+ d**7/12600 - d**4/12 - 2*d. Let n(a) be the third derivative of l(a). Suppose n(x) = 0. Calculate x.
0, 1
Let y be (2/3)/(3/(-9)*-6). Factor -y*v**2 - 1/3*v**5 + 0*v + 1/3*v**4 + 0 + 1/3*v**3.
-v**2*(v - 1)**2*(v + 1)/3
Suppose -2*n**2 + 0*n**2 - 78*n**3 + 76*n**3 = 0. What is n?
-1, 0
Factor 3/2 + 3/2*o - 3/2*o**3 - 3/2*o**2.
-3*(o - 1)*(o + 1)**2/2
Factor 2/3*i**4 - 8/3*i - 10/3*i**3 + 16/3*i**2 + 0.
2*i*(i - 2)**2*(i - 1)/3
Suppose -4 = -0*r - 2*r. Factor -y**2 + 3*y**4 - y**4 - r*y**4 + y**4.
y**2*(y - 1)*(y + 1)
Let g(o) = -o**3 - 8*o**2 - 8*o - 4. Let a be g(-7). Factor -2*f + f + 2*f + f**3 - 5*f**2 + a*f**2.
f*(f - 1)**2
Let a = -6 + 11. Let p(l) be the first derivative of 1/3*l + 2/15*l**a - 1/3*l**3 - 1/12*l**4 + 1 + 1/6*l**2. Factor p(x).
(x - 1)**2*(x + 1)*(2*x + 1)/3
Suppose 0 = -q - 2*q + 3. Let w(j) = 4*j**3 - 2*j**2 + 1. Let v be w(q). Find b such that 2/3*b**2 + 2/3*b - 2/3*b**4 - 2/3*b**v + 0 = 0.
-1, 0, 1
Let t(i) = -i**2 - 18*i - 13. Let p be t(-17). Suppose 131*f**p - 256*f - 8*f**4 - 288*f**2 - 15*f**4 - 64 = 0. Calculate f.
-2/3, 2
Let g = 368 - 363. Factor 0 - 2/5*s**4 + 0*s + 0*s**3 + 2/5*s**g + 0*s**2.
2*s**4*(s - 1)/5
What is r in 3/5*r**3 + 3/5*r - 6/5*r**5 - 6/5 - 3*r**4 + 21/5*r**2 = 0?
-2, -1, 1/2, 1
Let b(y) be the second derivative of 0 + y**4 + y**2 - 1/4*y**5 - 3/2*y**3 + 3*y. Factor b(w).
-(w - 1)**2*(5*w - 2)
Factor z**3 + 4*z - 3*z**2 - 1/8*z**4 - 2.
-(z - 2)**4/8
Let q be (-9 - 1)*2/(-84). Let l(h) be the second derivative of -1/6*h**4 + 2/7*h**2 + h - q*h**3 + 0. Factor l(i).
-2*(i + 1)*(7*i - 2)/7
Let t(r) = -r**2 + 14*r + 35. Let z be t(16). Factor -3/5*b**z + 1/5*b**5 + 0 + 0*b - 2/5*b**2 + 0*b**4.
b**2*(b - 2)*(b + 1)**2/5
Suppose -5*a + 5*n + 13 = 2*n, -2*a = n - 3. Suppose 2*k + k - u = 15, -a*k - 7 = 5*u. Factor x**2 - 3 - 3*x + 1 + k.
(x - 2)*(x - 1)
Let v be 2/4 + (-36)/(-24). Factor -4/3*y - 25/3*y**4 + 0 - 15*y**3 - 8*y**v.
-y*(y + 1)*(5*y + 2)**2/3
Suppose -q - 47 = 2*q - 2*u, 2*q + 5*u + 44 = 0. Let l = 19 + q. Determine b, given that -3/5*b**4 - 1/5*b**5 + 1/5 - 2/5*b**3 + 2/5*b**l + 3/5*b = 0.
-1, 1
Let i(u) be the second derivative of -1/4*u**4 - 1/6*u**3 - 1/30*u**6 + 0 - 3/20*u**5 + 0*u**2 + u. Factor i(k).
-k*(k + 1)**3
Factor c**3 - 2*c**2 + c + 5 - 2*c - 3.
(c - 2)*(c - 1)*(c + 1)
Suppose -4/5*f**2 + 1/5*f + 1/5*f**3 + 6/5 = 0. Calculate f.
-1, 2, 3
Let r(k) be the second derivative of -k**4/16 + k**3/4 + 9*k**2/8 - 16*k. Solve r(p) = 0.
-1, 3
Let v(w) be the third derivative of -w**8/1680 - w**7/1050 + w**6/600 + w**5/300 + 6*w**2. Let v(p) = 0. What is p?
-1, 0, 1
Let d(x) be the first derivative of x**5/15 + x**4/12 - 2*x**3/9 + 10. Determine w so that d(w) = 0.
