.
-1, 6/7
Suppose 5*h + 115*t = 117*t + 22, -2*h + 46 = -7*t. Factor 2/9*s**h - 10/9*s + 8/9.
2*(s - 4)*(s - 1)/9
Let y(v) be the first derivative of 0*v**2 + 2/27*v**3 + 10 - 2/9*v. Suppose y(d) = 0. What is d?
-1, 1
Suppose 0 = 5*f - 8 - 7. Suppose 3*n + 3*j + 6 = 0, 5*n - 3*n - 4 = 2*j. Factor 2/9*d**f - 4/9*d**2 + n + 2/9*d.
2*d*(d - 1)**2/9
Suppose -47*f + 6 = -45*f. Solve -7*y**2 - 12*y**f + 5*y**2 + 5*y**3 = 0.
-2/7, 0
Let j(n) be the first derivative of -n**3 - 63*n**2/2 - 114*n + 595. Factor j(i).
-3*(i + 2)*(i + 19)
Let a(u) be the first derivative of u**6/540 - u**5/90 - 11*u**3/3 - 14. Let n(b) be the third derivative of a(b). Factor n(r).
2*r*(r - 2)/3
Let s(z) be the first derivative of -z**7/84 - z**6/60 - 44*z + 37. Let x(q) be the first derivative of s(q). Let x(a) = 0. What is a?
-1, 0
Suppose 12*f + 120 = 4*f. Let w be -1 + 1 - (f - 1). Let -7*y - 3*y + 4*y**2 - w + 0*y - 2*y = 0. What is y?
-1, 4
Factor 3/2*a**2 + 33/2*a + 27.
3*(a + 2)*(a + 9)/2
Let v(t) = 2*t**2 - 60*t - 180. Suppose -i + 4 = 0, i = -4*j + 2*i - 28. Let l(q) = q**2 - 60*q - 180. Let s(r) = j*v(r) + 7*l(r). Factor s(x).
-5*(x + 6)**2
Suppose -2*j - 196 = 4*x - 4*j, 239 = -5*x + j. Let m = x + 47. Solve 0*i**3 - 4/9*i**2 + 2/9 + m*i + 2/9*i**4 = 0 for i.
-1, 1
Let y = 14008 - 154070/11. Let -56/11*g - 24/11 + y*g**4 + 60/11*g**3 + 2/11*g**2 = 0. What is g?
-3, -2/3, 1
Let k(t) be the second derivative of t**6/135 + 17*t**5/90 + 5*t**4/6 + 43*t**3/27 + 14*t**2/9 + 334*t. What is s in k(s) = 0?
-14, -1
Let z(i) be the second derivative of -i**6/315 - i**5/35 - i**4/42 + 10*i**3/63 - 608*i - 2. Solve z(a) = 0 for a.
-5, -2, 0, 1
Let k be 21/28 + (-9)/12. Suppose k*f + f - 2 = 0. Solve -3/4 + 1/2*w + 1/4*w**f = 0 for w.
-3, 1
Factor 9007*b**4 - 8995*b**4 + 3*b - 3*b + 4*b**5 + 8*b**3.
4*b**3*(b + 1)*(b + 2)
Suppose 2*j = -2*k + 2, -3*k - 6*j + 3 = -4*j. Let z = 0 + k. Factor -6*m**2 - 2*m - 13*m + 7 - 3*m**2 - z.
-3*(m + 2)*(3*m - 1)
Suppose -6*m = -2*y - 3*m - 12, -2*m = -3*y - 13. Let c be (-2 - -3)/((-1)/y). Factor -6*x**4 - c*x + x**3 + 5*x**4 + 3*x.
-x**3*(x - 1)
Let r(k) be the first derivative of -1/2*k**4 + 9 + 0*k**3 + 0*k + 1/5*k**5 + 1/6*k**6 + 0*k**2. Factor r(p).
p**3*(p - 1)*(p + 2)
Determine n so that -1/2*n**3 - 2*n**2 - 1 - 5/2*n = 0.
-2, -1
Suppose 18*z - 25*z = 7. Let v be (4/6 + z)*172/(-602). Factor -2/7*j - 8/21 + v*j**2.
2*(j - 4)*(j + 1)/21
Let v(t) be the second derivative of 2*t**7/189 + 8*t**6/135 - 8*t**5/45 - 10*t**4/27 + 46*t**3/27 - 20*t**2/9 - 233*t. Factor v(b).
4*(b - 1)**3*(b + 2)*(b + 5)/9
Let v(r) be the third derivative of -361*r**5/12 + 95*r**4/6 - 10*r**3/3 - 127*r**2. Factor v(x).
