 + 2)/2
Determine t, given that 4 - 3*t**4 + 389*t + 3*t**2 - 4 - 18*t**3 - 371*t = 0.
-6, -1, 0, 1
Let f(w) be the third derivative of 2*w**7/105 - 2*w**6 - 62*w**5/5 - 94*w**4/3 - 42*w**3 + 445*w**2. Factor f(z).
4*(z - 63)*(z + 1)**3
Let n(o) be the third derivative of o**7/210 - 7*o**6/120 + o**5/4 - 13*o**4/24 + 2*o**3/3 + 72*o**2. Suppose n(h) = 0. What is h?
1, 4
Let v = 12/167 - -23165/668. Let i = -67/2 + v. Factor w + 0 + 1/4*w**4 + i*w**3 + 2*w**2.
w*(w + 1)*(w + 2)**2/4
Let t(f) be the first derivative of -5*f**6/6 - 3*f**5 + 5*f**4/4 + 35*f**3/3 - 20*f + 105. Let t(h) = 0. What is h?
-2, -1, 1
Let c(o) be the second derivative of -o**4/24 + o**3/2 + 27*o**2/4 - 5*o - 8. Find k such that c(k) = 0.
-3, 9
Let y(o) be the third derivative of -o**5/3 - 3*o**4/2 - 8*o**3/3 + 3*o**2 + 14*o. Suppose y(u) = 0. Calculate u.
-1, -4/5
Factor -462*m + 3*m**3 + 333 + 81*m**2 + 58 + 185 + 0*m**3.
3*(m - 3)*(m - 2)*(m + 32)
Suppose -65*b - 2 = -66*b. Factor 93 + c - c**b - 91 + 0*c.
-(c - 2)*(c + 1)
Let x be 2 - 30/20 - 6/12. Suppose i**2 + 1/2*i**4 - 3/2*i**3 + 0*i + x = 0. Calculate i.
0, 1, 2
Let j(g) be the third derivative of -g**7/945 + g**6/270 + g**5/90 - g**4/27 - 4*g**3/27 - 90*g**2. What is s in j(s) = 0?
-1, 2
Let g be -11 + (-370)/(-40) - (-21)/12. Solve -2/11*r + 24/11*r**3 - 28/11*r**4 + 10/11*r**5 - 4/11*r**2 + g = 0.
-1/5, 0, 1
Factor -44*q**3 + 90*q**3 - 80*q**2 - 44*q**3.
2*q**2*(q - 40)
Factor -3/4*y**3 + 57/4*y**2 + 15*y + 0.
-3*y*(y - 20)*(y + 1)/4
Let c(g) = -13*g**4 + 21*g**3 + 13*g**2 - 16*g - 5. Let h(f) = -6*f**4 + 10*f**3 + 6*f**2 - 8*f - 2. Let t(w) = -2*c(w) + 5*h(w). Factor t(j).
-4*j*(j - 2)*(j - 1)*(j + 1)
Factor 5*u + 83*u - 12*u - 8*u**3 - 8 - 72*u**2 + 2*u - 12.
-2*(u + 10)*(2*u - 1)**2
Let j = 39 - 39. Suppose j = -2*a + 5 - 1. Factor -10*h + 25/3*h**a + 3.
(5*h - 3)**2/3
Let l(u) be the first derivative of 2*u**5/25 + 3*u**4/5 + 2*u**3/3 + 83. Suppose l(x) = 0. Calculate x.
-5, -1, 0
Let o(n) be the second derivative of 0 + 0*n**2 - 7*n - 1/8*n**3 - 1/48*n**4. Factor o(z).
-z*(z + 3)/4
Suppose 4/13 + 8/13*t**2 - 2/13*t**3 - 10/13*t = 0. What is t?
1, 2
Let r(d) be the second derivative of 5/8*d**4 - 5/8*d**3 + 1/8*d**6 - 1/56*d**7 - 3/8*d**5 + 0 - 7*d + 3/8*d**2. Factor r(v).
-3*(v - 1)**5/4
Find f such that -1/2*f**4 - 12*f**2 + 5*f**3 + 0*f + 0 = 0.
0, 4, 6
Let s be (-5)/(-10) - (-7)/2. Let -3 + 0 + 3*v**2 + s*v - v**2 - 3 = 0. Calculate v.
-3, 1
Let c be ((-6)/(-8))/(2/8). Let p(u) = 2*u**2 - 6*u + 2. Let o be p(c). Factor 45*z**3 - z + o*z**4 - 44*z**3 - z**4 + z**2 - 2*z**2.
z*(z - 1)*(z + 1)**2
Let g(h) be the first derivative of 49*h**4/4 + 742*h**3 + 16854*h**2 + 1191016*h/7 - 9. Let g(d) = 0. Calculate d.
