
Solve 85*v**3 - 12*v**2 - 15*v**4 - 61*v**3 + 3*v**5 - 3 + 3 = 0 for v.
0, 1, 2
Suppose -9*a = -5*a - 9*a. What is n in 2/3*n**2 + 2/9*n**4 + 2/3*n**3 + a + 2/9*n = 0?
-1, 0
Let f(a) = 17*a**4 - 58*a**3 - 53*a**2 - 11*a + 11. Let w(i) = -6*i**4 + 20*i**3 + 18*i**2 + 4*i - 4. Let v(z) = 4*f(z) + 11*w(z). Find q such that v(q) = 0.
-1, 0, 7
Factor 1/7*r**3 - 2/7*r**2 + 0*r + 0.
r**2*(r - 2)/7
What is m in 2 - 1 + 90*m - 184*m + 4*m**2 + 89*m = 0?
1/4, 1
Let l(t) be the second derivative of -1/9*t**2 - 1/54*t**4 + 0 - t + 2/27*t**3. Factor l(a).
-2*(a - 1)**2/9
Let h(f) be the second derivative of -1/135*f**6 + 0*f**2 + 0*f**3 - 1/54*f**4 - 1/45*f**5 - 2*f + 0. Factor h(d).
-2*d**2*(d + 1)**2/9
Suppose 3*d = 7*d + 204. Let m be d/(-15) - (3 + 0). Determine t, given that 0*t + 0 + m*t**2 + 2/5*t**3 = 0.
-1, 0
Suppose u - 3 = 12. Suppose p + 0*q + 3*q - u = 0, -p + 3*q - 15 = 0. Factor -1/3*s**3 + 0 + 2/3*s**4 - 1/3*s**5 + 0*s**2 + p*s.
-s**3*(s - 1)**2/3
Let d be ((-3)/2)/(6/32). Let z(k) = -k + 1. Let m(w) = 2*w**2 - 4*w + 10. Let u(h) = d*z(h) + m(h). Solve u(l) = 0 for l.
-1
Factor 0*w + 0 + 0*w**3 - 1/2*w**5 + 0*w**2 + 0*w**4.
-w**5/2
Let k(m) = -19*m**4 - 17*m**3 - 9*m**2. Let d(l) = -5*l**4 - 4*l**3 - 2*l**2. Suppose 5*v - 43 = -8. Let f = -16 + v. Let x(t) = f*d(t) + 2*k(t). Factor x(n).
n**3*(7*n + 2)
Let f(n) = 9*n**5 + 3*n**4 - 3*n**3 - 3*n**2 + 6*n. Let o(c) = 26*c**5 + 9*c**4 - 9*c**3 - 9*c**2 + 17*c. Let t(j) = 17*f(j) - 6*o(j). Factor t(w).
-3*w**2*(w - 1)*(w + 1)**2
Let j be 9/(-21) + (-3)/(-7). Suppose 2*t + 2*r = 12, -5*t + j = -4*r - 3. Factor -4/5*v**t + 0*v**2 + 2/5*v**5 + 0 + 0*v**4 + 2/5*v.
2*v*(v - 1)**2*(v + 1)**2/5
Let n(y) = -6*y**2 - 5*y - 5. Let k(d) = 2*d**2 - 2*d**2 - 2 + 1 - d**2. Let b(u) = 24*k(u) - 3*n(u). Factor b(f).
-3*(f - 1)*(2*f - 3)
Let s(v) be the second derivative of 4*v - 1/45*v**6 + 0 + 0*v**2 + 1/9*v**3 + 1/10*v**5 - 1/6*v**4. Let s(m) = 0. Calculate m.
0, 1
Let x = 1 + 4. Let p(y) be the third derivative of 0 + 0*y + 1/84*y**4 - 2/105*y**x + 3*y**2 + 1/140*y**6 + 0*y**3. Factor p(i).
2*i*(i - 1)*(3*i - 1)/7
Let n(k) be the third derivative of k**6/24 + k**5/3 + 25*k**4/24 + 5*k**3/3 + 23*k**2. Determine p, given that n(p) = 0.
-2, -1
Let y(q) = -q**3 - q**2 + q. Let d(l) = 9*l**3 + 13*l**2 - l + 2. Let g(w) = -2*d(w) - 14*y(w). Solve g(j) = 0.
-1
Suppose 5*r - 6 = p, 4*r + p + 12 = 6*p. Let g be ((-6)/9)/(r/(-9)). Factor 12 - 10*m**2 - 4*m - 12 + 14*m**g.
2*m*(m - 1)*(7*m + 2)
Let y = -2/537 + 478/179. Factor -2*r**2 + y*r - 2/3.
-2*(r - 1)*(3*r - 1)/3
Let i(x) be the second derivative of -x**7/840 - x**6/160 - x**5/120 + x**2 + 5*x. Let w(c) be the first derivative of i(c). Determine r so that w(r) = 0.
