3, 0
Let n = 80 - 76. Determine g, given that 27/5*g**3 - 21/5*g**2 - 3*g**n + 6/5*g + 0 + 3/5*g**5 = 0.
0, 1, 2
Let n = 71223/12035 + -213/83. Let t = -16/29 + n. Find r such that 0 + 4/5*r**2 - 18/5*r**3 + t*r**4 + 0*r = 0.
0, 2/7, 1
Factor -5*h**4 - h + 16*h**3 - 2*h + 8*h + 5*h**2 - 21*h**3.
-5*h*(h - 1)*(h + 1)**2
Let d be (-91)/(-52)*(-3)/(-7). Solve -d*i**3 + 3/2*i**2 + 0 - 3/4*i = 0.
0, 1
Determine g so that 0 + 16/7*g - 4/7*g**2 = 0.
0, 4
Suppose 2*i = -h + 8, 0*i = 3*h + 5*i - 23. Factor 0*g + 4*g**3 + 3*g - h*g - g**3.
3*g*(g - 1)*(g + 1)
Let n(c) be the first derivative of -7 + 1/2*c**4 + 0*c + 2/3*c**3 + 0*c**2. Factor n(i).
2*i**2*(i + 1)
Suppose -4 = -2*v - 0*v. Find n such that 2*n**4 - n**v - 7*n - n - 5*n**2 + 8 + 4*n**3 = 0.
-2, 1
Let p(i) be the third derivative of -i**7/70 - i**6/10 - i**5/4 - i**4/4 - i**2. Factor p(f).
-3*f*(f + 1)**2*(f + 2)
Let k(b) = -b**2 + 12*b + 4. Let a be k(12). Suppose a*o - 1 = -3*w + 2*o, 2*w = 5*o + 26. Factor 3*n**4 - n**4 + 4*n**3 + n**5 - 3*n**w.
n**3*(n + 1)**2
Let y be ((-20)/(-16))/((-20)/(-8)). Factor 1/4*v - y + 1/4*v**2.
(v - 1)*(v + 2)/4
Let f(b) be the third derivative of -1/30*b**6 + 1/12*b**4 - 1/5*b**5 + 0*b + b**3 - 7*b**2 + 1/168*b**8 + 1/35*b**7 + 0. Solve f(a) = 0.
-3, -1, 1
Let q be (-3 - (-4 + 2))/(-1). Let z be (-3)/(-6)*(1 + q). Suppose z - 3*s + s**2 + 0*s + s = 0. What is s?
1
Let h(w) = -w**3 + 21*w**2 - 19*w - 17. Let o be h(20). Suppose 2*z + 4*z**2 + 7/2*z**4 - 19/2*z**o + 0 = 0. Calculate z.
-2/7, 0, 1, 2
Let h be 2*-1 + 84/21. Factor 0*x + 1/3*x**5 + 0*x**h + 0 + 1/3*x**4 + 0*x**3.
x**4*(x + 1)/3
Let -15*m**2 - 12*m**3 + m - 12*m**2 - 7*m = 0. Calculate m.
-2, -1/4, 0
Let v(i) = 12*i**2 - 11*i - 1. Let h(w) = 13*w**2 - 11*w - 2. Let f(q) = 3*h(q) - 4*v(q). Factor f(d).
-(d - 1)*(9*d - 2)
Let n be (3/(-5))/(12/(-40)). Let o(y) be the first derivative of 0*y**3 - n - 1/2*y**4 + y**2 + y - 1/5*y**5. Factor o(s).
-(s - 1)*(s + 1)**3
Let 2/3*v**2 - 10/3*v + 8/3 = 0. What is v?
1, 4
Let v(w) be the third derivative of w**6/120 - w**5/15 + w**4/12 + 2*w**3/3 + 11*w**2. Let x be v(3). Solve 1/2*z + 1/2*z**2 - x = 0 for z.
-2, 1
Let l(t) be the second derivative of -t**5/20 + t**4/4 + 3*t**2/2 + 12*t. Let p be l(3). Find q, given that 8/5*q + 0 + 6/5*q**4 - 16/5*q**2 + 2/5*q**p = 0.
-2, 0, 2/3, 1
Suppose -4*r - 9 = -3*r. Let k be (-51)/r - (-4)/(-6). Let -11*g**3 - 7*g**2 - k*g**3 - g - g**2 = 0. Calculate g.
-1/4, 0
Factor 64 + 144*b + 39*b**2 - 10*b**3 - 36*b**3 - 3*b**4 - 198*b**2.
-(b - 1)*(b + 8)**2*(3*b + 1)
Let m(r) be the third derivative of 2*r**7/525 + r**6/200 - r**5/60 - r**4/40 + r**3/30 - 61*r**2. Factor m(y).
(y - 1)*(y + 1)**2*(4*y - 1)/5
Solve 3/2*h + 0 - 9/4*h**2 - 3/4*h**5 - 3/4*h**3 + 9/4*h**4 = 0 for h.
