q - 1/3*l**2 - 1/3*l**4 + 0*l.
-l**2*(l + 1)**2/3
Suppose 51*u - 317 - 193 = 0. Let d(w) be the first derivative of -u*w**2 + 12*w**3 + 4*w - 7*w**4 + 8/5*w**5 + 6. Factor d(t).
4*(t - 1)**3*(2*t - 1)
Let c(p) = -p**2 - p - 2. Let v(j) = -2*j**2 - 110*j - 320. Let t(w) = -10*c(w) + v(w). Let t(x) = 0. What is x?
-5/2, 15
Let q(a) be the second derivative of 0*a**2 + 0 - 1/3*a**3 - 1/120*a**6 + 4*a + 1/4*a**4 - 1/40*a**5. Let m(v) be the second derivative of q(v). Factor m(y).
-3*(y - 1)*(y + 2)
Let d(f) = 37*f + 4181. Let a be d(-113). Suppose a + 1/8*k**2 + 0*k - 1/8*k**3 = 0. Calculate k.
0, 1
Let c(m) be the second derivative of 1/21*m**4 + 0*m**3 + 0 + 0*m**2 - 10*m. Solve c(w) = 0.
0
What is k in 6/17*k**5 - 2/17*k**3 + 0 + 8/17*k**4 + 0*k - 4/17*k**2 = 0?
-1, 0, 2/3
Let k(i) be the third derivative of 0*i - 4/105*i**7 + 7/120*i**6 - 1/6*i**3 + 16*i**2 - 7/24*i**4 + 0 + 3/20*i**5. Solve k(f) = 0 for f.
-1, -1/8, 1
Let b(g) be the first derivative of -g**5/45 + 5*g**4/27 - 8*g**3/27 - 17*g + 13. Let w(s) be the first derivative of b(s). Factor w(f).
-4*f*(f - 4)*(f - 1)/9
Let -w**3 - 3*w**3 + 88 + 39*w**2 + 0*w**3 - 128*w - w**2 + 6*w**3 = 0. Calculate w.
-22, 1, 2
Let u(s) = -2*s**2 + 2*s - 2. Let m(d) = d**3 - d + 3. Let r(p) = -2*m(p) - 3*u(p). Factor r(o).
-2*o*(o - 2)*(o - 1)
Factor 5*n**2 - 12*n - 12*n**3 + 19*n**2 + 0*n + 14*n**2 + n**2 - 36.
-3*(n - 2)**2*(4*n + 3)
Let h(s) be the first derivative of -s**7/280 + s**6/160 + s**5/80 - s**4/32 + 9*s**2/2 + 7. Let t(p) be the second derivative of h(p). Factor t(j).
-3*j*(j - 1)**2*(j + 1)/4
Let -17/6*g + 1/6*g**2 + 0 = 0. What is g?
0, 17
Determine a, given that 148/7*a - 10/7*a**4 - 148/7*a**3 + 40/7*a**2 - 30/7 = 0.
-15, -1, 1/5, 1
Let u(f) be the third derivative of 5*f**2 + 0 + 4/21*f**3 + 0*f - 1/21*f**4 + 1/210*f**5. Suppose u(q) = 0. Calculate q.
2
Let f(u) be the third derivative of 0*u - 1/450*u**5 + 11*u**2 - 1/90*u**4 - 1/45*u**3 + 0. Factor f(d).
-2*(d + 1)**2/15
Let l(m) be the first derivative of m**8/112 - 3*m**7/70 + 3*m**6/40 - m**5/20 + m**2 + 2. Let q(z) be the second derivative of l(z). Solve q(d) = 0 for d.
0, 1
Let i be 21 + (-3 - (-4)/(-4)). Let q = 18 - i. Determine a, given that -9*a - 3*a**3 + 4 - q - 6 - 9*a**2 = 0.
-1
Let w = 4213675/78 - 54020. Let n = w - -1/39. Factor n*t + 0 - 12*t**2 + 24*t**3.
3*t*(4*t - 1)**2/2
Let s(i) be the second derivative of -i**7/315 + i**5/15 + 2*i**4/9 + i**3/3 - 7*i**2/2 + 8*i. Let x(m) be the first derivative of s(m). Factor x(b).
-2*(b - 3)*(b + 1)**3/3
Let d be ((-9)/(-6))/((-11)/(-7) + -2). Let g = 9 + d. Factor -1 - 7/2*a**3 - g*a - 8*a**2.
-(a + 1)**2*(7*a + 2)/2
Factor -1/3*b**4 + 0 + 0*b - 5/3*b**2 + 2*b**3.
