1/3*h + 1/3*h**2 - 1/3*h**4 + x.
-h*(h - 1)**2*(h + 1)/3
Factor 7/2 - 1/6*s**2 - 10/3*s.
-(s - 1)*(s + 21)/6
Let m(p) be the second derivative of -p**7/168 + 17*p**6/120 - 63*p**5/80 - 27*p**4/16 + 2*p - 34. Suppose m(v) = 0. What is v?
-1, 0, 9
Suppose -10/3*y**2 + 1/3*y**3 + 22/3 - 13/3*y = 0. Calculate y.
-2, 1, 11
Let w(z) = 20*z**3 - 155*z**2 - 600*z - 990. Let p(k) = -k**3 + 2*k**2 - 2. Let d(l) = -25*p(l) - w(l). Let d(r) = 0. What is r?
-13, -4
Let d(p) be the first derivative of p**4/54 - 20*p**3/27 + 100*p**2/9 + 20*p - 25. Let k(o) be the first derivative of d(o). Solve k(z) = 0 for z.
10
Let r(f) be the first derivative of 5*f**4/2 - 7*f**3/3 - f**2 - f + 6. Let j(i) = -3*i**3 + 2*i**2 + i. Let t(q) = 7*j(q) + 2*r(q). Let t(g) = 0. What is g?
-2, 1
Let w = -219 + 224. Let f(j) be the first derivative of -1/20*j**4 + 0*j**2 - w + 0*j - 1/15*j**3. Factor f(g).
-g**2*(g + 1)/5
Let l(f) = f**3 - 5*f**2 - 14*f. Suppose 0 = -2*h - 18 + 10. Let s(b) = -5*b**3 + 30*b**2 + 85*b. Let o(m) = h*s(m) - 25*l(m). Factor o(k).
-5*k*(k - 2)*(k + 1)
Let l = 2181/22 + -1074/11. Factor 15/4*t**2 - 3*t**3 + 0 - l*t + 3/4*t**4.
3*t*(t - 2)*(t - 1)**2/4
Suppose -10*a - 4 = -9*a - 2*z, 4*a = -z + 11. Factor 18*m**4 + 48*m**3 + 32/9 + 64/3*m + 48*m**a.
2*(3*m + 2)**4/9
Let h be -10 + 1332/135 + 92/240. Let v(o) be the second derivative of 0*o**2 + 0*o**3 + h*o**5 + 11*o + 0 + 5/6*o**4. Factor v(k).
5*k**2*(k + 2)
Suppose -7*u + 15 = -2*u. Factor -u*p - 15*p**2 - p**5 + 17*p**2 + 4*p**3 + 2 - 4.
-(p - 2)*(p - 1)*(p + 1)**3
Let d(p) be the third derivative of -p**8/504 - 38*p**7/315 - 16*p**6/9 + 80*p**5/9 + 210*p**2. Factor d(w).
-2*w**2*(w - 2)*(w + 20)**2/3
Let k(r) = 6*r + 22. Let h be k(0). Suppose 9*z + 34*z**4 + 4*z**5 - 21*z**4 - 3*z**5 - 21*z**4 - 24*z**2 + h*z**3 = 0. What is z?
0, 1, 3
Let 4/5*t**3 - 18/5*t**2 + 16/5 - 4/5*t + 2/5*t**4 = 0. What is t?
-4, -1, 1, 2
Let q(u) be the second derivative of u**7/105 + 2*u**6/15 - 27*u**5/50 - 14*u**4/15 + 92*u**3/15 - 48*u**2/5 - 242*u - 2. Suppose q(n) = 0. What is n?
-12, -2, 1, 2
Let h(l) be the third derivative of -l**7/420 - 11*l**6/240 - 7*l**5/20 - 4*l**4/3 - 8*l**3/3 + 148*l**2. Find b, given that h(b) = 0.
-4, -2, -1
Let g(w) be the second derivative of w**4/12 + 11*w**3/3 + 121*w**2/2 - 43*w. Let g(d) = 0. Calculate d.
-11
Let x(r) be the second derivative of -r**6/40 - 3*r**5/16 - 9*r**4/16 - 7*r**3/8 - 3*r**2/4 - 55*r. Factor x(f).
-3*(f + 1)**3*(f + 2)/4
Suppose 2*v + 2*x = 24 - 6, -5*v + x + 15 = 0. Let o(r) be the first derivative of 1/9*r**6 + 7 + 0*r**3 + 1/6*r**v + 4/15*r**5 + 0*r**2 + 0*r. Factor o(q).
2*q**3*(q + 1)**2/3
Suppose 0 = -y - 4*y - 425. Let t be 4 - ((275/y - -4) + 3). Factor 2/17*b**3 + 0 + 2/17*b + t*b**2.
