.
-4, -2/3
Suppose 5*s - 33 - 22 = 0. Suppose 5*y - s = 4. Factor 6*k**5 - 2 + 2*k - 4*k - 10*k**4 + 3*k**3 + y*k**2 - 7*k**3 + 9*k**2.
2*(k - 1)**3*(k + 1)*(3*k + 1)
Let y be (-2)/(3*(-2)/30). What is t in -10*t + 81 + 4*t**4 + y*t**3 + t**4 - 86 = 0?
-1, 1
Let r(c) be the third derivative of -5/84*c**8 + 1/42*c**7 + 0*c**4 + 11*c**2 + 0*c**3 + 0*c + 0 - 1/12*c**5 + 1/6*c**6. Suppose r(l) = 0. Calculate l.
-1, 0, 1/4, 1
Suppose 0 = -j + 5*j - 24. Factor -j*a + 2*a**2 - a**3 + 3*a + 3*a.
-a**2*(a - 2)
Let b be (-12)/(-78) - ((-1815)/(-390) - 5). Factor -b*z**3 + 0 - 7/2*z**2 - 3*z.
-z*(z + 1)*(z + 6)/2
Let c(r) = r**2 + 40*r + 2. Let k = -107 + 67. Let y be c(k). Determine p, given that 0 + 1/7*p**4 - 1/7*p**y + 1/7*p**3 - 1/7*p = 0.
-1, 0, 1
Let n**2 - 60*n**3 + 23*n**3 + 36*n**3 = 0. What is n?
0, 1
Suppose 0 = -4*s - 4*c + 76, 6 = -4*s + c + 57. Determine j so that -1 - 7 - 19*j - 1 + 12*j**2 - s*j = 0.
-1/4, 3
Let 11/2*h**4 - 21/2*h**3 + 7/2*h + 0 + h**5 + 1/2*h**2 = 0. What is h?
-7, -1/2, 0, 1
Let s be ((-38)/(-10))/(-1) + (-8)/(-2). Let y(c) be the first derivative of s*c**2 + 7 + 2/15*c**3 - 4/5*c. Factor y(u).
2*(u - 1)*(u + 2)/5
Solve 49/4*r - 1/8*r**2 - 2401/8 = 0.
49
Let w(m) = 0*m + 5*m**2 + m + 1 + 2*m - m**2. Let g be w(-1). Determine r, given that -21 + 18 - 24*r - 21 - 12 - 4*r**g = 0.
-3
Let m(z) be the second derivative of 1/3*z**3 + 0*z**2 - 1/42*z**4 + 2*z + 0. What is b in m(b) = 0?
0, 7
Let n be ((-4)/7)/((-570)/2660) - 1/(-3). What is r in 6/7*r**5 - 72/7*r + 54/7*r**n - 36/7*r**4 + 24/7*r**2 + 0 = 0?
-1, 0, 2, 3
Let x = 149/791 - -11/113. Factor -x*j**4 + 2/7*j - 4/7*j**3 + 2/7*j**5 + 4/7*j**2 - 2/7.
2*(j - 1)**3*(j + 1)**2/7
Let o(w) be the first derivative of w**3/8 - 111*w**2/8 - 225*w/8 - 221. Factor o(r).
3*(r - 75)*(r + 1)/8
Let t(a) = -a**3 + 2*a**2 + a. Let p(c) = -c**4 + 10*c**3 - 17*c**2 - 4*c. Let w(r) = p(r) + 6*t(r). Suppose w(m) = 0. Calculate m.
0, 1, 2
Let g(u) = 2*u**2 + u + 1. Let m(o) = -8*o**2 - 2*o - 30. Let i(r) = -6*g(r) - m(r). Determine d, given that i(d) = 0.
-3, 2
Suppose 0 = -30*j - 34*j + 63*j. Let g(l) be the first derivative of 4/15*l**6 + 1 + 0*l**3 - 1/10*l**4 - 6/25*l**5 + 0*l + j*l**2. Factor g(t).
2*t**3*(t - 1)*(4*t + 1)/5
Suppose -116*k + 113*k + 33 = 5*q, -3*q = -4*k + 15. Solve -k*c + 4*c**2 + 0 - 2/3*c**3 = 0.
0, 3
Let z = 2/201749 - 150504772/1815741. Let l = z + 83. Factor l - 2/9*a + 1/9*a**2.
(a - 1)**2/9
Let r(z) = 3*z**2 - 5*z - 7. Let l be r(-3). Let q = -139/4 + l. Factor 0 - 1/8*d - 1/8*d**3 - q*d**2.
-d*(d + 1)**2/8
Let q = 4339/13 + -334. Let p = -2/65 - q. Suppose 0 - p*k - 1/5*k**2 + 1/5*k**3 + 1/5*k**4 = 0. Calculate k.