-2, 0, 1
Let c(n) = n**3 - n**2 - n + 5. Let i be c(0). Determine x so that 6*x**4 - 3*x**5 + 4*x**5 - 6*x**3 - 3*x**i + 2*x**2 = 0.
0, 1
Let c(g) = 15*g**4 - 13*g**3 + 11*g**2 - 13*g + 13. Let w = 15 - 9. Let m(r) = 7*r**4 - 6*r**3 + 5*r**2 - 6*r + 6. Let t(j) = w*c(j) - 13*m(j). Factor t(n).
-n**2*(n - 1)*(n + 1)
Suppose 16 = -t + 21. Let -8*c**3 - 191*c**2 - 36*c**4 - 28*c**t + 191*c**2 = 0. Calculate c.
-1, -2/7, 0
Let g(p) = 8*p**3 - 3*p**2 + p - 1. Let s(k) = k**3 + k**2 - k + 1. Let u(t) = -2*g(t) - 2*s(t). Factor u(b).
-2*b**2*(9*b - 2)
Determine j so that -7*j**2 + 11*j**2 - 3*j - 3*j**2 + 2 = 0.
1, 2
Let j(t) be the second derivative of t**6/30 + t**5/10 - 11*t. What is z in j(z) = 0?
-2, 0
Let z(c) be the first derivative of c**6/240 + c**5/40 + 10*c**3/3 + 9. Let x(d) be the third derivative of z(d). Suppose x(m) = 0. What is m?
-2, 0
Let k(y) be the second derivative of y**6/150 - y**4/12 + 2*y**2/5 + 4*y. Let k(c) = 0. Calculate c.
-2, -1, 1, 2
Let x(b) be the third derivative of 0*b**3 + 0 + 0*b + b**2 + 1/40*b**5 + 0*b**4 + 1/80*b**6. Let x(v) = 0. What is v?
-1, 0
Let t(r) be the third derivative of -r**5/20 + 9*r**4/4 - 81*r**3/2 + 10*r**2. Determine h, given that t(h) = 0.
9
Let t(w) be the third derivative of -w**7/42 - w**6/12 + w**5/12 + 5*w**4/12 - 2*w**2 + 3. Solve t(p) = 0 for p.
-2, -1, 0, 1
Let i = 5 + -1. Let w(h) = h**3 - 4*h**2. Let v be w(i). Factor 3/2*m**4 + 0 + 1/2*m**2 - 2*m**3 + v*m.
m**2*(m - 1)*(3*m - 1)/2
Let m be 5/(-4)*16/(-40). Let y(i) be the third derivative of m*i**4 + 1/20*i**5 + 4*i**2 + 3/2*i**3 + 0*i + 0. Determine n, given that y(n) = 0.
-3, -1
Let k = 43 - 22. Let g = k + -13. Factor g*t + 2*t**2 - 2*t**3 - 8*t.
-2*t**2*(t - 1)
Solve 1/3*v + 0 - 1/3*v**2 = 0 for v.
0, 1
Suppose -3*r - 6 = -3. Let t be 4 + r - (-10)/(-6). Factor -1/3*p**3 - 8/3*p + t + 5/3*p**2.
-(p - 2)**2*(p - 1)/3
Let f = 191/335 + 2/67. Factor 0 + 3/5*y - 6/5*y**2 + f*y**3.
3*y*(y - 1)**2/5
Let i be (9/12)/(2/8). Suppose -s = -3*l + 14, -s + 11 = 5*l + 1. Factor 0 - 1 + t**l + t**i - 2*t + t**2.
(t - 1)*(t + 1)*(2*t + 1)
Let x = 0 - -4. Suppose -x*d = 4*s + 12, 1 = 4*s + 2*d + 3. Find v such that 0*v**2 - v**2 + 3*v**s + 2*v**3 = 0.
-1, 0
Let m = 26 + -51/2. Let k(b) be the first derivative of -m*b**2 - 2/9*b**3 - 1/3*b - 2. Factor k(s).
-(s + 1)*(2*s + 1)/3
Determine j, given that -2/9*j**5 + 0 - 2/9*j**3 + 0*j + 4/9*j**4 + 0*j**2 = 0.
0, 1
Determine j so that -j - 1/10*j**2 - 9/10 = 0.
-9, -1
Let j(x) be the first derivative of 3*x**4/32 + 3*x**3/8 + 3*x**2/8 - 1. Factor j(c).
3*c*(c + 1)*(c + 2)/8
Let u(b) = 4*b**2 - 3*b + 2. Let m(x) = x + 1. Let f(r) = m(r) - u(r). Let f(q) = 0. What is q?
1/2
Factor 0 + 0*y**3 + 8/7*y**2 + 0*y - 6/7*y**4 - 2/7*y**5.