2*b*(b + 1)**2/17
Suppose -22/17*y**3 - 6/17 + 22/17*y - 8/17*y**4 + 14/17*y**2 = 0. Calculate y.
-3, -1, 1/4, 1
Let v(m) = 6*m**3 + 3*m**2 - 3. Let p be ((-6)/(-4))/(16/32). Let j(i) = -7*i**3 - 2*i**2 + i + 4. Let w(h) = p*j(h) + 4*v(h). Suppose w(a) = 0. Calculate a.
-1, 0
Let q(f) be the third derivative of -f**8/36 + 32*f**7/315 - 2*f**6/45 - 14*f**5/45 + 11*f**4/18 - 4*f**3/9 + f**2 - 27. Find c, given that q(c) = 0.
-1, 2/7, 1
Let y(v) be the first derivative of -2*v**5/65 + 2*v**4/13 - 2*v**3/13 - 4*v**2/13 + 8*v/13 + 180. What is c in y(c) = 0?
-1, 1, 2
Let h(j) = 4*j**2 - 8 - 5*j**2 + 6*j + 7*j - 5*j. Let b be h(6). Factor -5*a - 7*a - 4*a**b - 2*a**5 + 12*a.
-2*a**4*(a + 2)
Let g(a) = -a + 18. Let t be g(0). Let k = 37 - t. Determine n so that -42*n**5 + 6*n**2 + 19*n - 33*n**4 + 15*n**3 - k*n = 0.
-1, -2/7, 0, 1/2
Let h(c) = -20*c**4 + 24*c**3 - 16*c**2 + 32*c. Let f(v) = 4*v**4 - 5*v**3 + 3*v**2 - 6*v. Let s(p) = 16*f(p) + 3*h(p). Determine q, given that s(q) = 0.
0, 2
Suppose -4*a = -4*j - 1 + 33, -5*a - 16 = 3*j. Suppose 7*q = 2*q. Find f, given that -f**4 + 2*f**5 - 2*f**3 + 4*f**j + q*f**3 - 3*f**4 = 0.
0, 1
Suppose 2*b + 291 - 199 = 0. Let w = b + 46. Find h, given that 3/4 - 9/4*h**2 + w*h - 3/2*h**3 = 0.
-1, 1/2
Let p(m) = -m**2 - 8*m - 9. Let v be p(-6). Suppose v = 3*u - 2*c - 13, 0 = -2*u + 2*c + 12. Factor -2*a**u + a - a - 2*a + a**3 + 2*a**2 + a**3.
-2*a*(a - 1)**2*(a + 1)
Suppose -6*g = -8 - 16. Suppose -g*r + 13*r = 18. Factor 2/3*y**4 + 0*y**r + 2/3*y**3 + 0*y + 0.
2*y**3*(y + 1)/3
Let a(d) be the second derivative of d**5/30 - d**3/3 + 5*d**2/2 + 8*d. Let j(m) be the first derivative of a(m). Factor j(s).
2*(s - 1)*(s + 1)
Suppose -3*h + 0*h + 18 = 0. Let j = -4 + h. Solve -5 + 3*l**j + 3*l + 2 + 0*l**2 + 2*l**3 - 5*l**3 = 0 for l.
-1, 1
Suppose -4*d + 14 = 2. Solve -d*h**4 - 10*h**2 + 8*h**4 + 30 - 46 + 21 = 0.
-1, 1
Let k(q) = -53*q**2 + 957*q - 54. Let z be k(18). Find c such that z*c + 9/5*c**2 + 3/5*c**3 + 0 = 0.
-3, 0
Let v be 19/76 + ((-91)/12)/(-7). Factor -v*r**4 - 4*r**3 + 0*r - 8/3*r**2 + 0.
-4*r**2*(r + 1)*(r + 2)/3
Let b(s) be the first derivative of -s**5 + 5*s**4/2 + 5*s**3 - 10*s**2 - 20*s - 454. Find v such that b(v) = 0.
-1, 2
Let k(c) = c**2 - 6*c - 4. Let z be k(7). Let w be (-1 + z)*13/26. Solve -w + 6*r - 7 + 1 - r**2 - 2 = 0 for r.
3
Let l(u) = -u**2 + u - 20. Let m(w) = -3*w**2 - w - 41. Let x(t) = -5*l(t) + 2*m(t). Suppose x(i) = 0. What is i?
-9, 2
Let a(h) = -31*h**4 - 669*h**3 - 323*h**2 + 5*h. Let y(l) = 14*l**4 + 334*l**3 + 162*l**2 - 2*l. Let j(w) = -2*a(w) - 5*y(w). Factor j(v).
-4*v**2*(v + 41)*(2*v + 1)
Let h(k) be the second derivative of 1/2*k**2 + 1/12*k**3 - 1/24*k**4 + 12*k + 0. Factor h(q).
