4 + 5043/4*b**2 - 123/2*b = 0. What is b?
1/41
Let t(m) = 132*m + 4494. Let r be t(-34). What is x in 45/2*x**2 - 21/4*x**3 + 0 - r*x = 0?
0, 2/7, 4
Let c(t) = t**2 + t - 1. Let m(d) = -23*d**2 + 7*d - 29. Let g(o) = 3*c(o) - m(o). Let u(x) = -5*x**2 + x - 5. Let b(q) = -3*g(q) - 16*u(q). Factor b(l).
2*(l - 1)**2
Let o(x) = 9*x**4 + 65*x**3 - 5*x**2 + 5*x. Let z(w) = 4*w**4 + 32*w**3 - 2*w**2 + 2*w. Let t(b) = 2*o(b) - 5*z(b). Determine h, given that t(h) = 0.
-15, 0
Let v(y) be the second derivative of y**6/40 - 9*y**5/80 + y**4/8 + 138*y. Determine c, given that v(c) = 0.
0, 1, 2
Let h(p) be the first derivative of p**6/2880 - p**5/960 - p**4/96 - 11*p**3/3 - 19. Let s(t) be the third derivative of h(t). Factor s(f).
(f - 2)*(f + 1)/8
Let w(v) be the second derivative of 1/10*v**5 + 0*v**4 - v**3 + 0 + 2*v**2 + 18*v. Factor w(x).
2*(x - 1)**2*(x + 2)
Let n(g) be the third derivative of -g**7/135 + 2*g**6/27 - 23*g**5/270 - 47*g**4/54 - 8*g**3/9 + 187*g**2. Find y such that n(y) = 0.
-1, -2/7, 3, 4
Suppose 4*w + l - 5 = -2*l, 0 = 2*w + 3*l - 1. Factor q**4 + 0*q + 0*q + q**4 + w*q**3 - 2*q - 2*q**2.
2*q*(q - 1)*(q + 1)**2
Let -36*a**2 - 31*a + 33*a**2 - a**4 + 31*a + 4*a**3 = 0. What is a?
0, 1, 3
Factor -1/4*j**2 + 5/4*j + 3/2.
-(j - 6)*(j + 1)/4
Suppose 0 = b + 5*b - 402. Let f = b - 65. Let -8/11*x**f - 4/11 + 2/11*x**3 + 10/11*x = 0. What is x?
1, 2
Let m(q) be the second derivative of q**4/4 - 7*q**3 - 45*q**2/2 - 38*q. Factor m(a).
3*(a - 15)*(a + 1)
Let i be (-480)/440 - 128/(-77). Factor 0 + i*g**2 - 2/7*g - 2/7*g**3.
-2*g*(g - 1)**2/7
Let b(w) be the first derivative of -w**5/20 - w**4/12 + w**3/6 + w**2/2 + w - 2. Let o(s) be the first derivative of b(s). Factor o(x).
-(x - 1)*(x + 1)**2
Solve x**2 + 37*x**3 + 37*x**3 + 34*x**3 - 40 + 0*x**2 - 109*x**3 + 22*x = 0.
-5, 2, 4
Let w(u) be the second derivative of u**7/1080 + u**6/2160 - 4*u**4/3 + 33*u. Let x(m) be the third derivative of w(m). Factor x(q).
q*(7*q + 1)/3
Let s(k) be the second derivative of 1/60*k**4 + 0 + 3/10*k**2 + 16*k - 1/6*k**3 + 1/100*k**5. Determine q so that s(q) = 0.
-3, 1
Let o = -29 + 34. Factor -4*n**o + 72*n**2 + 28*n**4 - 83*n**2 - 32*n**3 - 53*n**2.
-4*n**2*(n - 4)**2*(n + 1)
Let t(y) = y**3 - 9*y**2 + 15*y - 4. Let q be t(7). Factor -3*w + 38*w**q - w - 40*w**3 + 6*w**2 - 12*w**2.
-2*w*(w + 1)*(w + 2)
Suppose -26 - 31 = -3*d. Factor 6*i**2 - 40*i**3 + 4*i**2 + 6*i + d*i + 1 + 4.
-5*(i - 1)*(2*i + 1)*(4*i + 1)
Let h(t) be the third derivative of -t**8/20160 - t**7/5040 + t**5/6 + 2*t**2. Let u(m) be the third derivative of h(m). Find p such that u(p) = 0.
-1, 0
Suppose -s - 8 = -3*q - 3*s, -16 = -2*q + 4*s. Let c(i) be the first derivative of q + 3/4*i**4 - 4/5*i**3 + 3/10*i**2 + 0*i - 6/25*i**5. Factor c(p).
-3*p*(p - 1)**2*(2*p - 1)/5
Suppose 2/7*p**4 + 6/7*p**2 + 0 + 2/7*p + 6/7*p**3 = 0. What is p?