-2, -1, 0
Find m, given that 3*m + 6 - 8*m**2 + m**2 + m**2 - 5*m**3 + 2*m**3 = 0.
-2, -1, 1
Let u be (-108)/210*-5 + -2. Find x, given that -u*x**2 + 8/7*x**3 + 2/7*x**5 - 4/7 + 8/7*x**4 - 10/7*x = 0.
-2, -1, 1
Let j(d) be the third derivative of d**7/70 + d**6/100 - d**5/20 - d**4/20 - 9*d**2. Let j(x) = 0. What is x?
-1, -2/5, 0, 1
Let n(o) be the second derivative of -4*o**7/525 - 7*o**6/300 - o**5/75 + o**4/60 + o**2/2 + o. Let w(k) be the first derivative of n(k). Factor w(i).
-2*i*(i + 1)**2*(4*i - 1)/5
Let w be ((-1 + 0)/(-14))/((-42)/(-168)). Find g such that 10/7*g + w*g**2 - 4/7*g**3 + 4/7 = 0.
-1, -1/2, 2
Let a be (-5)/((-5)/(-6)) + 32 + -23. Factor -4/5*t**a - 12*t - 36/5 - 28/5*t**2.
-4*(t + 1)*(t + 3)**2/5
Factor 0 + 2/11*g**2 + 0*g - 2/11*g**4 + 0*g**3.
-2*g**2*(g - 1)*(g + 1)/11
Determine b so that 2*b**2 - 46*b + 19*b + 8 + 17*b = 0.
1, 4
Let l(m) be the first derivative of 3*m**5/25 + 3*m**4/20 - m**3/5 - 3*m**2/10 + 9. Factor l(n).
3*n*(n - 1)*(n + 1)**2/5
Let o be ((-72)/135)/((-2)/5). Let x(b) be the second derivative of -o*b**3 - 4/3*b**4 - 1/2*b**2 + 0 - b. Determine w, given that x(w) = 0.
-1/4
Let v(f) be the second derivative of -f**5/5 + 2*f**3 + 4*f**2 - 35*f. Solve v(t) = 0.
-1, 2
Factor 0 + 2*i + 3*i - 9*i - 4*i**2 + 8.
-4*(i - 1)*(i + 2)
Let l = 13 + -51/4. Factor -1/4*w**2 - l*w**4 + 0 + 0*w + 1/2*w**3.
-w**2*(w - 1)**2/4
Solve 0 - 1/5*t**4 + 1/5*t**5 + 0*t**3 + 0*t**2 + 0*t = 0.
0, 1
Let d be 0*(-3 + 10/4). Let n be 2*1*3/21. Determine p, given that -2/7*p + 0*p**3 + n*p**5 + 4/7*p**2 - 4/7*p**4 + d = 0.
-1, 0, 1
Let g(q) be the first derivative of 4*q**5/5 - 3*q**4 + 4*q**3 - 2*q**2 + 8. Factor g(s).
4*s*(s - 1)**3
Let f = -24 + 97/4. Suppose -1 = 5*p - 6. Factor -p - h - f*h**2.
-(h + 2)**2/4
Let j = -1580 - -14234/9. Let 0 + j*t**2 + 4/9*t - 4/9*t**3 - 14/9*t**4 = 0. What is t?
-1, -2/7, 0, 1
Let t be 52/(6/(-45)*-9). Let x = 44 - t. Suppose x*u**2 + 0 + 4/3*u = 0. What is u?
-2, 0
Let p(k) = -k**4 + k**2 + 1. Let m(f) = 2*f**4 - 2*f**3 + 6*f**2 - 6*f - 4. Let o(t) = m(t) + 4*p(t). Factor o(h).
-2*h*(h - 1)**2*(h + 3)
Let q(p) = p**2 - 2*p - 3. Let c be q(3). Determine f, given that 0*f**4 - 2*f**2 - f**3 + 2*f**4 - f**3 + c*f**3 + 2*f = 0.
-1, 0, 1
Suppose 0 = z - f + 7, 4*z + f + 3*f - 4 = 0. Let t(j) = -j**3 - 4*j**2 - 4*j. Let d be t(z). Solve 0*k + 2/5*k**d - k**4 + 0 + 0*k**2 + 2/5*k**5 = 0.
0, 1/2, 2
Suppose 0 = -5*z + 15, z = 4*k - 5 - 12. Let g be 0/((-4)/(-20)*k). Solve -2/7*o**3 + 0*o**2 + 2/7*o + g = 0.
-1, 0, 1
Factor -5*r**2 + 5*r - 7*r**3 + 0*r + 2*r**3 + 5.
-5*(r - 1)*(r + 1)**2
Let i = 13 + 2. Let x be (-24)/(-10) - i/(-25). Factor 9*y**2 - 3 - 2*y**4 + 3*y**3 + x - 10*y**2.
