 9 = 39. Let v(q) = q**2 + q + 1. Let g(r) = 10*r**2 + 10*r + 9. Let y(j) = l*g(j) - 36*v(j). Determine k, given that y(k) = 0.
-1, 0
Let i(m) be the first derivative of m**6/120 - m**5/60 - m**4/24 + m**3/6 - m**2/2 + 15. Let y(x) be the second derivative of i(x). Solve y(t) = 0 for t.
-1, 1
Let l = 83 + -58. Determine a, given that -14*a - 60*a**4 - 5*a**3 + 60*a**2 - 5*a - a + l*a**5 = 0.
-1, 0, 2/5, 1, 2
Let t be (-388)/(-44) + (-2)/(-11). Factor 42*r**3 + t*r**4 + 0*r**2 + r**4 - 17*r**3 + 5*r + 20*r**2.
5*r*(r + 1)**2*(2*r + 1)
Suppose 0 = -4*w - 10 + 34. Solve i**4 + w*i**3 + 0*i**4 - 3*i**3 - i**3 = 0 for i.
-2, 0
Let 10*o**4 + 6*o**4 + 552*o**2 + 128 - 65*o**3 - 99*o**3 - 616*o - 24*o = 0. Calculate o.
1/4, 2, 4
Let t(q) = -q**3 + q + 1. Let m be t(0). Suppose -3*d - m - 12 = h, -2*h = 5*d + 21. Factor -2*f**2 - 6*f + 4*f**2 + 6*f**3 + h*f**4 - 2*f**2 - 4 + 2*f**2.
2*(f - 1)*(f + 1)**2*(f + 2)
Let i be (-4)/(-6)*(-24)/(-8). Let y be 3 + 13/(-4) + (-25)/(-100). Factor y + 2/9*w**i + 2/9*w.
2*w*(w + 1)/9
Let b(a) be the first derivative of -1/3*a**4 - 9 + 2/15*a**5 + 0*a**3 + 2/3*a**2 - 2/3*a. Factor b(i).
2*(i - 1)**3*(i + 1)/3
Let m(k) be the first derivative of 3*k**5/40 + 9*k**4/4 - 254. Factor m(x).
3*x**3*(x + 24)/8
Let w(l) be the first derivative of 2/3*l**3 - 1/2*l**4 + 4*l**2 - 8*l - 6. Let w(r) = 0. Calculate r.
-2, 1, 2
Let m(o) = -2*o**3 + 12*o**2 + 24*o - 60. Let z(h) = 2*h**3 - 11*h**2 - 23*h + 59. Let x(c) = 5*m(c) + 6*z(c). Suppose x(q) = 0. Calculate q.
-3, 3
Let x = 36 + -34. Let p(d) be the second derivative of 0*d**x - 3/40*d**5 + 0 + 8*d + 0*d**3 + 1/4*d**4. Factor p(w).
-3*w**2*(w - 2)/2
Suppose -82*n + 3 = -79*n + 3*j, 0 = -4*n - j + 10. Factor 6/5*u**4 + 0 - 4/5*u**2 + 0*u + 2*u**n.
2*u**2*(u + 2)*(3*u - 1)/5
Let p = -167/22 - -133/11. Solve 0 + 3/2*g**3 - 3*g + 9/2*g**2 + 3/2*g**5 - p*g**4 = 0.
-1, 0, 1, 2
Let j be 276/528 - ((-90)/33 + 3). Solve -2 - 1/2*q**2 + j*q**4 + 3/4*q**3 - 3*q = 0 for q.
-2, -1, 2
Let z = -7 + 12. Suppose 4*h + 10 = z*h + 4*o, -17 = -h + 3*o. Factor -h*b - 3*b**2 - 2 - 4 + 5*b.
-3*(b + 1)*(b + 2)
Suppose 3*l + 4*b - 5 - 8 = 0, 4*b + 5 = 3*l. Suppose 0*u + u = 0. Factor u*f + 8*f**l + 3*f**2 + 11*f - 23*f**3 - 9 + 6*f**4 + 4*f.
3*(f - 1)**2*(f + 1)*(2*f - 3)
Let y = -1/13012 - -26027/39036. Suppose 0*c**3 + 0 - c**2 - y*c + 1/3*c**4 = 0. What is c?
-1, 0, 2
Let w(y) = -y**3 - 7*y**2 + 7*y + 2. Let u be w(-8). Suppose u = 3*c + 1. Let -c*k**2 + 2*k - 8*k - k**2 + k**2 - 3 = 0. What is k?
-1
Let c(r) be the first derivative of r**4/4 + r**3 - 11*r + 4. Let q(u) be the first derivative of c(u). Find o such that q(o) = 0.
-2, 0
Let a = 11 + 0. Let u = 13 - a. Let 3/5*b**u + 0*b - 1/5*b**3 + 0 = 0. Calculate b.