-1, 0
Find r, given that -225*r - 246*r - 239*r + 106*r + 79*r + 3*r**2 = 0.
0, 175
Let y be 6/(-4)*(-10 + 8). What is d in -y*d**3 - 1 + d**3 - 14*d + 23*d - 7*d + d**4 = 0?
-1, 1
Solve 2/7*d**2 + 162/7 - 36/7*d = 0 for d.
9
Let p(n) be the third derivative of n**7/420 - n**6/180 - 13*n**3/6 + 29*n**2. Let a(b) be the first derivative of p(b). Factor a(d).
2*d**2*(d - 1)
Let b be ((-18 - -2) + 16)/((2 - 1) + 1). Factor -12/5*w + 4/5*w**3 + b + 8/5*w**2.
4*w*(w - 1)*(w + 3)/5
Let s(d) be the second derivative of -1/10*d**6 + d**4 + 0*d**2 - 3/70*d**5 + 0 + 4/7*d**3 + 34*d. Determine t so that s(t) = 0.
-2, -2/7, 0, 2
Find b such that 10*b**4 - 25*b**2 - 18*b**4 + 6*b**3 + 6*b**4 - 30*b + 4*b**3 + 7*b**4 = 0.
-3, -1, 0, 2
Suppose 415 = -7*d + 163. Let u be d/21*(-336)/180. Factor u - 24/5*t + 12/5*t**2 - 2/5*t**3.
-2*(t - 2)**3/5
Let w = 31 - 27. Suppose -6*g + w*g = 0. Factor g*v + 0*v**2 + v**4 + 2/3*v**3 + 0.
v**3*(3*v + 2)/3
Factor -20*b - 68*b**2 - 349/5*b**3 - 9/5*b**5 - 102/5*b**4 + 0.
-b*(b + 5)**2*(3*b + 2)**2/5
Suppose -15*u - 35271 + 35316 = 0. Find s such that 3/8*s**u + 3/4*s**4 + 0 + 0*s**2 + 3/8*s**5 + 0*s = 0.
-1, 0
Let g(y) = -9*y**3 + 16*y**2 + 9*y - 16. Let i = 64 - 61. Let x(p) = 8*p**3 - 17*p**2 - 8*p + 17. Let j(l) = i*g(l) + 4*x(l). Factor j(a).
5*(a - 4)*(a - 1)*(a + 1)
Let p be (-2)/(((-6)/(-9))/(28/(-42))). Let l(z) be the first derivative of 0*z - 1/2*z**6 - 9/2*z**4 + 12/5*z**5 + 4*z**3 - 3/2*z**p - 5. Factor l(g).
-3*g*(g - 1)**4
Solve -9/4*y**2 - 3/2 + 3/4*y**4 + 3/4*y**3 - 15/4*y = 0.
-1, 2
Let f = 4353/4 - 1087. Let v(p) be the first derivative of f*p**4 - p**3 + 8 - 5/2*p**2 + 4/5*p**5 - p. Determine i so that v(i) = 0.
-1, -1/4, 1
Let z = 25885/23016 - -1/2877. Factor 0 - 3/4*g + z*g**2 - 3/8*g**3.
-3*g*(g - 2)*(g - 1)/8
Let p(m) = -m**3 + 12*m**2 + 13*m. Let n be p(13). Suppose -4*y - 10 = 4*f - 26, 5*y - 2*f + 8 = n. Determine z, given that y*z + 2/7*z**2 + 1/7*z**3 + 0 = 0.
-2, 0
Let x = -4975/21 - -237. Let j(k) be the first derivative of -1 + 2/35*k**5 + 1/7*k**2 + 0*k - 1/14*k**4 - x*k**3. Solve j(o) = 0.
-1, 0, 1
Determine y, given that -1/5*y**2 + 6/5 - y = 0.
-6, 1
Let a = 21 - 21. Let y(b) be the third derivative of 4*b**2 + a + 1/4*b**4 + 1/3*b**3 + 1/10*b**5 + 0*b + 1/60*b**6. Let y(m) = 0. What is m?
-1
Let d(f) = -f**4 - 10*f**3 + f**2 + 37*f - 37. Let g(s) = s**3 + s**2 - s + 1. Let t(k) = 3*d(k) + 15*g(k). Determine l so that t(l) = 0.
-4, 1, 2
Let q(k) = -k**5 - 5*k**4 + 3*k**3 + 3*k**2 - 5*k - 5. Let z(g) = -g**5 - 4*g**4 + 3*g**3 + 2*g**2 - 4*g - 4. Let w(b) = -4*q(b) + 5*z(b). Factor w(m).