-1, 0, 1, 2
Factor -5/2*q**3 - 25/2*q - 5 - 10*q**2.
-5*(q + 1)**2*(q + 2)/2
Suppose 3*z**4 - 8*z**4 + 21*z - 6*z**2 + 12*z**4 + 7*z + 8 - 19*z**3 = 0. Calculate z.
-1, -2/7, 2
What is x in 6 + 27*x - 47*x + 25*x - x**2 = 0?
-1, 6
Let p(j) = 3*j**3 + 4*j**2 + 4*j + 4. Let m(n) = -4*n**3 - 5*n**2 - 5*n - 5. Let y(u) = 4*m(u) + 5*p(u). Factor y(w).
-w**3
Suppose 2 = -4*u - 22. Let h(n) = n**2 + 4*n - 7. Let g be h(u). Solve 4*c**g - 3*c**3 - 3*c**2 + 0*c**2 - c**5 + 3*c**4 = 0 for c.
-1, 0, 1
Let m(v) = -2*v - 5. Let i be m(-4). Suppose -4*g**2 - 3*g**i + 3*g**2 + 4*g**2 + 6*g**3 = 0. Calculate g.
-1, 0
Let c(n) be the third derivative of -n**7/1155 - n**6/660 + n**5/330 + n**4/132 + 3*n**2. Factor c(s).
-2*s*(s - 1)*(s + 1)**2/11
Let y(k) be the second derivative of -k - 1/8*k**3 - 3/8*k**2 - 1/40*k**6 + 3/40*k**5 + 0 + 1/8*k**4 - 1/56*k**7. Factor y(h).
-3*(h - 1)**2*(h + 1)**3/4
Let s = 344 - 1016/3. Let c(r) be the first derivative of -s*r**3 + 4*r - 5/2*r**4 - r**2 + 1. Factor c(t).
-2*(t + 1)**2*(5*t - 2)
Let r(h) = -h**2 + 5*h - 3. Let l be r(7). Let z = l + 35/2. Factor 0 + z*o**2 + 0*o - 1/2*o**3 - 1/2*o**4 + 1/2*o**5.
o**2*(o - 1)**2*(o + 1)/2
Let n(i) = -2*i - 8. Let b be n(-6). Let s(f) be the first derivative of 1/6*f**2 + 0*f + 0*f**3 + 2 - 1/12*f**b. Determine r so that s(r) = 0.
-1, 0, 1
Suppose m**4 + 4*m**3 + 0*m**3 + 0*m**3 + 3*m**2 = 0. What is m?
-3, -1, 0
Let h(x) = -x**3 - 5*x**2 - 8*x - 3. Let n be h(-3). Solve 2/7*d**n - 2/7*d + 0 - 2/7*d**2 + 2/7*d**4 = 0 for d.
-1, 0, 1
Let o = 1/94 - -87/658. Factor 1/7*q**2 + o + 2/7*q.
(q + 1)**2/7
Let r(t) be the second derivative of -t**5/35 - t**4/7 - 2*t**3/7 - 2*t**2/7 + 10*t. What is f in r(f) = 0?
-1
Factor -3*v**2 + 7*v + v + 15*v**2.
4*v*(3*v + 2)
Let s = 289/3 + -865/9. Let k(o) = -3*o. Let w be k(-1). Factor -2/9*i**2 + 2/9*i**w + s - 2/9*i.
2*(i - 1)**2*(i + 1)/9
Let i be 28/72 + -4*(-5)/180. Suppose 1/4 + i*x**2 - 1/2*x**3 - 3/4*x**4 - 1/4*x**5 + 3/4*x = 0. Calculate x.
-1, 1
Let z(p) be the second derivative of -p**5/100 - p**4/60 + p**3/15 - p. Factor z(w).
-w*(w - 1)*(w + 2)/5
Let w = -183 - -554/3. Factor 2/3 - a - w*a**2.
-(a + 1)*(5*a - 2)/3
Factor -8/3*v - 2/3*v**2 + 10/3.
-2*(v - 1)*(v + 5)/3
Suppose 3*b + 0*b - 12 = 0. Suppose 0 = h + 4, -g + b*h + 22 - 4 = 0. Factor -6*d**3 - 6*d**5 + 3*d**4 - d**4 + 7*d - 2*d**g - 3*d + 8*d**5.
2*d*(d - 1)**2*(d + 1)*(d + 2)
Let l = -101 + 101. Determine v so that l*v + 0*v**4 + 2/3*v**5 - 2/3*v**3 + 0 + 0*v**2 = 0.
-1, 0, 1
Suppose 3*k - 6 + 3 = 0. Let g be (-57)/(-18) - k/6. Factor 0 - 2/5*i**4 - 4/5*i**g - 2/5*i**2 + 0*i.