-5*(19*x - 2)**2
Suppose w + 14 - 34 = 3*g, -5*w + 3*g + 64 = 0. Suppose 4*y - 13 = w. Determine l, given that -5*l**4 + y*l**3 - 6*l + 0*l**4 - 3 + 8*l**4 = 0.
-1, 1
Let x(a) be the third derivative of -8*a**6/15 + 1544*a**5/15 + 775*a**4/6 + 194*a**3/3 - 350*a**2. Factor x(w).
-4*(w - 97)*(4*w + 1)**2
Suppose -3*n + k = -18, -3*n = 3*k - 8*k - 30. Factor 4*l**2 + 3*l + 0*l**2 - 2*l**2 - n*l**2.
-3*l*(l - 1)
Let k(i) be the second derivative of i**7/4200 - i**6/900 - i**5/200 - 17*i**3/6 + 16*i. Let g(f) be the second derivative of k(f). Factor g(j).
j*(j - 3)*(j + 1)/5
Suppose 5*r + 4*j = 32, -3*j + j = -5*r + 14. Let h(t) be the second derivative of 1/20*t**5 + 2/15*t**6 + 0 + 2*t + 0*t**3 + 0*t**2 - 1/24*t**r. Factor h(q).
q**2*(2*q + 1)*(4*q - 1)/2
Let u(v) be the first derivative of -v**7/105 - v**6/25 - 3*v**5/50 - v**4/30 - v + 29. Let s(f) be the first derivative of u(f). Solve s(m) = 0.
-1, 0
Let b = 720 - 713. Let d(c) be the third derivative of -2/105*c**b + 2*c**2 + 0*c - 1/5*c**5 + 0 + 1/10*c**6 + 0*c**3 + 1/6*c**4. Factor d(g).
-4*g*(g - 1)**3
Let w(k) be the second derivative of 4/3*k**4 - 1/5*k**5 + 12*k**2 + 22/3*k**3 + 24*k + 0. Solve w(x) = 0 for x.
-1, 6
Find p such that -64/3*p**2 - 32/3 + 26/3*p**3 + 6*p**4 - 104/3*p = 0.
-2, -1, -4/9, 2
Let z(j) be the third derivative of j**8/50400 - j**7/2700 + j**6/675 + j**5/60 + 2*j**2. Let g(x) be the third derivative of z(x). Solve g(w) = 0 for w.
2/3, 4
Let y = -12/175 + 62/175. Factor -6/7*q + y + 6/7*q**2 - 2/7*q**3.
-2*(q - 1)**3/7
Factor -9 - 3/4*m**2 + 39/4*m.
-3*(m - 12)*(m - 1)/4
Let r(f) be the second derivative of 5*f**4/12 - 110*f**3/3 + 1210*f**2 - f - 6. Let r(s) = 0. Calculate s.
22
Let k(b) be the third derivative of -b**5/120 - b**4/12 + b**3 - 146*b**2. Determine c, given that k(c) = 0.
-6, 2
Suppose 3*g - 1 = -x, -2*g - 4*x + 1 = -3. Let j be g*(1/4 - (-6)/24). What is w in -2/3*w**2 + 0 - 2/3*w**4 - 4/3*w**3 + j*w = 0?
-1, 0
Let d(f) be the second derivative of -f**4/8 - 13*f**3/2 - 507*f**2/4 + 44*f. Factor d(n).
-3*(n + 13)**2/2
Let r(k) = -k**2 + 2*k + 5. Let o(l) = -l**3 + 3*l**2 + 6*l - 5. Let n be o(4). Let f be r(n). Solve -2 + z**f - 2*z**3 + 2 - 3*z**2 = 0.
-1, 0
Factor -5 + 4*f**4 + 3 - 10 - 16*f + 3*f**2 + 16*f**3 + 5*f**2.
4*(f - 1)*(f + 1)**2*(f + 3)
Suppose 0 = 17*t - 7*t - 30. Let j = 13 + -8. Factor -2*w**4 + w**t - w**3 - 2*w**j + 4*w**5.
2*w**4*(w - 1)
Let u(h) be the second derivative of h**6/2 - 201*h**5/20 + 59*h**4 - 42*h**3 - 2*h + 29. Factor u(g).
3*g*(g - 7)*(g - 6)*(5*g - 2)
Let i = -5241 - -5246. Factor -4/5*u**i + 0 + 0*u**2 + 0*u + 16/5*u**4 - 16/5*u**3.
-4*u**3*(u - 2)**2/5
Let x(h) be the first derivative of h**3/6 + 4*h**2 - 18*h - 99. Determine g, given that x(g) = 0.
-18, 2
Let n = -1/62638 + 510061249/939570. Let c = 1667/3 - n. Solve -c*d**2 - 4*d**3 - 16/5*d + 0 + 28/5*d**4 = 0 for d.
-1, -2/7, 0, 2
Find d, given that -11/3 - 1/6*d**2 + 23/6*d = 0.
