z = -6 - g. Find v such that z*v + 1/2*v**2 + 0 - 1/2*v**3 = 0.
0, 1
Let c = -3/161 - -167/322. Solve 1/2 + c*o**3 - 1/2*o - 1/2*o**2 = 0 for o.
-1, 1
Let h(b) be the second derivative of b**10/151200 - b**9/37800 + b**7/6300 - b**6/3600 - b**4/4 - 2*b. Let z(s) be the third derivative of h(s). Factor z(q).
q*(q - 1)**3*(q + 1)/5
Let q(g) = 2*g**3 - 7*g**2 + 10*g + 5. Let r(x) = -x**2 - 1. Let n(o) = q(o) + 5*r(o). Factor n(u).
2*u*(u - 5)*(u - 1)
Determine i, given that 2/3*i**3 - 1/3 + 11/6*i**2 + 5/6*i = 0.
-2, -1, 1/4
Let j(c) = c + 11. Suppose 4*n + 4*i + 33 = i, 4 = 4*i. Let h be j(n). Let 0*k + 0 + 2/3*k**h = 0. Calculate k.
0
Let c(m) = 2*m**2 - 4*m + 5. Let l(s) be the second derivative of s**4/12 - s**3/3 + s**2 - s. Let j(i) = -4*c(i) + 10*l(i). Suppose j(n) = 0. Calculate n.
0, 2
Let f(k) be the first derivative of -29/3*k**3 - 5*k**4 - 1 - k - 5*k**2. Factor f(p).
-(p + 1)*(4*p + 1)*(5*p + 1)
Suppose 0*t - t = -r - 2, -r - 6 = -3*t. Find n such that 0*n**3 - 1/5*n**4 + 2/5*n**2 + r*n - 1/5 = 0.
-1, 1
Suppose -3*i + 5*d + 27 = 0, 0*d = 3*i + 4*d. Let t = i - 0. Solve 8*g**2 - 4*g**4 - 5*g - t*g**2 + 2*g**5 + 3*g = 0 for g.
-1, 0, 1
Let d(w) be the third derivative of 0*w**4 + 0*w - 1/45*w**5 + 0 + 2*w**2 + 1/15*w**6 - 1/18*w**7 + 0*w**3. Factor d(a).
-a**2*(5*a - 2)*(7*a - 2)/3
Let h = 5 + -3. Let n(z) = -z**3 - 7*z**2 - 6*z + 4. Let a be n(-6). Factor -2/3*p**5 - a*p**3 + 0 - 2/3*p + 8/3*p**h + 8/3*p**4.
-2*p*(p - 1)**4/3
Suppose -5*o + 5*g + 0*g = 25, -o - g = -3. Let j(w) = -6*w - 3. Let s be j(o). Factor 0 + 10/7*i**4 - 2/7*i**5 + 2*i**2 - 18/7*i**s - 4/7*i.
-2*i*(i - 2)*(i - 1)**3/7
Let 594 - 594 + 8*g**4 + 4*g**5 = 0. What is g?
-2, 0
Suppose 5*l = -5*j + 20, -3*l + 6*l + 5*j - 10 = 0. Factor -11*p**2 + 3*p**2 - 264*p**4 + 493*p**5 - 150*p**l + 84*p**3 - 30*p**4.
p**2*(7*p - 2)**3
Factor 0 + 2/3*j + 1/3*j**2.
j*(j + 2)/3
Let b(n) be the first derivative of 3 - 3/4*n**4 + 0*n - n**3 + 0*n**2. Factor b(i).
-3*i**2*(i + 1)
Let c(n) be the second derivative of -n**6/15 - 7*n**5/50 - n**4/15 - 10*n. Factor c(f).
-2*f**2*(f + 1)*(5*f + 2)/5
Let -23/3*a - 10/3*a**2 - 4 + 1/3*a**3 = 0. What is a?
-1, 12
Let t(u) be the third derivative of -u**6/90 + u**4/6 - 4*u**3/3 - 5*u**2. Let b(i) be the first derivative of t(i). Factor b(f).
-4*(f - 1)*(f + 1)
Let c(f) be the second derivative of f**5/20 + f**4/3 - 2*f**2 + 2*f. Let k be c(-3). Factor 2/5*v**k + 0 + 0*v + 0*v**3 + 3/5*v**4 - 1/5*v**2.
v**2*(v + 1)**2*(2*v - 1)/5
Let g(c) be the first derivative of c**6/30 - c**5/15 - c**4/6 + 2*c**3/3 + c**2 + 3. Let z(b) be the second derivative of g(b). Suppose z(p) = 0. Calculate p.
-1, 1
Let d(o) be the second derivative of -o**6/6 + 11*o**5/4 + 25*o. Solve d(t) = 0 for t.
0, 11
Let v(s) = s**2 + s - 1. Let r(o) = -4*o**2 - 4*o + 6. Let x(j) = r(j) + 2*v(j). Factor x(b).
-2*(b - 1)*(b + 2)
Let w(k) = k - 3. Let d be w(4). Let o = -2 + d. Let b(u) = 4*u**2 + 8*u - 8. Let f(j) = -j**2. Let s(p) = o*b(p) - 6*f(p). Factor s(a).
