*t**5 + m*t**6 + 6*t**2 + 0 + 2/21*t**3 + 5/84*t**4. Factor q(z).
2*(z + 1)**2*(z + 2)/7
Let i(t) be the third derivative of -t**9/20790 + t**8/7392 - t**7/13860 - 13*t**4/8 - 10*t**2. Let y(c) be the second derivative of i(c). Solve y(l) = 0.
0, 1/4, 1
Suppose 25 - 13 = 2*j. Let l(k) be the first derivative of 2/5*k**2 + 3/10*k**4 - 1 + 2/3*k**3 - 1/15*k**j + 0*k - 2/25*k**5. Solve l(q) = 0.
-1, 0, 2
Let m be ((9 - 9)/(1 + -3))/1. Let z(y) be the first derivative of 0*y + m*y**2 + 5/6*y**6 + 0*y**3 + 4 + 0*y**5 - 5/4*y**4. Suppose z(u) = 0. What is u?
-1, 0, 1
Find c such that 11*c**4 - 10*c - 73/2*c**3 + 34*c**2 + 0 + 3/2*c**5 = 0.
-10, 0, 2/3, 1
Let j = 153 - 117. Let x be 1*(-2)/(-12)*j/24. Determine i, given that x*i**3 + 1/2*i**2 - 1/2 - 1/4*i = 0.
-2, -1, 1
Let j(t) be the second derivative of -1/3*t**4 + 0 + 7*t - 2/3*t**3 - 1/15*t**5 + 7/2*t**2. Let g(v) be the first derivative of j(v). Solve g(m) = 0 for m.
-1
Let p(m) be the first derivative of 2/9*m**3 + 13 + 10/3*m**2 + 0*m. Find r such that p(r) = 0.
-10, 0
Let q(i) = -8*i**2 - 3*i + 5. Let v(s) = -15*s**2 - 5*s + 10. Let u = 44 + -47. Let y(x) = u*v(x) + 5*q(x). Factor y(d).
5*(d - 1)*(d + 1)
Let g = 4/47 + 82/141. Factor g*l**4 - 2/9 + 2/3*l - 2/9*l**5 - 4/9*l**2 - 4/9*l**3.
-2*(l - 1)**4*(l + 1)/9
Let z(q) be the second derivative of q**6/180 - q**5/45 + q**4/36 + 5*q**2/2 + 8*q. Let o(l) be the first derivative of z(l). Determine n, given that o(n) = 0.
0, 1
Let q(a) = -3*a**2 + a**2 + 139 + 6*a**2 + 13*a**2 - 49*a. Let b(l) = -9*l**2 + 24*l - 69. Let c(y) = -11*b(y) - 6*q(y). Factor c(u).
-3*(u - 5)**2
Let y = -96 + 100. Let o be (y/8 + -1)*0. Find q such that o + 1/5*q - 1/5*q**3 + 0*q**2 = 0.
-1, 0, 1
Let i(j) be the first derivative of 0*j - 2/5*j**3 + 1/10*j**4 - 6 + 0*j**2. Factor i(k).
2*k**2*(k - 3)/5
Suppose -11*j + 7*j = -3*k + 608, -2*k + 302 = -2*j. Let o = j + 157. Factor 2/3*m - 1/3*m**o + 0.
-m*(m - 2)/3
Suppose -6 = l - 9. Let g(d) be the first derivative of -4/3*d**l + 4/5*d**5 - d**2 + 0*d**4 + 1/3*d**6 + 0*d - 2. Factor g(x).
2*x*(x - 1)*(x + 1)**3
Suppose 4*z + 4*a - 8 = 0, 0 = -2*z - 38*a + 33*a + 4. Determine x, given that 8/7*x**4 + 0*x**3 + 4/7*x**5 - 8/7*x**z - 4/7*x + 0 = 0.
-1, 0, 1
Let p(s) be the second derivative of -s**7/84 - s**6/15 + s**5/40 + s**4/6 + 10*s + 1. Suppose p(x) = 0. Calculate x.
-4, -1, 0, 1
Let v(u) be the third derivative of -49*u**6/3 + 133*u**5/3 + 205*u**4/12 + 5*u**3/2 + 112*u**2 + 2. Factor v(k).
-5*(2*k - 3)*(14*k + 1)**2
Let o = -5477 + 5482. Factor 2*g**o + 4/7*g**3 + 0*g**2 - 18/7*g**4 + 0*g + 0.
2*g**3*(g - 1)*(7*g - 2)/7
Suppose 0*y = 3*y + 2*y. Solve -2*x**2 + y*x**4 + 3*x**2 - x**4 = 0 for x.
-1, 0, 1
Let a(h) be the third derivative of 