-2*i**2*(i + 1)**2/5
Find r, given that 5/4*r + 5/4*r**5 + 5/2*r**2 - 5/2*r**3 - 5/4*r**4 - 5/4 = 0.
-1, 1
Let m(w) be the second derivative of w**4/42 + w**3/21 + w. Determine t, given that m(t) = 0.
-1, 0
Let v(p) be the first derivative of p**4/42 + p**3/21 - 2*p - 3. Let q(b) be the first derivative of v(b). What is s in q(s) = 0?
-1, 0
Let j(q) be the second derivative of -q**5/30 + 23*q**4/84 - 2*q**3/7 - 2*q**2 - 7*q. Let o(b) be the first derivative of j(b). Suppose o(y) = 0. What is y?
2/7, 3
Let l(m) be the third derivative of -7*m**6/60 + 2*m**5/5 + m**4/3 + m**2. Factor l(b).
-2*b*(b - 2)*(7*b + 2)
Let u(g) = 3*g**2 - 4*g - 2. Let v(x) = 13*x**2 - 15*x - 8. Let m(z) = -9*u(z) + 2*v(z). Let i be m(6). Determine q so that -2*q**2 + i*q + 1 + 6 - 3 = 0.
-1, 2
Let c(a) = a**2 - a. Let b(h) = -4*h**2 + 5*h. Let r(j) = 6*b(j) + 22*c(j). Suppose r(z) = 0. What is z?
0, 4
Let t(s) = -s**3 + 28*s**2 - 52*s + 2. Let u be t(26). Let 57/8*h**u + 21*h**4 - 171/8*h**3 - 6*h**5 + 0 - 3/4*h = 0. Calculate h.
0, 1/4, 1, 2
Let p(k) be the first derivative of k**6/3 + 18*k**5/35 - 5*k**4/14 - 6*k**3/7 - 2*k**2/7 + 4. Let p(l) = 0. What is l?
-1, -2/7, 0, 1
Let x(d) be the second derivative of 0*d**2 + 0*d**4 + 0 + 1/720*d**6 - d + 1/240*d**5 + 1/6*d**3. Let z(a) be the second derivative of x(a). Factor z(t).
t*(t + 1)/2
Let j(u) = -u**3 + 5*u**2 - 3*u - 1. Let p be j(4). Factor 3*w**p - 8*w + 5*w - 6 - 2*w**2 + 8*w**2.
3*(w - 1)*(w + 1)*(w + 2)
Suppose -24 = 4*h - 8*h. Let d be 8/3*(-24)/(-16). Find w, given that 2*w**2 - h*w + d - 2 + 2*w = 0.
1
Let v(k) be the second derivative of -1/6*k**4 + 3/20*k**5 + 0*k**2 + 0*k**6 - 1/42*k**7 + 0*k**3 + 0 + 9*k. Suppose v(s) = 0. Calculate s.
-2, 0, 1
Suppose 0 = -3*a + 3, i + 2*a = -2*a + 8. Let g(o) be the second derivative of 0*o**2 + 1/20*o**i + 1/50*o**5 + 1/30*o**3 + 0 + o. Factor g(y).
y*(y + 1)*(2*y + 1)/5
Let z(f) be the first derivative of 2*f**3/3 + f**2 - 9. Factor z(v).
2*v*(v + 1)
Let u = 5363/5 - 1069. Determine w, given that -12/5*w - 2/5*w**2 - u = 0.
-3
Let i(u) be the first derivative of -u**5/20 - u**4/8 - u**3/12 - 8. Solve i(t) = 0 for t.
-1, 0
Let b be 18/6 - 4/2. Let o be (-2)/b + 60/25. What is f in -o*f**4 + 4/5*f**3 - 4/5*f + 2/5 + 0*f**2 = 0?
-1, 1
Let g(b) be the first derivative of -3 + 0*b**2 + 0*b + 1/18*b**3 + 1/12*b**4 + 1/30*b**5. Let g(f) = 0. What is f?
-1, 0
Suppose -2*d - 2 = -d. Let z = d + 6. Factor 4*v**4 - 3*v**z + v**4.
2*v**4
Let n(b) = -15*b**4 + 15*b**3 - 3*b**2 - 24*b + 9. Let u(w) = -7*w**4 + 8*w**3 - 2*w**2 - 12*w + 5. Let i(l) = -4*n(l) + 9*u(l). Factor i(d).
-3*(d - 3)*(d - 1)**2*(d + 1)
Let q(l) = l**5 - 2*l**4 + 3*l**3 - 2*l**2 - 2. Let p(i) = -5*i**5 + 10*i**4 - 16*i**3 + 11*i**2 + 11. Let r(y) = 4*p(y) + 22*q(y). Factor r(n).
2*n**3*(n - 1)**2
Let x = 11 - 8. Suppose 21 = 2*n + x*j, -2*n - 4 = -4*j + 10. Let -2/9*o**4 +