-1, 0, 1
Let o = -125 + 134. Solve -o*f**2 + 24*f**3 - 36*f**5 - 3*f**2 - 9*f**5 + 33*f**4 = 0 for f.
-2/3, 0, 2/5, 1
Let l(t) be the second derivative of 0*t**2 + 25/18*t**3 + 1/180*t**6 - 1/15*t**5 + 0 + 4*t + 5/72*t**4. Determine n so that l(n) = 0.
-2, 0, 5
Let q(x) be the second derivative of x**5/50 - 3*x**4/10 - 2*x**3/3 - 183*x. Factor q(z).
2*z*(z - 10)*(z + 1)/5
Let s(d) be the second derivative of -13*d**4/16 - 27*d**3/8 - 3*d**2/4 + 67*d + 2. Factor s(u).
-3*(u + 2)*(13*u + 1)/4
Suppose 0 = 2*v - 2*a + 68 - 64, 31 = 2*v + 5*a. Solve 0 - 1/2*x**2 - v*x = 0 for x.
-6, 0
Let n(k) = -7*k**2 + 25*k - 57. Let v(t) = -22*t**2 + 74*t - 172. Let j(x) = 16*n(x) - 5*v(x). Find b, given that j(b) = 0.
2, 13
Let f be (-5)/10 + -4*155/(-1200). Let n(b) be the third derivative of 2*b**2 + 0 + 1/6*b**3 + 0*b + f*b**5 - 1/12*b**4. Factor n(d).
(d - 1)**2
Let k(c) be the third derivative of c**5/270 - 2*c**4/9 - 25*c**3/27 - 32*c**2. Factor k(o).
2*(o - 25)*(o + 1)/9
Factor 6*u**2 - 2*u + 0 + 7/2*u**3.
u*(u + 2)*(7*u - 2)/2
Factor 0 + 4/3*x + 3*x**2 + 2/3*x**3.
x*(x + 4)*(2*x + 1)/3
Let o(x) be the third derivative of x**8/1344 - x**7/504 - x**6/72 + 43*x**4/24 + x**2. Let z(l) be the second derivative of o(l). Factor z(f).
5*f*(f - 2)*(f + 1)
Suppose -3/2*r + 0 - 3/4*r**2 = 0. What is r?
-2, 0
Let r(t) = 4*t - 28. Let a be r(11). Suppose 2*b = 4*g - a, 3*g - 12 = -0. Factor 0*p + 0*p**2 - 2/9*p**4 + b - 4/9*p**3.
-2*p**3*(p + 2)/9
Let u = 32 - 46. Let s = 18 + u. Factor -g**4 - 5*g + 4*g - g**s + 2*g**2 + g**5.
g*(g - 1)**3*(g + 1)
Let -21/5*b**4 - 1/5*b**5 + 0 - 324/5*b - 351/5*b**2 - 27*b**3 = 0. Calculate b.
-12, -3, 0
Let r be 4/80*(-308)/(-21)*15/9. Find p, given that -1/9*p**3 - 35/9*p + r*p**2 + 25/9 = 0.
1, 5
Let y(n) be the first derivative of -n**8/560 + n**7/280 + n**6/120 - n**5/40 + 5*n**3 - 10. Let l(h) be the third derivative of y(h). Factor l(t).
-3*t*(t - 1)**2*(t + 1)
Let m(d) = -17*d**3 - 58*d**2 + 15*d - 3. Let k(f) = -47*f + 405*f**2 - 58*f + 3*f**3 - 22*f**3 + 139*f**3 + 20. Let j(r) = -3*k(r) - 20*m(r). Factor j(l).
-5*l*(l + 3)*(4*l - 1)
Let d be ((-5)/(-3))/((-1)/(-3)). Suppose 3*t - 16 = -t, -3*b + 26 = d*t. Factor -12*f**3 + f**4 + 3*f**4 + 39*f**2 - 31*f**b.
4*f**2*(f - 2)*(f - 1)
Let k = 200 + -195. Suppose -4*f + 0*a = a - k, f + 4*a = 20. Find w, given that -w**4 + 5/4*w**3 + 0*w + 1/4*w**5 + f - 1/2*w**2 = 0.
0, 1, 2
Suppose -2*k + 4*u + 164 = 0, 3*u + 16 - 1 = 0. Let l = 74 - k. Determine r so that 1/6 + 1/6*r**l + 1/3*r = 0.
-1
Let c(b) be the first derivative of -2*b**3 - 7*b**2 + 12*b + 156. Factor c(l).
-2*(l + 3)*(3*l - 2)
Let f be (-1 - -5) + (1/5)/((-16)/280). What is m in 10/3*m**2 + 2/3*m - 35/3*m**4 + 0 - f*m**3 + 49/6*m**5 = 0?