-b**2*(b - 5)*(b - 1)/3
Let f(j) = -3*j**3 - 69*j**2 - 3*j + 78. Let l(p) = -6*p**3 - 140*p**2 - 4*p + 155. Let k(q) = -5*f(q) + 3*l(q). Factor k(m).
-3*(m - 1)*(m + 1)*(m + 25)
Let c(j) be the second derivative of -j**9/60480 - j**8/8960 - j**7/5040 - 13*j**4/12 - 9*j. Let u(t) be the third derivative of c(t). Factor u(b).
-b**2*(b + 1)*(b + 2)/4
Let a be (-1 - 2)*(-23)/2484. Let o(y) be the second derivative of 0*y**5 + 0 - 2*y + 0*y**3 - a*y**4 + 0*y**2 + 1/90*y**6. Solve o(m) = 0.
-1, 0, 1
Let -5919*p**3 - 5445*p**2 + 1593*p**3 - 2329*p**3 - 135 - 262*p - 1223*p = 0. What is p?
-3/11
Let u(h) be the first derivative of 3*h**5/20 - 3*h**4/8 - 3*h**3/4 + 3*h**2 - 3*h + 88. Determine d so that u(d) = 0.
-2, 1, 2
Suppose 2/9*u**3 - 130/9*u - 50/3 + 22/9*u**2 = 0. What is u?
-15, -1, 5
Suppose -f = 5*i - 8, 0 = 2*f - 7*f - 10. Find j, given that 0*j**i + 18*j**3 - 17*j**3 + 3*j**2 = 0.
-3, 0
Let t = -41201/42 + 981. Let s(y) be the third derivative of 8*y**2 + 0 + 0*y - t*y**4 - 1/7*y**3 + 1/210*y**5. Factor s(m).
2*(m - 3)*(m + 1)/7
Let p(z) = z**2 - 12*z - 6. Let r be p(12). Let x(y) = 77*y**2 + 213*y + 27. Let v(o) = -39*o**2 - 106*o - 14. Let a(m) = r*x(m) - 13*v(m). Factor a(l).
5*(l + 2)*(9*l + 2)
Let m(v) = -4 + 2*v + v - v**2 + 16 - 6*v. Let q be m(-5). Factor q*w + w**2 - 2 + 0*w + 4 + w.
(w + 1)*(w + 2)
Let a(d) be the third derivative of 7*d**8/48 + 59*d**7/30 + 377*d**6/40 + 261*d**5/20 - 45*d**4 - 216*d**3 - 86*d**2. What is x in a(x) = 0?
-3, -12/7, 1
Let k = 772/5715 + -2/1143. Let a(n) = -n**3 + 5*n**2 - 6*n + 2. Let v be a(2). Factor 0*z - k + 2/15*z**v.
2*(z - 1)*(z + 1)/15
Let i be 59/(-5) - -8 - -5. Suppose 4*c**2 - i*c**3 - 18/5*c + 4/5 = 0. What is c?
1/3, 1, 2
Let f(o) be the first derivative of -o**7/560 + o**6/120 - 7*o**3/3 - 12. Let n(i) be the third derivative of f(i). Solve n(q) = 0.
0, 2
Let g(d) be the second derivative of 2/15*d**4 - 4/5*d**2 + 35*d + 1/50*d**5 + 0 - 1/15*d**3. Find b such that g(b) = 0.
-4, -1, 1
Let k = -35/134 - -2297/4690. Let g = 10/7 - k. Solve 2/5*v**2 + 4/5 + g*v = 0 for v.
-2, -1
Let l(z) = -z - 1. Let f be l(-6). Suppose -f - 1 = -3*h. Factor 3*x**2 + x**2 - x**h - 1 + 9*x + 7.
3*(x + 1)*(x + 2)
Let u be (1204/(-630) + 2/18)/((-3)/5). Solve -1/3*o + 1/3*o**u - o**2 + 1 = 0 for o.
-1, 1, 3
Let m be 4 - (-3 - -5)*-32. Suppose 0 = -t - 66 + m. Factor -4/15*l + 2/15*l**t + 0.
2*l*(l - 2)/15
Let n = 1/418 - -1249/2090. Factor 0*v + 0*v**3 - 6/5*v**2 + 3/5 + n*v**4.
3*(v - 1)**2*(v + 1)**2/5
Suppose 0 = -s - u - 5 + 7, 0 = 3*s + 2*u - 8. Let -25*i**2 - 5*i**4 + i**4 + 20 + 5*i**4 + s*i**4 = 0. What is i?
-2, -1, 1, 2
Let x(g) be the first derivative of -7 + 0*g**2 - 4*g + 1/3*g**3. Factor x(m).