0, 3
Let a = -8356 - -58493/7. Factor a*d**5 - 5/7*d**3 + 4/7 + 1/7*d**2 + 8/7*d - 1/7*d**4.
(d - 2)**2*(d + 1)**3/7
Let a(m) be the first derivative of m**7/420 + m**6/72 - m**5/40 - 10*m**3/3 - 3. Let n(o) be the third derivative of a(o). Determine u so that n(u) = 0.
-3, 0, 1/2
Let v = 317 - 41843/132. Let x(q) be the third derivative of -v*q**4 + 0 + 5*q**2 + 0*q**3 - 2/165*q**5 - 1/220*q**6 + 0*q. Solve x(b) = 0.
-1, -1/3, 0
Let w(l) be the third derivative of -l**7/105 - l**6/60 + 2*l**5/15 + l**4/3 + 2*l**2 + 13*l. Let w(x) = 0. What is x?
-2, -1, 0, 2
Factor -21*g**4 + 19*g**3 + 3*g**5 + 1944*g**2 + 87*g**4 + 521*g**3 + 2592*g.
3*g*(g + 4)*(g + 6)**3
Let d be -3 - (15/6 + (-30)/4). Let k(s) be the second derivative of -1/12*s**4 + 1/2*s**3 - 6*s - s**d + 0. Find l, given that k(l) = 0.
1, 2
Let p(h) = 15*h**3 - h**2 - 12*h - 7. Let q(v) = 2*v**3 - 1. Let m(g) = 5*p(g) - 35*q(g). What is j in m(j) = 0?
-3, 0, 4
Let m(v) be the second derivative of -5/3*v**3 - 5/12*v**4 - 30*v + 0 + 15/2*v**2. Find x, given that m(x) = 0.
-3, 1
Suppose -3*s - 2*s - 4*c + 3 = 0, -3*c = 9. Suppose -18 + 2 = -4*r. Suppose 8*o**s - r*o**2 - 9*o + 7*o + 2*o - 4*o**4 = 0. What is o?
0, 1
Let t be (-2)/(-2 - (-14 + 13)). Factor 1/2 + o + 1/2*o**t.
(o + 1)**2/2
Factor 1/3*l**2 + 1/12*l**3 - 1/3 - 1/12*l.
(l - 1)*(l + 1)*(l + 4)/12
Let i(f) be the third derivative of f**7/735 + 4*f**6/35 + 311*f**5/105 + 92*f**4/7 + 529*f**3/21 - 24*f**2 - 2. Determine b so that i(b) = 0.
-23, -1
Let z be 170/(0 + -2) - 0/1. Let s = z - -85. Factor 2/5*t**2 + 0*t + s - 3/5*t**3 + 1/5*t**5 + 0*t**4.
t**2*(t - 1)**2*(t + 2)/5
Let w(i) be the first derivative of 3*i**4/4 + 248*i**3/3 + 5207*i**2/2 + 3362*i - 265. Factor w(x).
(x + 41)**2*(3*x + 2)
Let g(a) be the first derivative of -a**5/420 - a**4/168 - 3*a**2 + 24. Let l(j) be the second derivative of g(j). Factor l(m).
-m*(m + 1)/7
Let j(d) = -3*d**2 + d + 10*d**2 - 5*d**2 + 1. Let y be j(-1). Factor -27*a**2 - 20*a**3 + 19*a**4 + 2*a**y + 10*a - a**4 - 3*a**4.
5*a*(a - 2)*(a + 1)*(3*a - 1)
Factor -416/3*d**2 - 6 - 169/3*d**3 - 55*d.
-(d + 2)*(13*d + 3)**2/3
Let a(t) be the first derivative of -20 - t**4 - 4/3*t**3 + 0*t**2 + 0*t. Find x, given that a(x) = 0.
-1, 0
Let p be (-2)/(-4*5/80). Suppose -k - f = -10, 0*f - 15 = -5*k + 2*f. Let -14*c**2 + 1 + p*c**2 - k + 14*c = 0. Calculate c.
1/3, 2
Let w = 18 - 15. Suppose 4/3*p - 2/3*p**2 + 8/3 - 1/3*p**w = 0. Calculate p.
-2, 2
Suppose -3*t - a = -7, t - 4*a = -0*a - 2. Let r = 8 + -4. Determine x, given that -3*x - 14*x**2 - 9*x**r - 3*x + 29*x**t + 12*x**3 = 0.
-1, 0, 1/3, 2
Let l(a) be the first derivative of 34445*a**3/3 + 415*a**2 + 5*a - 371. Find k such that l(k) = 0.
-1/83
Let l = 195 - 193. Suppose -30 = l*j - 36. Solve 0 + 2/7*s**4 + 6/7*s**j + 0*s + 4/7*s**2 = 0 for s.
