, 1
Let z(n) = -7*n**3 - 12*n**2 - 7*n + 2. Let q(i) = 15*i**3 + 25*i**2 + 15*i - 5. Let g(d) = -2*q(d) - 5*z(d). Solve g(r) = 0.
-1, 0
Let q(p) be the first derivative of 0*p**2 + 0*p - 3 + 1/3*p**3. Find y such that q(y) = 0.
0
Let d(f) be the first derivative of f**8/1344 + f**7/420 + f**6/480 + 2*f**2 - 1. Let h(l) be the second derivative of d(l). Solve h(y) = 0 for y.
-1, 0
Factor -2/7 - 2/21*w + 2/7*w**2 + 2/21*w**3.
2*(w - 1)*(w + 1)*(w + 3)/21
Let v(t) = -5*t**4 - 8*t**3 + 6*t**2. Let w(c) = 3*c**4 + 4*c**3 - 3*c**2. Let h(x) = -4*v(x) - 7*w(x). What is f in h(f) = 0?
0, 1, 3
Suppose 2*i - 4*i = -5*d, -5*d = 0. Find j, given that 0*j - 1/5*j**4 + i + 0*j**3 + 1/5*j**2 = 0.
-1, 0, 1
Let a(w) = 3*w**2 - 6*w - 7. Let h be a(-1). Let -2/9*r**h - 32/9 + 16/9*r = 0. What is r?
4
Suppose -4*m + 78 - 22 = 0. Factor -m*t + 18*t**2 + 2*t**4 - 11*t**3 + 1 + 3 + t**3.
2*(t - 2)*(t - 1)**3
Let l(o) be the first derivative of -7*o**6/540 - o**5/36 + o**4/18 + o**3 + 7. Let t(n) be the third derivative of l(n). Factor t(h).
-2*(h + 1)*(7*h - 2)/3
Suppose -2*c - 4*t + 56 = -9*t, -3*c + 5*t + 74 = 0. Let l be ((-4)/c)/(4/(-6)). Factor -2/3 + l*m + 2*m**2 - 4/3*m**3 - 4/3*m**4 + m**5.
(m - 1)**3*(m + 1)*(3*m + 2)/3
Let l = 596 + -1191/2. Find h, given that -l*h**2 - 9/2 - 3*h = 0.
-3
Let f(t) be the second derivative of 4/15*t**6 - 1/3*t**3 + 0 + t**4 + 0*t**2 - 2*t - 9/10*t**5. Factor f(m).
2*m*(m - 1)**2*(4*m - 1)
Let o(k) = -k**2 - 1. Let x(n) = n + 11. Let g be x(-8). Suppose 2*v + g*v + 5 = 0. Let i(l) = l**2 + l + 2. Let w(c) = v*i(c) - 2*o(c). Factor w(b).
b*(b - 1)
Let t = 45 - 42. Factor 4/7*w**2 + 3/7 + 9/7*w**4 + 30/7*w**t - 2*w.
(w + 1)*(w + 3)*(3*w - 1)**2/7
Let k = 1852/5 - 370. Factor 4/5*m**3 - 2/5*m - 4/5*m**2 + k + 2/5*m**4 - 2/5*m**5.
-2*(m - 1)**3*(m + 1)**2/5
Let n(b) = 9*b**2 + 6*b - 3. Let x(o) = 8 - 16*o**2 - 3*o**2 - 13*o - 2. Let g(r) = 5*n(r) + 3*x(r). Factor g(h).
-3*(h + 1)*(4*h - 1)
Solve q + 1/2*q**2 + 1/4*q**4 - q**3 - 3/4 = 0 for q.
-1, 1, 3
Let i(k) be the second derivative of -k**5/20 - k**4/2 + k**3/6 + 4*k**2 - 3*k. Let g be i(-6). Find n such that 1/4 + 1/4*n - 1/4*n**g - 1/4*n**3 = 0.
-1, 1
Let p(f) be the third derivative of -f**8/40320 + f**7/3360 - f**5/12 - f**2. Let c(x) be the third derivative of p(x). Factor c(y).
-y*(y - 3)/2
Let o(w) = w**2 + 4*w. Let z be o(-4). Suppose 3*j = z, -5*j + 6 = v + 2*v. Find x, given that 2/5*x**v - 6/5*x + 4/5 = 0.
1, 2
Factor 0*m + 0*m**4 + 1/4*m**5 + 0*m**2 + 0 + 0*m**3.
m**5/4
Let k(r) be the first derivative of -r**3/3 + 9*r**2/2 - 8*r - 44. What is v in k(v) = 0?
1, 8
Let p(z) = 2*z - 15. Let u be p(9). Suppose 19 = u*b + 10. Factor -3/5*m**2 + 1/5*m**4 + 4/5 + 2/5*m**b - 4/5*m.