(m - 2)*(m + 2)
Let z(p) be the second derivative of p**5/90 - p**4/6 + 5*p**3/9 + 25*p**2/9 + 69*p. Suppose z(h) = 0. What is h?
-1, 5
Let f(b) = 29*b**2 - 19*b - 5. Let p be f(1). Determine w, given that 5*w**2 + p*w**3 + 0 + 5/3*w + 5/3*w**4 = 0.
-1, 0
Let r(l) be the first derivative of -5*l**4/4 - 55*l**3/3 + 477. Factor r(m).
-5*m**2*(m + 11)
Let i(y) be the second derivative of -1/48*y**4 - 1/120*y**6 + 1/40*y**5 + 0*y**3 + 0 + 0*y**2 - 9*y. Factor i(p).
-p**2*(p - 1)**2/4
Factor 27/4 - 3/4*w**2 + 6*w.
-3*(w - 9)*(w + 1)/4
Suppose 7*g - u - 24 + 11 = 0, -g + 4 = 2*u. Let -2/7*q**g + 0 + 4/7*q = 0. Calculate q.
0, 2
Let v(g) be the second derivative of g**8/26880 - g**6/2880 + 7*g**4/12 - 9*g. Let b(t) be the third derivative of v(t). Suppose b(p) = 0. What is p?
-1, 0, 1
Let i = -306 - -161. Let s = 1019/7 + i. Solve -s*x**5 + 2/7*x**3 + 2/7*x - 6/7*x**2 + 6/7*x**4 + 0 = 0 for x.
-1, 0, 1/2, 1
Let r(d) = -d**2 - 3*d - 2. Let z(k) = -5*k**2 + 420*k - 15127. Let q(a) = -2*r(a) + z(a). Determine t so that q(t) = 0.
71
Let q(s) be the first derivative of -s**7/126 - s**6/45 - s**5/180 + s**4/36 - 7*s**2 - 20. Let h(n) be the second derivative of q(n). Factor h(f).
-f*(f + 1)**2*(5*f - 2)/3
Let a(h) be the third derivative of -h**6/60 + h**5/6 - h**4/2 + h**2 + 53. Let a(y) = 0. Calculate y.
0, 2, 3
Let o(u) be the first derivative of u**6/660 - u**5/330 - u**4/132 + u**3/33 + 3*u**2 - 13. Let j(q) be the second derivative of o(q). Factor j(n).
2*(n - 1)**2*(n + 1)/11
Solve -4332 - 76*r - 1/3*r**2 = 0.
-114
Suppose 3*z + 3 = -0*z. Let p = 2 - z. Factor -5*l + 2*l**p - 3*l + 2 - 2*l**2 + 2*l + 4*l.
2*(l - 1)**2*(l + 1)
Let o(z) be the third derivative of z**7/70 - z**6/10 + z**5/5 + 11*z**2. Find j such that o(j) = 0.
0, 2
Let y be 13*(-108)/(-342) - 4. Determine j so that 128/19 - 32/19*j + y*j**2 = 0.
8
Let x(o) = -5*o**3 + 2*o**2 + 7*o + 6. Let c(t) = 9*t**3 - 4*t**2 - 15*t - 12. Let m(i) = 3*c(i) + 5*x(i). Let m(r) = 0. Calculate r.
-1, 3
Let h be -4 - (2/(-2) - 31). Factor l**3 - 2*l**3 - 6*l**2 + 20 - h - 12*l.
-(l + 2)**3
Let c = -24 - -6. Let u = c - -20. Factor 16 + 36*r**5 - 60*r**u - 159*r + 60*r**4 - 20*r**3 + 159*r.
4*(r + 1)**3*(3*r - 2)**2
Suppose -v + 25 = 4*i - 22, 4*v - 112 = 3*i. Find a such that -4 - v*a + 15*a + 7*a**2 - 3*a**4 + a**3 + 16*a - a**5 = 0.
-2, -1, 1
Let h = -42 + 44. Factor -10*o**h - 69*o**3 + 5*o - 65*o**3 + 139*o**3.
5*o*(o - 1)**2
Suppose 0 - 1/4*h**2 - 5/4*h = 0. What is h?
-5, 0
Let o(q) be the third derivative of -q**8/84 - 2*q**7/35 + q**6/5 + 2*q**5/3 - 7*q**4/2 + 6*q**3 - 108*q**2. Factor o(i).
-4*(i - 1)**3*(i + 3)**2
Let x be (8/10)/(-7 + 108/15). Solve -71*f**4 - 108*f**2 + 45*f**3 + 81*f + 138*f**4 - 73*f**x = 0 for f.
0, 3/2, 3
Let k(a) be the third derivative of -a**5/180 + 25*a**4/72 - 4*a**3/3 - 3*a**2 - a. Factor