Let d(y) = z*s(y) + 5*g(y). Factor d(x).
5*x**3*(x - 3)
Let d(r) be the second derivative of -180*r**2 + 1 - 139*r - 484*r**3 - 484/25*r**5 - 16/75*r**6 - 14881/30*r**4. Factor d(c).
-2*(c + 30)**2*(4*c + 1)**2/5
Suppose 0 = 2*z - 5*k - 28, -5*z + 24 = -3*z - 4*k. Suppose 3 = v - z. Factor 8 + 11*t - v*t - 2*t**2 - t**2 - t**2.
-4*(t - 2)*(t + 1)
Let b(v) = 6*v**2 - 8*v - 6. Let f be b(-3). Factor -f + 22*h**2 + 3*h + 2*h - 2*h**3 - 53*h.
-2*(h - 6)**2*(h + 1)
Let 1/2*f**2 + 29/2*f + 102 = 0. Calculate f.
-17, -12
Let u(y) = 20*y**2 - 78. Let x be u(-2). Determine q so that 121/3*q**x + 3 + 22*q = 0.
-3/11
Let o = -785 + 809. Suppose o*z - 20*z = 16. Determine l, given that 11/4*l**3 + 0*l + 7/4*l**5 + z*l**4 + 1/2*l**2 + 0 = 0.
-1, -2/7, 0
Let q(b) be the first derivative of -4*b**5 - 74*b**4 + 240*b**3 - 236*b**2 + 68*b - 4124. What is n in q(n) = 0?
-17, 1/5, 1
Let r = -25 + 117. Suppose -5*j + r = -108. What is f in f**3 - 3*f**3 + 10*f**2 + 6*f - j*f**3 - f**2 = 0?
-2/7, 0, 1/2
Solve -2268/5*i**2 + 1714608/5*i + 1/5*i**3 - 432081216/5 = 0 for i.
756
Suppose -5*x - 3*n - 222 = 0, -24*n = -2*x - 20*n - 94. Let u be (-1062)/x - (-1 - -5). Let 2/5*i**2 + u - 28/5*i = 0. What is i?
7
Let t = 2434 - 2425. Let b(y) be the third derivative of -t*y**2 + 0*y + 0*y**3 + 0 + 1/360*y**5 + 1/720*y**6 + 0*y**4. What is p in b(p) = 0?
-1, 0
Let r = 224 - 1116/5. Suppose 10*y = -218 + 238. Let -6/5*l**4 + 4/5*l**3 - 6/5*l + r*l**y + 2/5 + 2/5*l**5 = 0. Calculate l.
-1, 1
Let g(t) be the second derivative of -12/5*t**5 - 2*t + 3/2*t**6 - 31/4*t**4 + 6*t**2 - 37 + 2*t**3. Let g(d) = 0. What is d?
-1, -1/3, 2/5, 2
Let w = 993 - 987. Suppose -4 = 4*x - 4*n, 3*x - w*n = -2*n - 4. Factor 3/8*h**2 - 1/8*h**4 + x*h + 0 - 1/4*h**3.
-h**2*(h - 1)*(h + 3)/8
Let -106*b - 11*b**3 + 1/2*b**4 - 54 - 127/2*b**2 = 0. What is b?
-2, -1, 27
Let s(c) be the second derivative of 4/15*c**3 - 2*c + 15 - 1/15*c**4 + 6*c**2. Factor s(n).
-4*(n - 5)*(n + 3)/5
Solve -590/3*u + 0 - 2/3*u**2 = 0.
-295, 0
Suppose 3*m = -5*g + 11, -3*m = m - g - 7. Suppose 2*a - 6*a + 45 = 5*y, m*a - 25 = -3*y. Factor 3*k**4 + 3*k**4 + 4*k**4 + 5*k**3 - 5*k**4 - a*k**2 - 5*k**5.
-5*k**2*(k - 1)**2*(k + 1)
Let y(c) = -289*c + 1156. Let q be y(4). Let z(r) be the first derivative of q*r + 2*r**3 + 38 - 2*r**2 - 2/5*r**5 + 0*r**4. What is k in z(k) = 0?
-2, 0, 1
Let f(k) be the second derivative of 13/14*k**4 + 1/70*k**6 + 0 + 2/49*k**7 - 9/14*k**2 - 184*k - 2/7*k**3 - 18/35*k**5. Suppose f(w) = 0. Calculate w.
-3, -1/4, 1
Determine r so that -340/3*r**2 - 6468 + 5348/3*r - 4/3*r**3 = 0.
-99, 7
Let z(t) = -t**2 - 11*t + 6. Let f be z(-6). Suppose 4*p + 5*p - f = 0. Factor -5*q**3 + 15*q**3 + 10*q**5 + 23*q**p + 2*q**4.