-2/7, 0, 1
Let r(x) be the third derivative of 47*x**2 + x**5 + 0*x + 5/336*x**8 + 13/24*x**6 + 0*x**3 + 1/7*x**7 + 0 + 5/6*x**4. Factor r(p).
5*p*(p + 1)**2*(p + 2)**2
Let u(x) = -5*x**2 + 61*x + 213. Let g(i) = 5*i**2 - 59*i - 212. Let p(a) = 3*g(a) + 2*u(a). Let p(h) = 0. What is h?
-3, 14
Let h(z) be the first derivative of -z**6/21 + 8*z**5/35 + z**4/14 - 8*z**3/21 - 173. Find o, given that h(o) = 0.
-1, 0, 1, 4
Let p = 149/21 + -31/7. Let u(n) be the second derivative of -4*n - 1/2*n**4 + 0 - 4*n**2 + 1/15*n**6 - 1/5*n**5 + p*n**3. Factor u(m).
2*(m - 2)*(m - 1)**2*(m + 2)
Find a such that -1/4*a**3 + 9/4*a**2 + 0 + 9/4*a - 1/4*a**4 = 0.
-3, -1, 0, 3
Let w = -133 - 184. Let j = w + 1591/5. Solve 0*n**2 - 4/5 - j*n + 2/5*n**3 = 0 for n.
-1, 2
Let 6 + 24*g - 9/8*g**5 - 39/8*g**4 + 18*g**2 - 3/2*g**3 = 0. What is g?
-2, -1/3, 2
Let a be (-7)/35*-3*5. Let m be (a/(-6))/((-20)/192). Solve -2/5*d**3 + 12/5*d**2 + 16/5 - m*d = 0 for d.
2
Let y be 7/(-28) + (-36)/(-16). Suppose 16 = 9*k - y. Find n, given that 4/11*n - 2/11*n**k - 2/11 = 0.
1
Suppose -45*h - 175 = -80*h. Suppose -4*d = 4 - 16. Let 1/4*y - 1/4*y**4 - 1/2*y**d - 1/4 + 1/2*y**2 + 1/4*y**h = 0. Calculate y.
-1, 1
Let x(t) = -2*t**4 + t**3 + 2*t - 1. Let a(m) = -3*m**5 - 75*m**4 - 264*m**3 - 543*m**2 - 462*m - 165. Let k(r) = a(r) - 9*x(r). Suppose k(y) = 0. Calculate y.
-13, -2, -1
Let f be (-4 + 3)*-5 + -1. Suppose -m = f, 21 = 3*l - 2*l - 4*m. Determine v so that -6*v - 27*v**2 - 4*v**3 + 27*v**4 + 24*v**5 - 3*v**l - 11*v**3 = 0.
-1, -2/7, 0, 1
Let i(f) be the second derivative of -f**5/10 + 13*f**4/6 + 144*f. Let i(x) = 0. What is x?
0, 13
Let s(p) be the second derivative of -5*p**7/42 + 5*p**6/6 - 7*p**5/4 + 5*p**4/4 + 2*p + 37. Let s(u) = 0. What is u?
0, 1, 3
Let x = 42400 + -42397. Determine b, given that -7/8*b**2 + 1/8*b**4 + 9/4 - 15/8*b + 3/8*b**x = 0.
-3, 1, 2
Let i(m) be the second derivative of m**8/3360 - m**6/90 - m**4/3 + 22*m. Let k(r) be the third derivative of i(r). Factor k(l).
2*l*(l - 2)*(l + 2)
Let g(k) = -k**2 - 14*k + 9. Let p be g(-14). Suppose p*y - 6 - 12 = 0. Solve -1/2*q**y + 0 - q = 0.
-2, 0
Let x(h) be the first derivative of -3*h**4/4 - 41*h**3 - 237*h**2/2 - 117*h + 233. Find i, given that x(i) = 0.
-39, -1
Let q be 4/(-6)*-5 + (-6)/(-9). Suppose b**2 - b**2 + 25*b**5 + 11*b**q + 24*b**4 + 10*b**3 = 0. What is b?
-1, -2/5, 0
Let l(t) be the second derivative of 1/24*t**4 + 2*t - 3/4*t**3 - 5/2*t**2 + 3. Factor l(j).
(j - 10)*(j + 1)/2
Factor 47/2*v - 1/6*v**3 + 23/2*v**2 + 71/6.
-(v - 71)*(v + 1)**2/6
Let k(x) be the first derivative of -2*x**3/3 + 48*x**2 + 98*x - 65. Let k(p) = 0. What is p?
-1, 49
Let n(b) be the second derivative of -b**5/20 - 3*b**4/4 - 7*b**3/6 + 5*b**2 - 31*b. Let t be n(-8). Let -2/5*v**t + 2/5*v + 0 = 0. What is v?
0, 1
Factor 63*f + 1285 - 4*f**2 + 1485 - 2470