-y**2*(y - 1)*(2*y - 1)
Determine x so that 0 - 12/5*x**3 - 2/5*x - 2/5*x**5 - 8/5*x**2 - 8/5*x**4 = 0.
-1, 0
Let f(s) = 9*s**3 - 9*s**2 + 6*s - 3. Let r(i) = -i**4 + 27*i**3 - 27*i**2 + 17*i - 8. Let z be ((-16)/6)/(6/18). Let j(g) = z*f(g) + 3*r(g). Solve j(x) = 0.
0, 1
Suppose 0 = -3*d + q + 1, -4*d + 2 - 3 = q. Factor -4/5*z**4 + d - 2/5*z**5 + 0*z**2 + 0*z - 2/5*z**3.
-2*z**3*(z + 1)**2/5
Let c be 0*(-7)/70 + (-2)/(-16). Let t(v) be the second derivative of -3/40*v**5 + c*v**4 + 0 + 1/4*v**3 - v - 3/4*v**2. What is i in t(i) = 0?
-1, 1
Let r be (4/(-10))/((-12)/(-60))*-2. Factor 39/5*y + 3/5*y**3 - 18/5 - r*y**2.
(y - 3)**2*(3*y - 2)/5
Let d(y) = y**3 + 3*y**2 + y + 2. Let z be d(-3). Let s = z - -5. Factor -s*p + 6*p**3 - 10*p**4 + 5*p + 0*p**2 + 4*p**5 + 2*p**2 - 3*p.
2*p*(p - 1)**3*(2*p + 1)
Suppose -3*c - 12 = 0, -t + 2*c = -0*t - 8. Factor 2/3*p**4 + 4/3*p**3 + 0 + 2/3*p**2 + t*p.
2*p**2*(p + 1)**2/3
Let q(r) be the third derivative of -r**7/840 + r**6/240 - r**5/240 + 25*r**2. Factor q(y).
-y**2*(y - 1)**2/4
Let l(q) be the third derivative of q**8/336 + q**7/35 + 3*q**6/40 + q**5/15 - q**2 + 14*q. Suppose l(g) = 0. Calculate g.
-4, -1, 0
Let 0 - 2/13*p - 2/13*p**3 - 4/13*p**2 = 0. What is p?
-1, 0
Let v(y) be the first derivative of -2*y**6/15 + y**5/5 - y**4/8 - y**3 + 3. Let m(b) be the third derivative of v(b). Determine c, given that m(c) = 0.
1/4
Factor 92 - 111 - 61 + 35*m**2 - 270*m.
5*(m - 8)*(7*m + 2)
Suppose -5*n = -u + 37, n + 59 - 18 = 3*u. Suppose 6 = -l - 4*q, u = 3*l - 2*q - q. Solve -i + l*i**4 - 1 - 1 - 3*i + 4*i**3 = 0.
-1, 1
Let y(j) be the first derivative of -j**7/168 + j**6/160 + j**5/120 - 2*j**2 - 5. Let z(o) be the second derivative of y(o). Factor z(i).
-i**2*(i - 1)*(5*i + 2)/4
Let b(y) be the second derivative of -y**5/20 + 29*y**4/48 - 31*y**3/24 + 3*y**2/4 - 11*y. Factor b(m).
-(m - 6)*(m - 1)*(4*m - 1)/4
Let o(f) be the first derivative of -f**4/12 + f**2/6 - 3. Factor o(d).
-d*(d - 1)*(d + 1)/3
Let o(b) be the third derivative of 0*b**4 - 1/1008*b**8 + 0*b**3 - 1/360*b**6 + 0 - b**2 + 1/315*b**7 + 0*b**5 + 0*b. Factor o(w).
-w**3*(w - 1)**2/3
Let u(h) be the first derivative of 10*h**3/3 - 25*h**2/2 + 10*h + 17. Factor u(x).
5*(x - 2)*(2*x - 1)
Suppose -2*x - 85 = -5*h, -5*h + x = 3*x - 85. Factor 6*t + 16*t**3 - h*t**2 - 18*t**3 - 4*t**2 - 25*t**3.
-3*t*(t + 1)*(9*t - 2)
Let u = -123/4 - -31. Let b(a) be the first derivative of 1/5*a**5 - 1/3*a**3 - 2 + u*a**4 + 0*a - 1/2*a**2. Factor b(i).
i*(i - 1)*(i + 1)**2
Suppose 3*v + 6 = 12. Factor 11*m + 2*m**3 - 6 + 3*m - 9*m**2 - m**v.
2*(m - 3)*(m - 1)**2
Let n(v) = -6*v**4 - 6*v**3 + 12*v - 3. Let m(a) = -5*a**4 - 7*a**3 + 12*a - 2. Let i be 1 + ((-6)/(-2) - 6). Let g(t) = i*n(t) + 3*m(t). Factor g(d).
-3*d*(d - 1)*(d + 2)**2
Suppose -2 = -2*h + 160. Let 2*y**4 - 81 - 5*y**4 + h + 