-m**2*(m - 1)**2*(m + 2)
Let l(f) be the second derivative of 0 - 3/20*f**5 + 1/14*f**7 + 0*f**2 + 9*f + 0*f**3 - 1/4*f**4 + 1/10*f**6. Suppose l(a) = 0. What is a?
-1, 0, 1
Let m(r) be the first derivative of -1 + 10*r**3 + 25/2*r**4 - 21*r**5 - 15/2*r**2 + 15/2*r**6 - 5*r. Solve m(d) = 0.
-1/3, 1
Let f(g) be the first derivative of g**4/10 + 16*g**3/3 + 357*g**2/5 - 1764*g/5 - 24. Determine d, given that f(d) = 0.
-21, 2
Let h(t) be the second derivative of -t**5/4 - 35*t**4/12 - 20*t**3/3 + 40*t**2 + 49*t. Factor h(n).
-5*(n - 1)*(n + 4)**2
Let z be -3 + 7 - (-1 - -3). Solve -20*n**z + 35*n**2 - 11 - 9 - 5*n**3 = 0 for n.
-1, 2
Let a(y) be the first derivative of -1/3*y**4 + 16/3*y**2 + 16*y - 4/9*y**3 + 36. Factor a(r).
-4*(r - 3)*(r + 2)**2/3
Let n(c) = -c**3 - 13*c**2 + 4*c. Let t(v) = -6*v**2 + 2*v. Let k be ((-4)/(-12) + (-1)/(-6))*-10. Let j(l) = k*t(l) + 2*n(l). Suppose j(y) = 0. What is y?
0, 1
Let q(c) = -5*c - 15. Let p be q(-7). Suppose -p = -f + 5*f, 2*f + 18 = 4*s. Factor -2*g**3 + g**3 + g**2 + 0*g**s.
-g**2*(g - 1)
Let k = 14 + -6. Let c be k/(-12) - (-141)/9. Solve -7*p**4 - 6*p**2 - 2*p**3 + c*p**4 + 4 + 2*p - 6*p**4 = 0 for p.
-1, 1, 2
Determine s, given that 2/7*s**2 + 76050/7 - 780/7*s = 0.
195
Suppose 2*w + j = -2, 3*w - 3*j - 6 = w. Let u(p) be the first derivative of 6 + 1/5*p**5 + 1/12*p**6 + w*p + 0*p**3 + 1/8*p**4 + 0*p**2. Factor u(z).
z**3*(z + 1)**2/2
Let i(l) be the second derivative of l**4/36 + 17*l**3/9 + 11*l**2/2 - 60*l. Find h, given that i(h) = 0.
-33, -1
Suppose 0 = -15*j + 14*j + 2. Factor -10*k**2 + 0 + 4 - 2*k + 9*k**j - k.
-(k - 1)*(k + 4)
Suppose 130022*i**3 - 22*i**2 - 130046*i**3 - 48*i**2 - 2*i**4 = 0. Calculate i.
-7, -5, 0
Let j(s) = -s**2 + s + 33. Let u be j(6). Let w(f) be the first derivative of 1/5*f + 9/25*f**5 - 2/5*f**2 - 2/15*f**u + 1 + 3/5*f**4. Factor w(x).
(x + 1)**2*(3*x - 1)**2/5
Suppose -a + 3*v + 15 = 0, 0 = a - 0*v - v - 5. Let j(y) be the third derivative of 0*y**3 + 1/210*y**5 + a*y + 7*y**2 - 1/84*y**4 + 0. Factor j(m).
2*m*(m - 1)/7
Factor 28*r - 15*r**2 - 63*r**3 - 11*r**2 + 11*r**3 + 8*r**4 + 10*r**2 - 16*r**2.
4*r*(r - 7)*(r + 1)*(2*r - 1)
Let a(j) = -j**3 + 3*j**2 + 3. Let n be a(3). Suppose -13 = -4*d + 5*u + 40, 0 = 5*u + 5. Factor o**4 + d*o**n - 9*o - 3*o**3 - 3*o - 4*o**4.
-3*o*(o - 2)**2*(o + 1)
Let r(v) = 6*v**2 - 56*v - 48. Let s(g) = 5*g**2 - 55*g - 48. Let u(b) = -6*r(b) + 4*s(b). Factor u(d).
-4*(d - 8)*(4*d + 3)
Let f(q) = 11*q**2 - 25*q + 91. Let o(w) = -4*w**2 + 12*w - 46. Let y(z) = 2*f(z) + 5*o(z). Suppose y(r) = 0. What is r?
-8, 3
Suppose 0 = 4*x + 1 - 1. Suppose 3*k - 21 + 15 = x. Factor k*f + 0 - 2/3*f**2.
-2*f*(f - 3)/3
Let y(w) be the second derivative of -1/8*w**4 + 0*w**2 + 1/20*w**6 - 2*w + 0 + 0*w**3 - 9/80*w**5.