5*q**3*(q + 2)*(2*q + 1)
Let g be (-10)/27*(-16 + 36 - 29). Solve g - 4*r + 2/3*r**2 = 0 for r.
1, 5
Determine r, given that -5*r**5 - 395*r**4 - 1981*r**4 - 1067220*r**2 + 46*r**4 - 321108*r**3 + 45063*r**3 = 0.
-231, -4, 0
Let t(y) be the second derivative of 1/3*y**2 - y - 5/54*y**3 + 1/108*y**4 + 128. Find n, given that t(n) = 0.
2, 3
Let i = -100 - -102. Factor -6*p**2 - 12*p + 11*p**2 - 34*p - 7*p**i.
-2*p*(p + 23)
Suppose 2*q = -f + 9, 16*f = -5*q + 12*f + 24. Let b(r) be the second derivative of -32/7*r**2 + 0 - 3*r - 1/21*r**q - 16/21*r**3. Factor b(j).
-4*(j + 4)**2/7
Let z = 31656 - 31654. Factor -2/7*h**3 - 6/7*h**z + 0 + 0*h.
-2*h**2*(h + 3)/7
Suppose -60 + 180 = 64*x - 59*x. Let s(q) be the first derivative of -4/5*q**2 - 16/15*q**3 - 1/2*q**4 - 2/25*q**5 + 0*q - x. Solve s(w) = 0.
-2, -1, 0
Let q = -8438 - -8443. Let n(f) be the third derivative of 0*f - q*f**3 + 0 - 2*f**2 + 25/24*f**4 - 1/12*f**5. Factor n(p).
-5*(p - 3)*(p - 2)
Let j(n) be the first derivative of n**6/24 + n**5/4 + 5*n**4/12 + 115*n**2 - 157. Let l(w) be the second derivative of j(w). Factor l(o).
5*o*(o + 1)*(o + 2)
Let n(q) = 10*q**2 - 989*q + 1994. Let a(u) = 3*u**2 - 330*u + 664. Let i(f) = -28*a(f) + 8*n(f). Solve i(l) = 0 for l.
2, 330
Suppose -6*l - 43 = 2*m - 49, -5*l = -2*m - 5. Let p be 8/32 - (-5)/(-36). Determine h, given that -p*h**3 - 1/9*h**2 + 2/3*h + m = 0.
-3, 0, 2
Let r(z) be the second derivative of -z**4/18 - 203*z**3/9 - 202*z**2/3 + 154*z + 5. Suppose r(j) = 0. Calculate j.
-202, -1
Let a(c) be the first derivative of -c**3/18 + 59*c**2/12 - 29*c/3 - 1176. Solve a(k) = 0.
1, 58
Let l = -163 + 165. Suppose -3 = s, 5*b - l*s = -2 + 18. Factor 0 - 3/2*m**b - 9/4*m + 3/4*m**3.
3*m*(m - 3)*(m + 1)/4
Let i = -3332 - -3334. Let q(m) be the first derivative of -26 + 10*m**i + 20/3*m**3 - 65/4*m**4 + 5*m**5 + 0*m. Let q(h) = 0. What is h?
-2/5, 0, 1, 2
Let j be (-77567)/(-34) + (-5 - 12/4)*(-121)/8228. Factor j + 117*t + 3/2*t**2.
3*(t + 39)**2/2
Let r = 33 + -6. Determine g so that 25*g**4 + 22*g**3 - 4*g**2 - 26*g**4 - r*g**3 = 0.
-4, -1, 0
Let z = -905 - -594. Let n = 313 + z. Factor -1/2*l**3 + 0 + 0*l**n + 1/2*l.
-l*(l - 1)*(l + 1)/2
Suppose j - 20 = -4*d, 132 - 104 = 5*j + 2*d. Let z(r) be the first derivative of 3/4*r**j + 0*r**2 + 2/3*r**3 + 0*r + 5. Factor z(l).
l**2*(3*l + 2)
Let a(u) be the third derivative of -7*u**5/120 - 335*u**4/72 + 16*u**3/9 - 8765*u**2. Solve a(j) = 0.
-32, 2/21
Let k = -152 - -763/5. Let q = 74 - 70. Suppose -k*c**q + 3/5*c**2 + 1/5*c**3 - 2/5*c + 0 + 1/5*c**5 = 0. What is c?
-1, 0, 1, 2
Let s(d) = -39*d**2 - 792*d + 150544. Let a(v) = 5*v**2 + 2*v. Let x(w) = -40*a(w) - 5*s(w). Determine g, given that x(g) = 0.
