
Solve 1014/5*c**2 + 56/5 - 532/5*c**3 - 88*c - 98/5*c**4 = 0.
-7, 2/7, 1
Let b(s) be the second derivative of -s**6/90 + s**5/6 - 8*s**4/9 + 19*s**3/9 - 5*s**2/2 + 248*s. Suppose b(d) = 0. Calculate d.
1, 3, 5
Suppose 14*y = 19*y - 15. Let b(q) = -q**3 + 5*q**2 - 7*q + 5. Let u be b(y). Find t such that -2*t - 4/3 - 2/3*t**u = 0.
-2, -1
Let k(m) be the third derivative of 19/60*m**4 + 0*m - 7/150*m**5 + 0 + 2/5*m**3 - 12*m**2. Factor k(w).
-2*(w - 3)*(7*w + 2)/5
Let j be (176/(-77))/(-4*3/(-168)*-30). Factor 2/15*z**2 - j*z + 0.
2*z*(z - 8)/15
Let j(r) be the second derivative of -r**4/42 + 10*r**3/3 - 175*r**2 + 114*r. Determine z so that j(z) = 0.
35
Let k(p) be the third derivative of p**7/42 - p**6/24 - p**5/12 + 5*p**4/24 - 268*p**2. Factor k(f).
5*f*(f - 1)**2*(f + 1)
Let g be ((3 + 0)*1)/((-15)/(-10)). Factor 294*o - 297*o - o**3 + 6*o**2 - g*o**3.
-3*o*(o - 1)**2
Let m(z) be the second derivative of z**5/10 + 31*z**4/6 - 360*z - 2. Factor m(n).
2*n**2*(n + 31)
Suppose 3 - 38*i + 13*i**3 - 27 + 530*i**2 - 546*i**2 - 15*i**3 = 0. What is i?
-4, -3, -1
Suppose 5*c = -2*j + 2, -c + 42*j + 10 = 40*j. Solve 0 - 2/11*x**4 + 6/11*x**3 - 6/11*x**c + 2/11*x = 0 for x.
0, 1
Let o(z) = -3*z**3 - 6*z**2 - 11*z. Let s(t) = 3*t**3 + 9*t**2 + 12*t. Let v(c) = -3*o(c) - 4*s(c). Let v(b) = 0. Calculate b.
-5, -1, 0
Factor -2/3*h**2 - 8/3*h + 2/3*h**3 + 8/3.
2*(h - 2)*(h - 1)*(h + 2)/3
Suppose j - 4*y + 5*y - 5 = 0, -y + 5 = 5*j. Let -4/13*u**4 + 0 - 2/13*u**5 + 2/13*u + j*u**3 + 4/13*u**2 = 0. Calculate u.
-1, 0, 1
Let c(z) be the first derivative of -3*z**5/5 + 9*z**4/4 - z**3 - 9*z**2/2 + 6*z + 143. Factor c(p).
-3*(p - 2)*(p - 1)**2*(p + 1)
Let -28/19*z - 2/19*z**2 - 90/19 = 0. Calculate z.
-9, -5
Let d(s) be the second derivative of 0*s**3 + 4*s - 1/2*s**2 + 0 + 1/12*s**4. Factor d(y).
(y - 1)*(y + 1)
Suppose 2*x + 4*j = 30, -8 = -2*x + 9*j - 56. Factor -1/2*d**x + 3/2*d**2 + 1/2 - 3/2*d.
-(d - 1)**3/2
Suppose -3*h + 8 + 4 = 0. Suppose -u = h*x - 1, 4*x = u + 2*u - 3. Find a such that 2/7*a**3 - 2/7*a - 1/7 + 1/7*a**4 + x*a**2 = 0.
-1, 1
Let y = 1326 - 1321. Let x = -2/15 - -7/15. Find w, given that -x*w**3 - 1/3*w**y + 8/3 + 4/3*w + 4/3*w**4 - 10/3*w**2 = 0.
-1, 2
Let l(m) = 144*m**2 + 172*m - 20. Let j(c) = c**2 + 1. Let x(v) = 24*j(v) + l(v). Suppose x(t) = 0. What is t?
-1, -1/42
Factor -4*m + 1/4*m**2 - 9.
(m - 18)*(m + 2)/4
Suppose 4 + 16 = 2*s. Suppose -3*p = 2*p - s. Determine o so that -3*o**p - o**2 + 2*o**2 + 2 + 12*o - 20 = 0.
3
Factor 29*w + 124*w + 39 + 667*w**2 - 679*w**2.
-3*(w - 13)*(4*w + 1)
Let d be (0 - -1) + 6 + -4. Suppose 3*g = 4*f - 35, 2*f = d*f + g - 7. Find r, given that 3*r**3 - 16*r**2 + 8*r**4 - 19*r**3 + 8 + 4*r + f*r**3 + 4*r**5 = 0.
