z*b. Determine y so that -4*y**b + 15*y**5 + 4*y**4 + 6*y**4 - 9*y**5 = 0.
-2, 0, 1/3
Let g(x) be the third derivative of x**5/120 + 5*x**4/16 - 9*x**3/2 + 737*x**2. Let g(z) = 0. What is z?
-18, 3
Let w(i) be the first derivative of 8 + 1/42*i**4 + 0*i**2 + 0*i**3 - 7*i. Let h(v) be the first derivative of w(v). Determine b, given that h(b) = 0.
0
Factor 0 + 61250/9*d + 700/9*d**2 + 2/9*d**3.
2*d*(d + 175)**2/9
Let m(h) be the second derivative of -h**5/180 + 2*h**4/27 - 17*h**3/54 + 5*h**2/9 + h + 13. Solve m(b) = 0.
1, 2, 5
Let o(j) be the second derivative of -j**5/270 + j**4/108 - 7*j**2 + 17*j. Let k(u) be the first derivative of o(u). What is y in k(y) = 0?
0, 1
Let t(b) be the first derivative of 0*b**3 + 0*b - 3 - 5/2*b**4 + 0*b**5 + 5/6*b**6 + 5/2*b**2. Factor t(q).
5*q*(q - 1)**2*(q + 1)**2
Suppose 52913*n**2 - 10*n**4 + 7*n**3 - 52881*n**2 + 32 + 2*n**5 + n**3 - 64*n = 0. What is n?
-2, 1, 2
Let d(c) = -c**3 + 4. Let n be d(0). Let o = 57124/45 - 11423/9. Factor 0 + 1/5*x**n + o*x**3 - 1/5*x**2 - 1/5*x.
x*(x - 1)*(x + 1)**2/5
Let r(f) be the first derivative of -7*f**3/9 - 2*f**2 + 4*f/3 - 33. Determine x, given that r(x) = 0.
-2, 2/7
Let u = -122 + 126. Let n(m) be the first derivative of -3/8*m**u + 0*m + 0*m**2 - 1/12*m**3 - 9/20*m**5 - 1/6*m**6 - 5. Find v such that n(v) = 0.
-1, -1/4, 0
Let t = 612 + -1820/3. Let j = -31/6 + t. Solve 0*u + 0 + j*u**2 = 0.
0
Suppose 68*w**3 - 12*w**5 - 452*w + 56*w**3 + 148*w - 44*w**4 + 156*w**2 + 80 = 0. What is w?
-5, -2, 1/3, 1, 2
Let n(q) be the first derivative of -q**7/105 - q**6/20 - q**5/10 - q**4/12 + 3*q**2/2 - 10. Let r(h) be the second derivative of n(h). Factor r(k).
-2*k*(k + 1)**3
Let k(t) be the third derivative of -t**7/105 - t**6/12 - t**5/15 + 2*t**4/3 + 195*t**2. Factor k(q).
-2*q*(q - 1)*(q + 2)*(q + 4)
Factor 4/3*p**2 + 0*p - 4/3.
4*(p - 1)*(p + 1)/3
Solve -85/3*p + 100/3 - 7*p**2 + 1/3*p**4 + 5/3*p**3 = 0 for p.
-5, 1, 4
Factor 0*m**4 + 11*m**2 + 0*m**4 - 39*m**2 + 10*m**3 + 2*m**4.
2*m**2*(m - 2)*(m + 7)
Let t(f) be the third derivative of f**6/180 - 187*f**5/90 + 2945*f**4/12 - 961*f**3 + 51*f**2. Factor t(j).
2*(j - 93)**2*(j - 1)/3
Suppose 0 - 12/11*t**2 - 2/11*t**3 + 0*t = 0. Calculate t.
-6, 0
Let s = 343/982 - -74/491. Let -s - 5/4*w - 1/2*w**2 = 0. What is w?
-2, -1/2
Let t(k) = -41*k**2 - 40*k - 59. Let f(r) = 11*r**2 + 10*r + 15. Let p(h) = 22*f(h) + 6*t(h). Factor p(y).
-4*(y + 2)*(y + 3)
Let q(w) = 20*w**3 + 40*w**2 - 65*w + 50. Let m(b) = -b**3 - b**2 - 1. Let u(z) = -15*m(z) - q(z). Factor u(n).
-5*(n - 1)**2*(n + 7)
Let l(g) be the second derivative of -3*g**5/40 - g**4/2 - g**3 - 4*g - 5. Find u such that l(u) = 0.
-2, 0
Suppose 107 + 168 + 35 = 62*k. Suppose 2/7*a**3 + 2/7*a**4 + 0*a + 0 - 2/7*a**k - 2/7*a**2 = 0. What is a?