(m - 1)**2*(m + 2)**2/5
Let s(t) be the third derivative of t**6/120 - t**5/10 + t**4/4 + 2*t**2. Let r be s(5). What is c in r*c**2 + c - 2 + 0 - 4*c**2 = 0?
-2, 1
Suppose -3*i + 8 = -i. Find p such that -6*p - 10*p**5 - 9*p**3 + 9*p**5 + 15*p**2 + i*p**5 - 3*p**4 = 0.
-2, 0, 1
Let p = 44 + -41. Let g = -2057/65 - -159/5. Factor 2/13*h**5 + 2/13 + g*h - 4/13*h**p - 4/13*h**2 + 2/13*h**4.
2*(h - 1)**2*(h + 1)**3/13
Suppose 84*m**2 + 16/5 + 50*m**4 - 110*m**3 - 136/5*m = 0. Calculate m.
2/5, 1
Factor t**3 - 6*t + 8*t**4 - 4*t**5 - 14 + 7*t**3 + 6 - 32*t**2 + 34*t.
-4*(t - 1)**4*(t + 2)
Suppose 6 = j - s - 0*s, -2*s = j. Suppose 2*w = -j*n + 28, 2*w - n + 17 = 5*w. Solve -4*d**w + 9/4*d**5 - 5/4*d + 9/2*d**2 - 1/2 - d**3 = 0 for d.
-1, -2/9, 1
Suppose -28*p = 27*p - 56*p. Find u such that -2/13*u**2 + 2/13 + p*u = 0.
-1, 1
Let n(h) be the second derivative of -h**7/840 + h**6/240 - h**5/240 + 2*h**2 + h. Let c(t) be the first derivative of n(t). Factor c(s).
-s**2*(s - 1)**2/4
Let o(u) = -u + 8. Suppose 4*c - 3 = 29. Let f be o(c). Factor 2*r**4 + f*r**5 - 3*r**5 - 2*r**3 - 2*r**2 + 5*r**5.
2*r**2*(r - 1)*(r + 1)**2
Let l(k) be the second derivative of -k**7/126 + k**5/60 - 10*k. Factor l(w).
-w**3*(w - 1)*(w + 1)/3
Let o(z) be the second derivative of z**5/50 - z**4/30 - z**3/15 + z**2/5 - 17*z. Factor o(x).
2*(x - 1)**2*(x + 1)/5
Factor 0*i + i**4 - 1/2*i**3 + 0 - i**2 + 1/2*i**5.
i**2*(i - 1)*(i + 1)*(i + 2)/2
Factor 0*q**2 + 0*q**4 + 0 - 1/7*q - 1/7*q**5 + 2/7*q**3.
-q*(q - 1)**2*(q + 1)**2/7
Suppose -5*y - y = 0. Factor -1/4*m**4 + 1/4*m + 1/4*m**2 + y - 1/4*m**3.
-m*(m - 1)*(m + 1)**2/4
Factor -2*r**3 - 2*r**2 - 4*r**2 + 2*r + 6*r**2.
-2*r*(r - 1)*(r + 1)
Determine l so that -2/3*l**2 + 2*l - 4/3 = 0.
1, 2
Let z(k) be the first derivative of 1/3*k**3 + 0*k + k**2 - 1/4*k**4 + 4. What is n in z(n) = 0?
-1, 0, 2
Let a = -803/5 + 161. Let -a*l**3 + 0 - 2/5*l**2 + 2/5*l**4 + 0*l + 2/5*l**5 = 0. Calculate l.
-1, 0, 1
Factor -28*i**4 - 738 - 76*i**3 - 100*i**2 + 722 - 4*i**5 - 29*i - 35*i.
-4*(i + 1)**3*(i + 2)**2
Let i be 10/3 - (-12)/18. Suppose v**2 - 3*v**3 - v + 9*v**3 + 2*v**2 - i*v**2 = 0. What is v?
-1/3, 0, 1/2
Let z be ((-2)/6)/(4/(-6)). Let y be -3 + 1/(-1)*(-15)/3. Factor 1/2*g + 1 - z*g**y.
-(g - 2)*(g + 1)/2
Factor 39/8*d - 15/8*d**2 - 9/4.
-3*(d - 2)*(5*d - 3)/8
Let o(q) be the second derivative of q**4/4 + 3*q**3 + 27*q**2/2 - 14*q. Solve o(u) = 0.
-3
Let g(o) be the second derivative of o**9/4320 - o**8/2688 - o**7/2520 - o**4/6 + 2*o. Let x(b) be the third derivative of g(b). Let x(h) = 0. What is h?
-2/7, 0, 1
Factor -20*n**2 - 20*n**4 + 1447*n**3 + 5*n + 4*n**5 - 1417*n**3 + n**5.
5*n*(n - 1)**4
Let s(j) be the third derivative of j**8/1176 - j**6/70 - 4*j**5/105 - j**4/28 + 2*j**2. Let s(r) = 0. Calculate r.