388
Let t(s) = -s**3 - 19*s**2 - 2*s - 34. Suppose -12 = 2*n + 26. Let u be t(n). Let -4*f**3 - u*f**3 + f**3 - 9*f**2 + 4*f**3 + 27*f - 15 = 0. Calculate f.
-5, 1
Let l = 82049 - 164097/2. Let -1/2*s**2 + 0 - l*s = 0. Calculate s.
-1, 0
Suppose 14946/13*c**2 - 1786524/13 - 196630/13*c + 2/13*c**4 - 306/13*c**3 = 0. What is c?
-6, 53
Let n(s) = 283*s**3 + 2230*s**2 + 1989*s + 63. Let m(f) = 141*f**3 + 1114*f**2 + 995*f + 31. Let c(p) = 14*m(p) - 6*n(p). Factor c(k).
4*(k + 1)*(k + 7)*(69*k + 2)
Let c(x) be the third derivative of -x**7/525 + x**6/75 + 7*x**5/150 - 11*x**4/30 - 8*x**3/5 + 19*x**2 + 45*x. Determine r so that c(r) = 0.
-2, -1, 3, 4
Find g, given that 1/3*g**2 - 34/3*g + 289/3 = 0.
17
Let a = -147829/7 + 443501/21. Let 8/3*y**2 + a*y**3 + 28/3 - 38/3*y = 0. Calculate y.
-7, 1, 2
Let o(i) be the third derivative of -i**6/60 - 23*i**5/15 + 8*i**4 - 8589*i**2. Factor o(q).
-2*q*(q - 2)*(q + 48)
Suppose -106*w = -32*w - 81548. Let l = 1104 - w. Factor 0 + 1/4*y**3 + 5/4*y**l + y.
y*(y + 1)*(y + 4)/4
Let f(v) be the first derivative of 0*v + 125 + 7/6*v**3 + 0*v**4 + 3/2*v**2 - 1/10*v**5. What is m in f(m) = 0?
-2, -1, 0, 3
Let o be (-11 - (48/(-20) + -10)) + 2/(-5). Let a(y) be the first derivative of y**2 + 0*y - 1/6*y**3 + o. Determine m, given that a(m) = 0.
0, 4
Let t(o) be the first derivative of o**3/2 + 69*o**2/2 - 141*o/2 + 1814. Factor t(q).
3*(q - 1)*(q + 47)/2
Let x = 68 - 66. What is k in 11*k - 23*k**3 + 54*k**4 - 18*k + 34*k**x - 58*k**4 = 0?
-7, 0, 1/4, 1
Suppose 4*u - 2*k = 0, -26 + 0 = 3*u + 5*k. Let y be (16 - 13)*u - (-25)/4. Let -1/4*z**4 + 1/2*z**3 + 0*z**2 - 1/2*z + y = 0. What is z?
-1, 1
Let y = 1083/14 - 552/7. Let w = y + 5/3. Factor 0 + w*r**2 + 0*r.
r**2/6
Let k = -4221/152 + 530/19. Let j(o) be the first derivative of -1/5*o**5 - k*o**2 + 0*o - 1/2*o**4 + 29 - 5/12*o**3. Determine r, given that j(r) = 0.
-1, -1/2, 0
Let v = -4186 + 4189. Let b(g) be the second derivative of -5/12*g**4 - 90*g**2 + 0 + 18*g - 10*g**v. Let b(t) = 0. Calculate t.
-6
Let n(l) be the third derivative of -l**8/1512 - 2*l**7/945 + l**5/135 + l**4/108 - 1748*l**2 + 2*l - 2. Factor n(o).
-2*o*(o - 1)*(o + 1)**3/9
Let o(m) = -2 + 1 + 3*m**2 + 0*m**2 - 5*m**2. Let y(w) = -13*w**2 + 5*w + 18. Let a(z) = -6*o(z) + y(z). Solve a(v) = 0.
-3, 8
Let d be (2/(-2))/((-4)/52). Suppose -4*i + d + 22 = 3*k, -i - 20 = -5*k. Factor -329 + i*j**2 + 329.
5*j**2
Let b = 81 - 187. Let r = b + 110. Factor 8*h - 340 + 4*h**2 + 340 - 8*h**3 - r*h**4.
-4*h*(h - 1)*(h + 1)*(h + 2)
Let a(i) = -2*i**4 + 322*i**3 - 13124*i**2 - 2. Let f(z) = 2*z**4 - 321*z**3 + 13125*z**2 + 3. Let r(j) = 3*a(j) + 2*f(j). Solve r(x) = 0.
0, 81
Let g be 1 + (-10)/(-5) - 5096/1699. Let y = 6813/28883 - g. Determine k so that 0*k**3 - 2/17*k - y*k**4 + 4/17*k**2 + 0 + 2/17*k**5 = 