-1, 0, 1
Let x be (-412)/(-1200) - (-1 + 4/3). Let m(s) be the second derivative of 0 - 5*s - x*s**5 + 1/60*s**4 + 0*s**3 + 0*s**2. Factor m(y).
-y**2*(y - 1)/5
Suppose 8*t - 15*t = 42. Let x(j) = j**2 + 7*j + 6. Let r be x(t). Let 0 + 14/11*n**3 + r*n + 4/11*n**2 = 0. Calculate n.
-2/7, 0
Suppose -5*g = 4*l - 198 + 35, -g + 41 = -2*l. Let i be -1 + 4/(100/g). Factor -i + 2/5*v**2 - 2/5*v**3 + 2/5*v.
-2*(v - 1)**2*(v + 1)/5
Suppose -14*c + 10 = -15*c. Let v be ((-30)/(-25))/((-6)/c). Let 4/3 - 8/3*h + 4/3*h**v = 0. Calculate h.
1
Let h = 109674/11 + -9970. Factor -16/11*n - 8/11*n**2 + h*n**3 + 2/11*n**4 + 0.
2*n*(n - 2)*(n + 2)**2/11
Let t(y) = 28*y**5 + 78*y**4 - 70*y**3 - 20*y**2 + 10. Let q(r) = -9*r**5 - 26*r**4 + 23*r**3 + 6*r**2 - 3. Let l(x) = 10*q(x) + 3*t(x). Factor l(w).
-2*w**3*(w + 5)*(3*w - 2)
Let z(s) be the second derivative of -11*s**5/70 + s**4/12 + s**3/21 + s. Suppose z(r) = 0. What is r?
-2/11, 0, 1/2
Suppose r - 3 + 0 = 0, 0 = 3*d - r - 6. Factor 11/3*s**3 - d*s**5 - 4/3*s**2 + 0 + 2*s**4 - 4/3*s.
-s*(s - 1)**2*(3*s + 2)**2/3
Let x = -36 - -40. Determine w, given that -1 - 8*w**3 + 4*w**2 - 159*w**4 + 1 + 163*w**x = 0.
0, 1
Factor -3*l**4 - 7*l + 5*l + 3*l**2 + l**3 - l + 2*l**3.
-3*l*(l - 1)**2*(l + 1)
Let q be -3 + -3*8/(-6). Suppose 5 - q = x. Factor 0*t - t**x + 0 + 1/4*t**2 - 3/4*t**3.
-t**2*(t + 1)*(4*t - 1)/4
Let o be (-17)/(-340)*(51/9 - 3). What is i in 2/5*i**4 - 4/15*i**3 - 4/15*i**2 + 2/5*i - 2/15*i**5 - o = 0?
-1, 1
Let a(m) = m**2. Let x(z) = 3*z**2 + z. Let b(f) = -f**2 + 6*f + 8. Let u be b(6). Suppose 0*w - u = -2*w. Let g(i) = w*a(i) - x(i). Factor g(s).
s*(s - 1)
Find j such that -3872/13 - 2/13*j**2 - 176/13*j = 0.
-44
Suppose 4*a + 0*a - g - 105 = 0, -5*g = 25. Suppose -2*o - 6 = -3*t, 4*t + 2*o = -o + a. Solve -5 + 32*s**t + 7*s**3 + 14*s**5 + 5 + s**3 = 0 for s.
-2, -2/7, 0
Let y be 5 + (-3 - (1 - 3)). Let a = y + -1. Factor -n**3 - 2*n**2 + 0*n**3 - 3*n**a - n**4 + n**3.
-n**2*(n + 1)*(n + 2)
Let p(n) = 278*n - 1390. Let z be p(5). Let 1/7*w**3 + z*w + 0 - 1/7*w**2 = 0. Calculate w.
0, 1
Let y = 401322/44143 + -2/4013. Let j = -189/22 + y. Factor 1/2 - j*w**2 + 0*w.
-(w - 1)*(w + 1)/2
Let l(t) be the second derivative of -t**5/4 + 5*t**4 + 65*t**3/6 + t - 261. Factor l(p).
-5*p*(p - 13)*(p + 1)
Let a = -3223 - -3226. Let -9/4*o**a + 3/2 - 3/4*o**4 - 3/4*o**2 + 9/4*o = 0. What is o?
-2, -1, 1
Let k(c) = -4*c**2 - c + 1. Let d(h) = -25*h**2 + 94*h + 107. Let i(p) = d(p) - 6*k(p). Factor i(n).
-(n - 101)*(n + 1)
Let z(y) = 4*y - 44. Suppose 3*m - 2*p - 33 = 6, 27 = 3*m + 2*p. Let u be z(m). Determine k, given that u*k + 0*k**2 + 0 - 1/2*k**5 + 1/2*k**3 + 0*k**4 = 0.
-1, 0, 1
Factor 9*f + 33/7 - 3/7*f**3 + 27/7*f**2.