-2, -1, 1
Let g(r) = 7 - 4*r**4 + 10*r + 4*r**2 - 6*r**3 + r**4 + 0*r**2. Let z(k) = -3*k**4 - 6*k**3 + 5*k**2 + 11*k + 8. Let d(j) = 5*g(j) - 4*z(j). Factor d(l).
-3*(l - 1)*(l + 1)**3
Let x(w) be the third derivative of w**7/105 + 53*w**6/60 + 101*w**5/30 - 53*w**4/12 - 34*w**3 + 1027*w**2. Find j, given that x(j) = 0.
-51, -2, -1, 1
Suppose 4*n = -0*n + 8. Let u = n - 0. Suppose 108*h + 11*h**u + 78 - 24 + 61*h**2 + 8*h**3 + 8*h**3 = 0. Calculate h.
-3/2
Let w(r) be the first derivative of 2*r**3/33 - 70*r**2/11 + 138*r/11 - 565. Suppose w(y) = 0. What is y?
1, 69
Factor -1/4*b**5 - 1/2*b**4 + 23/4*b**3 + 6*b**2 + 0 - 36*b.
-b*(b - 3)**2*(b + 4)**2/4
Let l = 17 + -14. Factor -4*i**5 + 5*i**5 + 5*i**5 + i**l - 7*i**5.
-i**3*(i - 1)*(i + 1)
Let w(i) be the first derivative of -i**5/180 - i**4/24 - i**3/9 - 17*i**2/2 - 15. Let g(l) be the second derivative of w(l). Factor g(h).
-(h + 1)*(h + 2)/3
Let z(k) = 5*k**2 - 126*k + 25. Let s be z(25). Factor 0*t + s - 8/7*t**3 + 4/7*t**2 + 4/7*t**4.
4*t**2*(t - 1)**2/7
Let r = -59 - -62. Suppose r*a + 25 - 31 = 0. Let 3/2*s**a - 3/2 + 3/2*s - 3/2*s**3 = 0. Calculate s.
-1, 1
Let x(u) be the first derivative of u**6/5 + u**5/10 - u**4/2 - u**3/3 + 15*u - 7. Let h(w) be the first derivative of x(w). Factor h(o).
2*o*(o - 1)*(o + 1)*(3*o + 1)
Let a(b) = -4*b - b + 4*b. Let n be a(-3). Suppose -9*s**2 + 13*s**2 + s**3 - n*s**2 - 1 - s = 0. What is s?
-1, 1
Let a be (-1)/(15/24)*5. Let b be (a/(-70))/(10/25). Find t such that 2/7*t**3 + 0 + b*t - 4/7*t**2 = 0.
0, 1
Let v(t) be the second derivative of -t**7/21 + t**6/5 + t**5/10 - t**4/2 - 208*t. Solve v(q) = 0.
-1, 0, 1, 3
Factor -30/7 - 3/7*q**2 - 3*q.
-3*(q + 2)*(q + 5)/7
Let d = -3 - -2. Let a = d - 14. Let v(j) = -4*j**3 - 4*j**2 - j - 6. Let y(n) = n**3 + n**2 + 1. Let c(x) = a*y(x) - 3*v(x). Solve c(k) = 0.
-1, 1
Let k(z) be the third derivative of z**6/8 - 25*z**5/12 + 5*z**4/3 + 2*z**2. Let k(n) = 0. What is n?
0, 1/3, 8
Let y = 10938/11 - 994. Factor 2/11*u + y - 2/11*u**2.
-2*(u - 2)*(u + 1)/11
Let l(t) = 3*t**2 + 11*t - 9. Let z be l(1). Let p(s) be the third derivative of 0 + s**2 + 0*s**4 + 0*s**3 + 0*s - 1/240*s**z. Suppose p(o) = 0. What is o?
0
Let w = 7 + -10. Let o(g) = 7*g**3 + 2*g**2 - 7*g + 4. Let z(l) = 8*l**3 + 2*l**2 - 6*l + 4. Let u(n) = w*z(n) + 4*o(n). Factor u(x).
2*(x - 1)*(x + 2)*(2*x - 1)
Let l(p) be the third derivative of 0*p**5 + 27*p**2 + 0 + 0*p - 1/80*p**6 + 1/2*p**3 + 3/16*p**4. What is x in l(x) = 0?
-1, 2
Let a(d) = -d**3 - 5*d**2 - 3*d - 2. Let k be a(-5). Let n = -11 + k. Suppose 180 - 180 - 32*l**n + 8*l + 30*l**3 = 0. Calculate l.
0, 2/5, 2/3
Let m(p) = 6*p**2 - 101*p + 389. Let s(c) be the third derivative of -3*c**5/20 + 19*c**4/3 - 292*c**3/3 - 8*c**2. Let r(d) = 8*m(d) + 5*s(d). Factor r(b).