-106/7
Suppose 1 = k + 5. Let g = -2 - k. Solve 23*p + 0 - 35*p + 2 + g*p**2 + 16 = 0 for p.
3
Let i(b) be the second derivative of 0 + 7/60*b**4 + 0*b**2 - 7/150*b**6 - 3/100*b**5 - 1/15*b**3 + 1/42*b**7 + 13*b. Find j such that i(j) = 0.
-1, 0, 2/5, 1
Let f(x) be the third derivative of x**8/6720 - x**6/720 + x**4/3 - 3*x**2. Let b(n) be the second derivative of f(n). Factor b(g).
g*(g - 1)*(g + 1)
Let q(t) be the first derivative of 1/70*t**5 - 1/7*t**2 - 3 + 1/42*t**4 - 1/21*t**3 + 7*t. Let k(f) be the first derivative of q(f). Factor k(m).
2*(m - 1)*(m + 1)**2/7
Solve 7/4*p**2 - 3/2 + 1/4*p - 1/4*p**3 - 1/4*p**4 = 0.
-3, -1, 1, 2
Suppose -5*p + 16 = -3*g, -4*p + 5*g + 5 = -0*p. Let b = 0 + p. Let 11 - b*k - 9*k**2 + 3*k**4 - 7*k + 6*k**3 + 1 = 0. Calculate k.
-2, 1
Let h(z) be the second derivative of 1/10*z**5 + 1/2*z**2 - 1/10*z**6 - 1/2*z**3 + 1/6*z**4 + 1/42*z**7 + 14*z + 0. Factor h(o).
(o - 1)**4*(o + 1)
Let x(c) be the first derivative of 55*c**4/12 + 100*c**3/9 + 35*c**2/6 - 10*c/3 - 10. Find q such that x(q) = 0.
-1, 2/11
Let f(m) = -3*m**4 + m**2 + m - 1. Let o(h) = 2*h**4 - 22*h**3 - 122*h**2 - h + 1. Let g(a) = 3*f(a) + 3*o(a). Determine r so that g(r) = 0.
-11, 0
Let w(l) be the first derivative of 1/8*l**2 + 0*l + 1/12*l**3 + 22. Factor w(o).
o*(o + 1)/4
Let g(s) = s**3 - s**2 + 3*s - 3. Let m = -179 + 180. Let z be g(m). Solve -1/2*b**2 - 1/6*b**3 + 0*b + z = 0 for b.
-3, 0
Let p(w) be the third derivative of -1/9*w**3 - 24*w**2 + 0 + 0*w - 1/180*w**5 + 1/24*w**4. Factor p(o).
-(o - 2)*(o - 1)/3
Let g(y) be the third derivative of y**6/600 + y**5/60 + 8*y**2. Factor g(r).
r**2*(r + 5)/5
Let v(i) = i**3 + 6*i**2 + 8*i + 12. Let w be v(-4). Suppose w = -4*b, 2*o - 3*b - b = 12. Factor 0 + 3/7*n**3 + o*n - 3/7*n**2.
3*n**2*(n - 1)/7
Let h(p) = -p**4 + p**3 + p. Suppose y + 0 = -1. Let g(n) = 45*n**5 + 13*n**4 - 38*n**3 - 20*n**2 + 2*n. Let z(x) = y*g(x) + 2*h(x). Let z(u) = 0. What is u?
-2/3, 0, 1
Let j = -1482 + 29649/20. Let x(v) be the third derivative of 0 + 1/2*v**3 + 0*v - 3/4*v**4 - 2*v**2 + j*v**5 - 1/10*v**6. What is n in x(n) = 0?
1/4, 1
Let r(p) be the first derivative of -2*p**5/5 + 2*p**4 - 4*p**3 + 4*p**2 - 2*p - 210. Solve r(u) = 0.
1
Suppose 2/7*y**2 - 32*y - 226/7 = 0. What is y?
-1, 113
Let j(n) be the second derivative of 1/3*n**3 + 0*n**4 + 0 + 0*n**2 + 1/420*n**5 - 1/1260*n**6 - 2*n. Let t(a) be the second derivative of j(a). Factor t(m).
-2*m*(m - 1)/7
Let b = 2 + -5. Let q(h) = 6*h**2 - 21*h - 49. Let v(j) = -j**2 + j. Let o(d) = b*q(d) - 21*v(d). What is m in o(m) = 0?
-7
Let h(w) be the third derivative of w**6/120 - 11*w**5/60 - 69*w**2. Factor h(l).
l**2*(l - 11)
Let t = 24 - 22. Determine p so that 3 + 3*p**t - 16*p**2 + 10*p**2 - 6 + 6*p = 0.