-2*y**2*(y - 1)*(y + 2)**2/7
Let p = 7 - 3. Suppose b + d - 9 = -1, 0 = -p*d + 20. Factor -q**3 - q + b*q**3 - q**3.
q*(q - 1)*(q + 1)
Let h(p) = p**3 - 4*p**2 + p - 1. Let w be h(4). Factor 0 + 0*x + 0*x**4 + 0*x**w + 0*x**2 + 2/7*x**5.
2*x**5/7
Let g(y) = -y**3 + y**2 + y - 1. Let l(f) = 3*f**3 - 10*f**2 - 4*f + 7. Let r(m) = 4*g(m) + l(m). Let n(k) be the first derivative of r(k). Solve n(b) = 0.
-4, 0
Let x(f) = -f**3 - 17*f**2 + 50*f + 64. Let l(u) = -3*u**3 - 35*u**2 + 101*u + 128. Let o(z) = -2*l(z) + 5*x(z). Find p such that o(p) = 0.
-1, 8
Let n(x) = x + 7. Let g be n(-4). Suppose -2*w + g = -5. What is d in -10*d**5 + d**3 - d**4 + 4*d**5 + w*d**5 = 0?
-1, 0, 1/2
Factor 8/3 + 2*h - 2/3*h**2.
-2*(h - 4)*(h + 1)/3
Let f be (-8 + 352/56)/(27/(-56)). Factor 4/9 + 80/9*p**2 + 34/9*p + f*p**3.
2*(p + 2)*(4*p + 1)**2/9
Let w = 5 + -3. Let r(v) = v**3 + 2*v**2 - 2*v + 3. Let d be r(-3). Let -2*z + 4*z**4 + 2*z**5 + d*z**5 - 4*z**w + 0*z**2 = 0. What is z?
-1, 0, 1
Let p(m) = m - 2. Let w be p(5). Factor 13*t**2 - 11*t + 5*t**4 - 23*t**3 + 2 + 8*t**2 + 6*t**w.
(t - 1)**3*(5*t - 2)
Factor -1/5*t**2 - 4/5*t - 4/5.
-(t + 2)**2/5
Suppose 10*k - 42 + 22 = 0. Factor 2/3 + 0*y - 2/3*y**k.
-2*(y - 1)*(y + 1)/3
Suppose -5*q - 4*k - 100 = 0, -2*q + 3*q + 20 = -5*k. Let n be (-11)/(-15) - (-8)/q. Factor -2/3*x**2 - 1/3*x**5 + n*x**4 - 1/3*x + 2/3*x**3 + 1/3.
-(x - 1)**3*(x + 1)**2/3
Suppose 10*o - 10 + 10 = 0. Let m(y) be the first derivative of -4 + o*y - 1/15*y**3 + 0*y**2. Suppose m(q) = 0. What is q?
0
What is d in -94*d**2 - 147*d**4 - 108*d - 138*d**2 - 378*d**3 - 12 - 95*d**2 = 0?
-1, -2/7
Suppose g = 3*g + 2*w - 2, -g + 4*w = -6. Solve 6*t**2 - g*t**2 - 2*t**2 = 0.
0
Suppose 0 = 4*m + a - 25, -2*a - 5 = m - 13. Find k such that -3*k**3 - 2*k**5 + 4*k**2 - m*k**4 + 6*k + 2 - k**3 + 0*k**2 + 0*k**3 = 0.
-1, 1
Let d(z) be the third derivative of 0*z - 1/40*z**5 + 0*z**3 - 2*z**2 + 1/24*z**4 + 1/240*z**6 + 0. Factor d(q).
q*(q - 2)*(q - 1)/2
Let k(x) be the second derivative of 7*x**6/50 + 3*x**5/50 - 21*x**4/20 - 2*x**3 - 6*x**2/5 - 27*x. What is o in k(o) = 0?
-1, -2/7, 2
Let f be (-21)/(-14) - (-25)/2. Suppose -f = -4*n - 2. Determine j, given that 3/2*j**4 - 3/4 - 9/4*j**n + 9/4*j - 3/4*j**2 = 0.
-1, 1/2, 1
Let u(q) be the second derivative of 0 - 1/24*q**4 + 1/6*q**3 + 1/120*q**6 + q - 1/60*q**5 - q**2. Let z(x) be the first derivative of u(x). Factor z(p).
(p - 1)**2*(p + 1)
Let s(m) be the third derivative of -m**8/168 - m**7/105 + m**6/30 + m**5/15 - m**4/12 - m**3/3 + 18*m**2. Factor s(h).
-2*(h - 1)**2*(h + 1)**3
Let y = -247 + 247. Suppose 8/3*m**2 - 2/3*m**5 - 2*m**4 + y*m**3 + 0 + 0*m = 0. What is m?
-2, 0, 1
Suppose -2*q - 21 = q - 5*r, -5*q - 19 = -3*r. Let d be (q/7)/(3/(-7)). Factor d + 2/3*b**2 + 4/3*b.
2*(b + 1)**2/3
Let z be (4/14)