1, 22
Let b(g) = 2*g**3 - 13*g**2 + 19*g - 5. Let n(u) = -u**2 + u + 1. Suppose q - 5 = 2*q, -4*q - 35 = -5*s. Let j(k) = s*n(k) - b(k). Factor j(i).
-2*(i - 2)**2*(i - 1)
Let q(u) be the first derivative of u**3/12 + 5*u**2/2 - 21*u/4 - 167. Factor q(i).
(i - 1)*(i + 21)/4
Factor -27/8*n**2 + 3/4*n + 21/8*n**3 + 0.
3*n*(n - 1)*(7*n - 2)/8
Suppose 4*d - 232 = 2*d. Let o = d - 810/7. Find l such that -3/7*l**3 - o*l + 0 - 8/7*l**4 + l**2 + 4/7*l**5 = 0.
-1, 0, 1/2, 2
Let b(r) = -45*r**2 + 186*r - 52. Let v(m) = -90*m**2 + 372*m - 105. Let o(a) = -9*b(a) + 5*v(a). Factor o(n).
-3*(3*n - 1)*(5*n - 19)
Suppose -2*x - w - 30 = 0, 0 = -x - 3*x - 4*w - 64. Let b(d) = -d**2 - 12*d + 28. Let a be b(x). Solve 1/4*y**2 + a + 0*y = 0.
0
Let n be ((-42)/(-112))/((-2)/(-112)*7). Factor -1 + 7/4*i**n + 19/4*i**2 + 2*i.
(i + 1)*(i + 2)*(7*i - 2)/4
Let a(i) = 4*i**4 - 3*i**3 + 16*i**2 + 3*i - 13. Let k(y) = -y**4 + y**3 - 5*y**2 - y + 4. Let m(l) = 4*a(l) + 14*k(l). Factor m(q).
2*(q - 1)**2*(q + 1)*(q + 2)
Suppose 10 = 4*j + 2*v, -5 = -3*j - 20*v + 21*v. Suppose 1/5 - 1/5*a**j + 0*a = 0. What is a?
-1, 1
Let l(k) be the third derivative of -19*k**2 + 0*k + 0 - 1/60*k**5 + 0*k**3 + 0*k**4 + 1/120*k**6. Find f, given that l(f) = 0.
0, 1
Suppose v = -4*c + 54, 2*v + v = -5*c + 148. Factor 3 + 1 - 40*x - 14*x**3 + v*x**2 + 0 + 4.
-2*(x - 2)*(x - 1)*(7*x - 2)
Let n = 34 + -19. Suppose 0*r = 3*r - n. Factor -2*j**2 - 2*j**4 + 54*j**3 + 4*j**4 - 56*j**3 + 2*j**r.
2*j**2*(j - 1)*(j + 1)**2
Let a(u) be the second derivative of 3/4*u**4 - 1/20*u**5 + 0 + 0*u**2 + 8*u - 4/3*u**3. Factor a(y).
-y*(y - 8)*(y - 1)
Let c(g) be the second derivative of -3*g + 5/8*g**2 + 13/48*g**3 - 1/32*g**4 + 0. Solve c(a) = 0.
-2/3, 5
Let m(y) be the second derivative of y**7/630 - y**5/60 + y**4/36 - 13*y**2/2 - 17*y. Let j(i) be the first derivative of m(i). Find g, given that j(g) = 0.
-2, 0, 1
Let z be (12/(-5))/((-3)/10). Suppose 0 = 2*p, p = 4*v - 4*p - z. Factor -3*w**3 + 9*w**2 - 3*w**v + 3*w**2.
-3*w**2*(w - 3)
Let t(z) be the third derivative of z**5/20 + 5*z**4/24 - 5*z**3/6 - 19*z**2. Let s(b) = -4*b**2 - 7*b + 7. Let h(o) = 5*s(o) + 7*t(o). Factor h(i).
i**2
Let b = 1510/1287 + -40/99. Factor 2/13*y**5 - 8/13*y**4 + 0*y + 0 + b*y**3 - 4/13*y**2.
2*y**2*(y - 2)*(y - 1)**2/13
Suppose 0 = -23*j + 21*j + s + 6, 4*j = -4*s. Let m(d) be the second derivative of 1/2*d**4 - 2/15*d**6 - 2/3*d**3 + 0 + 8*d + 3/10*d**5 + 0*d**j. Factor m(z).
-2*z*(z - 2)*(z + 1)*(2*z - 1)
Determine o so that 1/6*o**4 + 53/6*o**2 + 0 - 17/3*o - 10/3*o**3 = 0.
0, 1, 2, 17
Let d be (5 - 2 - -3*1)*32/256. Factor d*h**4 + 3/2*h**2 - 9/4*h**3