-2, -1, 0
Let v(o) be the second derivative of -2*o**5/25 + o**4/10 + o**3/15 + 2*o - 15. Factor v(w).
-2*w*(w - 1)*(4*w + 1)/5
Let o be 2080/16*(6/4 - 1). Suppose -2*j + 71 - o = 0. Factor 0 - 3/5*l**2 - 1/5*l**j - 2/5*l.
-l*(l + 1)*(l + 2)/5
Let a be -1*4*(-2)/4. Suppose -5*m + 3*w = -100, -a*w = -5*m - 4*w + 100. Suppose -m*d**4 + 17*d**4 - 4*d**2 - 5*d**2 + 9*d**3 + d + 2*d = 0. What is d?
0, 1
Suppose -36 + 4 = -4*r. Let b = -5 + r. Factor -2*q**3 + 6*q**3 + b*q**2 - 4*q**2 - q**4 - 2*q**3.
-q**2*(q - 1)**2
Let q be 144/(-96) - (-74)/48. Let i(c) be the second derivative of 1/60*c**6 - 1/40*c**5 + 1/12*c**3 + 0 - q*c**4 + 2*c + 0*c**2. Suppose i(b) = 0. What is b?
-1, 0, 1
Let i be ((-4)/(-6))/(7/(-21)). Let k be 0 + (-2)/i + (-5)/7. Factor -k*n**2 + 4/7*n + 6/7.
-2*(n - 3)*(n + 1)/7
Suppose -4 = x, -4*k - 6*x + 2*x - 64 = 0. Let w be (k/(-8))/(9/(-24)*-2). Factor -3/4*r - 1/4*r**w - 1/2.
-(r + 1)*(r + 2)/4
Let z(c) be the first derivative of -10 + c**2 - 4/3*c - 2/9*c**3. Factor z(j).
-2*(j - 2)*(j - 1)/3
Factor 26/5*h + 69/5 + 1/5*h**2.
(h + 3)*(h + 23)/5
Let r(x) = -2*x**2 - 4*x - 1. Let c(b) = -3*b**2 + 15*b - 1. Let f(u) = c(u) - r(u). Let f(v) = 0. Calculate v.
0, 19
Factor 2/3*l**2 + 0 + 2*l.
2*l*(l + 3)/3
Let x(c) be the third derivative of 3*c**7/455 + 107*c**6/390 + 56*c**5/13 + 352*c**4/13 - 1024*c**3/39 + 3*c**2 + 54*c. What is k in x(k) = 0?
-8, 2/9
Let c(o) be the second derivative of o**6/720 + 13*o**5/360 + o**4/3 + o**3 + 31*o**2/2 + 20*o. Let f(r) be the first derivative of c(r). Solve f(k) = 0.
-6, -1
Suppose 7*j = -7*j - 2*j + 80. Factor 0*q**3 + 0 + 3/2*q + 3*q**4 - 3*q**2 - 3/2*q**j.
-3*q*(q - 1)**3*(q + 1)/2
Let j be -3*(4 - (-232)/(-56)). Factor 9/7*f - 5/7*f**3 + 1/7*f**4 + j*f**2 + 0.
f*(f - 3)**2*(f + 1)/7
Suppose 7 = 3*b + 1. Let c(j) = -j**2 - j - 4. Let o(d) = d**2 + d + 1. Suppose -4*m - 10 = -14. Let n(v) = b*o(v) + m*c(v). Determine q, given that n(q) = 0.
-2, 1
Let 411/5*b - 3/5*b**2 + 414/5 = 0. What is b?
-1, 138
Let t(k) = 8*k**4 + 85*k**3 - 189*k**2 + 91*k - 5. Let a(q) = -q**4 + q**3 + q + 1. Let o(f) = -5*a(f) - t(f). Factor o(n).
-3*n*(n - 1)**2*(n + 32)
Let z be 37/(-37) + 41/8. Let a = z + -29/8. Factor -a*c**2 + 0*c**3 + 1/2*c**4 + 0 + 0*c.
c**2*(c - 1)*(c + 1)/2
Factor 360 + 1262 + 136*r - 466 + 4*r**2.
4*(r + 17)**2
Let h(x) be the first derivative of -5*x**6/9 - 44*x**5/15 - 23*x**4/6 - 4*x**3/3 - 323. Find s such that h(s) = 0.
-3, -1, -2/5, 0
Let d be 14/84 + 14/(-84). Let j = 5/24 + -1/24. Factor j*q**2 + 1/3*q + d.
q*(q + 2)/6
Suppose -16*j + 4 = -14*j. Suppose -u + 84 = 3*u. Factor 3*k - 15 + u - 3*k**j - 12 + 6*k**2.
3*(k - 1)*(k + 2)
Let h(s) = s**2 + 8*s + 9. Let d be h(-7). Let p b