1
Let k(q) be the third derivative of q**5/60 + 37*q**4/24 + 439*q**2. Factor k(i).
i*(i + 37)
Let x(u) be the third derivative of -3*u**6/40 + 4*u**5/5 + 67*u**4/8 - 12*u**3 + 4*u**2 + 47. Find y such that x(y) = 0.
-3, 1/3, 8
Suppose 0 = k - 4*k + 21. Suppose 0 = 12*f - 29 - k. Determine t so that -4*t**f + 8/5 - 36/5*t + 48/5*t**2 = 0.
2/5, 1
Determine i, given that 3/2 - 9/8*i - 3/8*i**2 = 0.
-4, 1
Solve -51/4*f**3 + 45/2 + 51/4*f - 3/4*f**4 - 87/4*f**2 = 0 for f.
-15, -2, -1, 1
Let t = -54 - -63. Let y be (1 + -2)/t - (-5)/15. Factor 2/9*w + 2/9*w**4 - 2/9*w**2 - y*w**3 + 0.
2*w*(w - 1)**2*(w + 1)/9
Let j be (3*3/162)/((-36)/(-270)). Let v(o) be the second derivative of 5/6*o**3 + j*o**4 + 0 - 9*o + 0*o**2. Factor v(r).
5*r*(r + 1)
Let q be ((-1)/1)/(6*9/2970). Let a be 4/q*25/(-10). Determine r so that -2/11*r**5 + 0 + 0*r - 2/11*r**4 + a*r**2 + 2/11*r**3 = 0.
-1, 0, 1
Let g(y) be the second derivative of -y**4/4 - 10*y**3 - 96*y**2 + 91*y - 3. Factor g(b).
-3*(b + 4)*(b + 16)
Let y be (-10)/(-27)*(-324)/(-135). Let t(b) be the first derivative of -2/45*b**5 - 256/9*b**2 - 512/9*b - 64/9*b**3 - 2 - y*b**4. Factor t(z).
-2*(z + 4)**4/9
Let o(q) be the first derivative of -30 - 2/7*q**3 + 1/28*q**4 - 15/14*q**2 - 8/7*q. Solve o(s) = 0 for s.
-1, 8
Let i(l) = -l**2 - l. Suppose -6*j - 5 = -j. Let k(c) = 16*c**2 + 56*c - 32. Let v(a) = j*k(a) - 20*i(a). Let v(f) = 0. What is f?
1, 8
Let v(m) be the third derivative of m**6/480 + 7*m**5/240 + 7*m**4/48 + m**3/3 - 38*m**2. Factor v(x).
(x + 1)*(x + 2)*(x + 4)/4
Factor -39227 + 39227 - 2*p**2 - 2*p**2 - 368*p.
-4*p*(p + 92)
Let z(w) be the third derivative of 0*w**4 + 1/140*w**6 + 0*w**3 + 0 + 0*w - 33*w**2 - 1/105*w**5 - 1/735*w**7. Factor z(l).
-2*l**2*(l - 2)*(l - 1)/7
Let g(d) be the first derivative of 7 + 0*d + 1/16*d**4 + 1/2*d**2 + 1/3*d**3. Let g(w) = 0. Calculate w.
-2, 0
Determine k so that 2*k**2 - 1/5*k**3 + 1/5*k - 2 = 0.
-1, 1, 10
Let x(p) = -p**2 - 9*p - 16. Let w be x(-6). Factor -5*n**2 + w*n**2 - 2*n**3 - 2*n**2 - 3*n**3.
-5*n**2*(n + 1)
Suppose -7*a = -4*a - 15. Let x(i) be the first derivative of 4/9*i - 1/27*i**6 + 16/27*i**3 + 7/9*i**2 - 4/45*i**a + 5 + 1/9*i**4. Factor x(k).
-2*(k - 2)*(k + 1)**4/9
Let h be (-12)/(-22) - (-744)/1056. Suppose -x**2 - 1/2 + 1/4*x**3 + h*x = 0. Calculate x.
1, 2
Factor 23/7*g - 22/7*g**2 + 0 - 1/7*g**3.
-g*(g - 1)*(g + 23)/7
Let y(i) be the second derivative of -i**7/14 - 2*i**6/3 - 27*i**5/20 - 5*i**4/6 + 62*i. Let y(j) = 0. What is j?
-5, -1, -2/3, 0
Let n(c) be the second derivative of c**6/1260 - c**5/210 + c**4/84 - c**3/63 + 2*c**2 - 21*c. Let j(s) be the first derivative of n(s). Factor j(y).
2*(y - 1)**3/21
Factor 71/10*t**3 - 108/5 + 207/5*t**2 + 2/5*t**4 + 378/5*t.
(t + 6)**3*(4*t - 1)/10
Let b(k)