-3*(f - 11)*(f + 1)**2/7
Let h = -7 - -24. Suppose 4*z - 22 = -5*s + 3*s, 0 = 5*z - s - h. Factor 36*m**3 + 8*m**5 + 13*m**z + 3*m + 17*m**4 + m**5 + 18*m**2.
3*m*(m + 1)**3*(3*m + 1)
Let z(c) be the third derivative of -c**7/1890 - c**6/270 + c**5/108 + 563*c**2. Find l, given that z(l) = 0.
-5, 0, 1
Suppose 0 = u - 5*w - 15, 28*u = 32*u - w - 3. Factor 0 - 8/7*g**2 + 2/7*g**3 + u*g.
2*g**2*(g - 4)/7
Let u(w) be the second derivative of -12*w - 1/2*w**5 + 0*w**3 + 5/4*w**4 + 0*w**2 - 1/6*w**6 + 0. Determine l, given that u(l) = 0.
-3, 0, 1
Let g(t) = t**2 + 23*t + 44. Let k be g(-21). Let s be 1/(-2)*k/(-4). Factor 1/8*o - 1/8*o**3 + 1/4*o**2 - s.
-(o - 2)*(o - 1)*(o + 1)/8
Let t = 28 - 22. Let t*u + 8*u**2 + 22 + 2*u**3 - 5 - 17 = 0. Calculate u.
-3, -1, 0
Suppose 122*b = 121*b + 3. Let u(j) be the first derivative of -1/20*j**4 + 4/15*j**3 - 2/5*j**2 + b + 0*j. Determine o, given that u(o) = 0.
0, 2
Suppose -4*z + 18 = -0*z + 2*a, a = 5. Solve 9*c - 2 + 3 + 0 + 5 + 3*c**z = 0 for c.
-2, -1
Let f = -185 + 189. Let c(v) be the second derivative of 2*v**2 - 6*v + 0 - 10/3*v**3 + 19/12*v**f + 3/4*v**5. Let c(y) = 0. Calculate y.
-2, 1/3, 2/5
Let a(t) be the third derivative of 0 + 17/240*t**5 + 0*t - 1/24*t**3 - 2/105*t**7 + 0*t**4 + 0*t**6 - 3*t**2. Let a(v) = 0. What is v?
-1, -1/4, 1/4, 1
Suppose -2*n = n. Let u be -10 - (-17)/((-85)/(-60)). Solve -3/5*j + n - 3/5*j**3 + 6/5*j**u = 0 for j.
0, 1
Let q(u) = -u**2 + 9*u. Let t(m) = 12*m - 6*m**2 + 24*m + 3*m**2. Let b(l) = 15*q(l) - 4*t(l). Factor b(w).
-3*w*(w + 3)
Let v(b) be the third derivative of -b**7/70 + b**6/8 - 3*b**5/20 - 9*b**4/8 + 20*b**2. Factor v(m).
-3*m*(m - 3)**2*(m + 1)
Let p(o) be the first derivative of o**4/3 - 8*o**3/3 + 22*o**2/3 - 8*o - 278. Factor p(h).
4*(h - 3)*(h - 2)*(h - 1)/3
Determine c, given that -704/5*c**2 - 492/5*c + 484/5*c**3 - 72/5 = 0.
-3/11, 2
Let l(i) be the second derivative of -i**4/36 + i**3/2 + 11*i**2/3 - 58*i + 1. Find p, given that l(p) = 0.
-2, 11
Factor 2/3*i**2 - 2*i + 0 + 1/6*i**3.
i*(i - 2)*(i + 6)/6
Let o(w) = w**2 + 8*w - 3. Let p(z) = z**2 + 7*z - 2. Let m(v) = 2*o(v) - 3*p(v). Find c such that m(c) = 0.
-5, 0
Suppose -5*j + 4 = -56. Let g = 15 - j. Factor 0*t**5 + 8*t**4 + 4*t**g + 4*t**5 + t - t.
4*t**3*(t + 1)**2
Let g(w) = w**3 - w**2 + w + 1. Let c = -32 + 33. Let i(f) = -f**3 + 17*f**2 + 7*f - 1. Let u(m) = c*i(m) + 5*g(m). Let u(z) = 0. What is z?
-1
Let n(w) be the first derivative of w**4/22 - 4*w**3/33 - 5*w**2/11 + 12*w/11 - 192. Factor n(p).
2*(p - 3)*(p - 1)*(p + 2)/11
Let c(q) = -2*q**2 + 6*q + 36. Let b(h) = 2*h**2 - 5*h - 37. Let a(k) = 4*b(k) + 3*c(k). Factor a(s).
2*(s - 5)*(s + 4)
Let b(c) be the first derivative of 4*c + 1/8*c**5 - 2/3*c**4 + 7/60*