-(q - 2)*(q + 1)/2
Suppose 2*r + 6 = -r - 2*s, 3*s = -4*r - 9. Let i(c) be the second derivative of r - 4*c - 1/4*c**3 + 1/4*c**2 - 1/40*c**5 + 1/8*c**4. Factor i(m).
-(m - 1)**3/2
Let z(o) be the first derivative of 9/26*o**4 - 12 + 4/39*o**3 + 0*o**2 + 0*o + 14/65*o**5. Factor z(k).
2*k**2*(k + 1)*(7*k + 2)/13
Suppose 0*f = 3*v + 4*f - 4, -5*f - 17 = v. Suppose -6*n - v = -10*n. Factor -h**3 + 0 + 2/3*h - 1/3*h**n + 1/3*h**5 + 1/3*h**4.
h*(h - 1)**2*(h + 1)*(h + 2)/3
Let r(m) be the second derivative of -m**6/60 + 11*m**5/10 - 73*m**4/4 - 253*m**3/3 - 529*m**2/4 - 695*m. Factor r(x).
-(x - 23)**2*(x + 1)**2/2
Let m(v) = v**2 + v. Suppose -5*x - 75 = -2*h, 4*x + 3*h + 2*h + 60 = 0. Let d(j) = -18*j**2 - 36*j. Let n(t) = x*m(t) - d(t). Factor n(b).
3*b*(b + 7)
Suppose 0*q + 2*q = -5*x - 364, 4 = -2*q. Let j be (-16)/x + (-2)/(-18). Factor 1/3*b**2 - 2/3 - j*b.
(b - 2)*(b + 1)/3
Let t(l) = l**3 - 2*l**2. Let y(q) = -q**4 - 12*q**3 + 9*q**2 + 10*q. Let v(u) = 6*t(u) + y(u). Find k such that v(k) = 0.
-5, -2, 0, 1
Let x(g) = -170*g**3 + 200*g**2 - 40*g. Let w(f) = 85*f**3 - 100*f**2 + 21*f. Let p(b) = 5*w(b) + 3*x(b). Find r, given that p(r) = 0.
0, 3/17, 1
Let r(c) be the second derivative of 5/24*c**3 + 1/16*c**4 + 0 - 38*c + 1/4*c**2. Factor r(p).
(p + 1)*(3*p + 2)/4
Suppose 2*w - 4*f = -12, 5*w + 15 = 5*f - 0*f. Suppose -2*v + w*v + 4 = 0. Factor 6*r**v - 2 - 5*r**2 + r**2.
2*(r - 1)*(r + 1)
Let l(j) be the third derivative of j**5/180 - 79*j**4/72 + 13*j**3/3 + 110*j**2. Determine r, given that l(r) = 0.
1, 78
Let z(i) = 3*i**3 - 21*i**2 + 16*i + 12. Let d(y) = 6*y**3 - 43*y**2 + 32*y + 20. Let t(k) = -2*d(k) + 5*z(k). Find c, given that t(c) = 0.
-2/3, 2, 5
Let p(r) = -r**3 - 5*r**2 + 4*r - 10. Let o be p(-6). Determine j so that 0*j**2 - 9*j**2 + 4*j**5 + j**o - 4*j**3 + j**4 + 7*j**4 = 0.
-2, -1, 0, 1
Suppose 52*h + 67*h = h. Factor 0 - 3/2*w**2 + h*w.
-3*w**2/2
Let c = -53 + 59. Factor 5*n**2 - 2*n**2 + c*n - 1 + 4.
3*(n + 1)**2
Let f(l) be the second derivative of l**5/25 - 22*l**4/15 - 46*l**3/15 - 3*l - 38. Factor f(t).
4*t*(t - 23)*(t + 1)/5
Let m(f) = -2*f**3 + 6*f**2 - 9*f. Let d(k) = -3*k**3 + 7*k**2 - 10*k. Let t(w) = -5*d(w) + 6*m(w). Determine u, given that t(u) = 0.
-4/3, 0, 1
Let y(h) be the second derivative of h**8/7560 + h**7/945 - 20*h**3/3 - 30*h. Let d(v) be the second derivative of y(v). Factor d(t).
2*t**3*(t + 4)/9
Suppose 0 = o - 3*o. Suppose 2 = n - o*n. Suppose 2*v**4 - 4*v + 0*v**3 + 4*v**3 + 4*v + n*v**2 = 0. What is v?
-1, 0
Let o(s) be the third derivative of 1/60*s**6 + 0*s + 0*s**3 + 1/105*s**7 + 11*s**2 - 1/6*s**5 + 0 + 1/4*s**4. Suppose o(q) = 0. What is q?
-3, 0, 1
Let h(t) be the first derivative of 2/3*t**2 + 3 + 0*t - 16/9*t**3 - 14/15*t**5 + 23/12*t**4 + 1/6*t**6. So