3*(b - 8)**2
Let c = -22 - -24. Let 17 + 0 - 9 + 4*d**3 - 4*d - d**c + 4*d**4 - 11*d**2 = 0. What is d?
-2, -1, 1
Let h = -2343 - -1546381/660. Let u(s) be the third derivative of 0 + h*s**6 + 0*s**3 - 5*s**2 + 0*s - 1/330*s**5 - 1/66*s**4. Factor u(f).
2*f*(f - 2)*(f + 1)/11
Let w(c) be the first derivative of -5*c**4/4 - 25*c**3/3 + 15*c**2 + 120. Let w(o) = 0. What is o?
-6, 0, 1
Let l be 3/30 + 52/130. Let b(u) be the first derivative of l*u**6 - 3/2*u**4 - 3*u + 2*u**3 + 3/2*u**2 - 3/5*u**5 - 8. Factor b(w).
3*(w - 1)**3*(w + 1)**2
Let o(d) be the third derivative of -9*d**5/20 + 33*d**4/2 - 242*d**3 + 33*d**2. Factor o(u).
-3*(3*u - 22)**2
Let n(r) = -r**4 - r**3 + r**2 - 2*r + 2. Let g(d) = 7*d**4 - 160*d**3 + 6715*d**2 + 13956*d + 7044. Let c(i) = -g(i) - 6*n(i). Factor c(t).
-(t - 84)**2*(t + 1)**2
Let j = 191 + -179. Let c be -6*(j - 10 - 18/8). Find v, given that 3/4 + c*v + 3/4*v**2 = 0.
-1
Let g(s) be the third derivative of s**8/112 - 6*s**7/35 - s**6/40 + 3*s**5/5 + 431*s**2. Solve g(t) = 0.
-1, 0, 1, 12
Let j(k) = 9 - 3 + 12*k - 3*k**2 + 9*k**2 - 3*k**4. Let n(v) = 3*v**4 + v**3 - 7*v**2 - 13*v - 6. Let w(i) = 2*j(i) + 3*n(i). Let w(z) = 0. Calculate z.
-1, 2
Let p(r) = r**3 - 17*r**2 - 17*r - 16. Let w be p(18). Factor 17 - 24*z - 7*z - w - 4*z + 25*z**2 - 5*z**3.
-5*(z - 3)*(z - 1)**2
Let l be (-23)/(-4) + (-1)/(-4). Suppose 3*y - 2*y + 3*c = -9, -2*y + 4*c + 22 = 0. Factor -l*a - 6 + 6 - y*a**2.
-3*a*(a + 2)
Let p be (15/42)/(-4 - -1 - 438/(-126)). Factor 0*n + 1/2*n**3 + 1 - 9/4*n**2 + p*n**4.
(n - 1)**2*(n + 2)*(3*n + 2)/4
Let z(k) be the first derivative of k**8/420 - k**7/210 - 5*k**3/3 + 18. Let h(n) be the third derivative of z(n). Factor h(u).
4*u**3*(u - 1)
Let t(y) be the second derivative of -y**4/6 - 14*y**3 + 88*y**2 + 422*y. Factor t(r).
-2*(r - 2)*(r + 44)
Let m(t) be the second derivative of 7*t**5/110 + 2*t**4/3 + 68*t**3/33 + 16*t**2/11 + 3*t - 75. Factor m(r).
2*(r + 2)*(r + 4)*(7*r + 2)/11
Let k be 2 - (1 + 0) - (-192)/64. Let j(x) be the third derivative of 4*x**2 + 0*x**3 + 0*x + 0*x**k - 1/210*x**7 + 0 + 1/120*x**6 + 1/30*x**5. Factor j(q).
-q**2*(q - 2)*(q + 1)
Let s(f) be the third derivative of 1/280*f**6 - 3/56*f**4 + 1/70*f**5 + 0*f**3 + 0*f - 15*f**2 + 0. Factor s(m).
3*m*(m - 1)*(m + 3)/7
Suppose -11*k + 18 = -5*k. Suppose a - 4*a = -3*i + 3, 4*a + k*i = 3. Let a*q - 1/8*q**2 + 0 = 0. What is q?
0
Suppose -130*u - 129*u = -250*u. Let x(w) be the second derivative of 1/30*w**6 + 0*w**3 + 0*w**2 + 1/20*w**5 + u*w**4 + 0 + w. Factor x(o).
o**3*(o + 1)
Suppose 0 = -3*y + y - 2*g, 0 = y - 2*g. Let f(b) be the third derivative of -1/540*b**6 + 0*b + 0 + y*b**5 + 1/108*b**4 - 6*b**2 + 0*b**3. Factor f(d).
-2*d*(d - 1)*(