-1, 0, 3
Let g(q) = -6*q**2 - 15*q - 6. Let r(z) = -z**2 - z - 1. Let t(n) = -g(n) + 9*r(n). Find y such that t(y) = 0.
1
Suppose 0 = 2*g - 27 - 5. Suppose 2*s + 4*u = g, 3*u - 4 = 4*s + 2*u. Factor 5*m**2 - m**2 - m**2 - 3*m + s*m**2.
3*m*(m - 1)
Let x be (-1)/(-2)*12 - 2. Find u such that 3*u**x - 6*u**2 + 0 + 3*u - 6*u**5 - 9*u + 12*u**3 + 3 = 0.
-1, 1/2, 1
Let p = 110 - 549/5. Let j(d) be the first derivative of -p*d**3 + 7/10*d**2 + 2 - 2/5*d + 1/5*d**5 - 7/20*d**4. Factor j(h).
(h - 1)**2*(h + 1)*(5*h - 2)/5
Let 0*h**3 - 1/2*h**2 + 1/6*h**4 + 0 + 1/3*h = 0. What is h?
-2, 0, 1
Let r(v) = -3*v**2 + 10*v + 4. Let j(x) = 8*x**2 - 31*x - 12. Let w be 3/(-3) + 2/2. Suppose 0 = -w*y + y + 4. Let o(u) = y*j(u) - 14*r(u). Factor o(g).
2*(g - 2)*(5*g + 2)
Find g, given that -36*g**3 - 90*g**2 + 84*g**4 - 9*g + 6 + 16*g**3 + 2*g + 27*g**5 = 0.
-3, -1, -1/3, 2/9, 1
Solve 0*z**2 - 4 - 2*z**3 - 2*z**2 - 10*z - 3*z**2 - 3*z**2 = 0 for z.
-2, -1
Let n(d) = 2*d**2 - 8*d - 16. Let u(p) be the first derivative of -5*p**3/3 + 8*p**2 + 32*p - 5. Let m(t) = -7*n(t) - 3*u(t). Suppose m(v) = 0. Calculate v.
-4
Let a(c) be the first derivative of c**4/4 - c + 9. Let g(y) = 3*y**3 - 8*y**2 + 16*y - 2. Let q(d) = 2*a(d) - g(d). Factor q(i).
-i*(i - 4)**2
Factor 3 + 27/2*z**2 - 27/2*z.
3*(3*z - 2)*(3*z - 1)/2
Let y(b) be the second derivative of -b**9/90720 + b**8/40320 + b**7/15120 - b**6/4320 + 5*b**4/12 + 2*b. Let p(s) be the third derivative of y(s). Factor p(f).
-f*(f - 1)**2*(f + 1)/6
Let q be (-1)/(38/(-6) + (-7)/21). Let w(l) be the first derivative of -3/8*l**2 + 1/24*l**6 + q*l**5 - 1/4*l + 1/8*l**4 - 1/6*l**3 - 1. Factor w(c).
(c - 1)*(c + 1)**4/4
Let r(k) = -3*k + 41. Let w be r(12). Let b(v) be the second derivative of -3/70*v**w - 1/21*v**4 + 0*v**2 + 1/21*v**3 + 0 - v. Solve b(c) = 0.
-1, 0, 1/3
Suppose -2*f - 4*l + 0 = 14, 0 = -2*l + 8. Let y be (-177)/f - 6/3. What is n in y*n**2 - 28/5*n + 4/5 = 0?
2/7
Let h(f) be the third derivative of -f**8/84 - f**7/210 + f**6/10 + 11*f**5/60 + f**4/12 + 6*f**2. Suppose h(v) = 0. What is v?
-1, -1/4, 0, 2
Let r(m) = -12*m**3 + 16*m**2 - 8*m - 4. Let g(l) = 24*l**3 - 32*l**2 + 15*l + 7. Let h(q) = -4*g(q) - 7*r(q). Factor h(d).
-4*d*(d - 1)*(3*d - 1)
Let r = 12 - 9. Let u be (-1)/(-8 + (r - 0)). Factor 0 + 0*l - u*l**2 + 1/5*l**5 - 1/5*l**3 + 1/5*l**4.
l**2*(l - 1)*(l + 1)**2/5
Determine f, given that 1/8*f**3 + 1/4*f**2 + 0*f - 1/8*f**5 - 1/4*f**4 + 0 = 0.
-2, -1, 0, 1
Find z, given that 3/4*z**2 + 9 - 21/4*z = 0.
3, 4
Let g(c) be the first derivative of -c**7/120 - c**6/72 + c**5/60 + 5*c**3/3 + 3. Let i(p) be the third derivative of g(p). Let i(k) = 0. What is k?
-1, 0, 2/7
Let g(z) be the second derivative of -2*z**7/21 - 2*z**6/1