2*(a - 2)**2
Let k = -209 - -329. Let r be (-2)/15 + 76/k. Factor 0 - r*s - 1/2*s**2 + 1/2*s**4 + 1/2*s**3.
s*(s - 1)*(s + 1)**2/2
Let p(b) = -2*b**2 - 16*b - 20. Let y(t) = -2*t**2 - 17*t - 21. Let s(u) = 5*p(u) - 4*y(u). Suppose s(h) = 0. Calculate h.
-4, -2
Suppose 4/3*y**4 + 1/3*y + 4/3*y**2 + 2*y**3 + 1/3*y**5 + 0 = 0. What is y?
-1, 0
Let f be 22/99 + 4/(-45). Let u(h) be the second derivative of 0*h**2 + 0*h**4 + 1/10*h**5 + 0*h**3 - 4*h + 0 + 1/21*h**7 - f*h**6. Suppose u(w) = 0. What is w?
0, 1
Let y(h) be the second derivative of h**6/40 - h**4/16 - 23*h + 2. Factor y(k).
3*k**2*(k - 1)*(k + 1)/4
Suppose 20 = 2*g + 2*g. Let v be ((-2)/g)/(3/(-30)). Factor 2*i**2 + i**v - 10*i**2 - 8*i**3 - 3*i**4.
-2*i**2*(i + 2)**2
Let r(b) = -b**3 - b. Let t be r(-1). Let c(j) be the first derivative of -1 + 1/2*j**t + 0*j + 1/4*j**4 + 2/3*j**3. Factor c(w).
w*(w + 1)**2
Let q(j) be the third derivative of j**9/5040 - j**8/560 + j**7/210 - j**4/12 + 2*j**2. Let y(p) be the second derivative of q(p). Factor y(m).
3*m**2*(m - 2)**2
Factor 0*t**2 - 2/17*t**4 - 4/17*t**3 + 0 + 0*t.
-2*t**3*(t + 2)/17
Suppose j**3 + 12*j**5 - 26*j**4 - 8*j**2 - 14*j**4 + 35*j**3 = 0. Calculate j.
0, 1/3, 1, 2
Let b(r) = 2*r**4 - 3*r**3 - r**2 + 2. Let a(m) = -m**4 + m**3 + m**2 - 1. Let t = -9 + 6. Let n(j) = t*a(j) - b(j). Factor n(u).
(u - 1)**2*(u + 1)**2
Let t(w) be the second derivative of -2*w + 0*w**4 + 1/30*w**6 - 1/21*w**7 + 0*w**2 + 0*w**3 + 0 + 1/20*w**5. Determine u, given that t(u) = 0.
-1/2, 0, 1
Let m(j) = -9*j + 48. Let c be m(5). Factor 7/6*o**c + 4/3*o - 19/6*o**2 + 2/3.
(o - 2)*(o - 1)*(7*o + 2)/6
Factor 3/2*q**4 + 3/2*q**5 + 0 - 15/2*q**2 - 3*q - 9/2*q**3.
3*q*(q - 2)*(q + 1)**3/2
Let a = -68 + 71. Let g(i) be the first derivative of -2/3*i**3 - 2*i + a - 2*i**2. Factor g(t).
-2*(t + 1)**2
Let k = 1/413 + 5777/2065. Find n, given that 14/5*n**2 + 0 - k*n**4 + 4/5*n - 2*n**5 + 6/5*n**3 = 0.
-1, -2/5, 0, 1
Let o = 9 + -7. Solve -2 + 3*k + 0 - k**3 - 2*k + 2*k**o = 0.
-1, 1, 2
Let i(w) be the third derivative of w**7/924 + 2*w**6/495 - w**5/165 - 2*w**3/3 - 8*w**2. Let t(y) be the first derivative of i(y). Let t(p) = 0. What is p?
-2, 0, 2/5
Let k be (-2)/(-4) - (-21)/(-98). Factor -k*g**2 + 0*g + 0.
-2*g**2/7
Let v(t) be the first derivative of -2*t**3/3 - 2*t**2 - 2*t - 11. Let v(o) = 0. What is o?
-1
Let o(d) be the third derivative of -d**5/210 + d**4/12 + 2*d**2 - 3*d. Solve o(p) = 0.
0, 7
Factor 3*h + 3*h**2 - 5*h**2 - 4*h.
-h*(2*h + 1)
Let t be (-12*(-8)/336)/((-8)/(-7)). Factor 1/4*q**3 - t*q**2 + 0 + 0*q.
q**2*(q - 1)/4
Let p(m) be the second derivative of m**4/6 - 2*m**3/3 + m**2 - 6*m. Solve p(a) = 0 for a.
1
Let p be (5 + 11/(-3))/((-14)/(-3)). Suppose 2/7 + 2/7*m - 2/7*m**2 - p*m**3 = 0. Calculate m.
-1, 1
Let n = 236 - 376. Let f = 702/5 + n. Let f*b**3 - 4/5*b**2 + 2/5*b + 0 = 0. What is b?
0, 1
Let d(y) be the third derivative of y**5/20 + 5*y**4/4 + 25*y**3/2 - 16*y**2. Let d(q) = 0. What is q?
-5
Let k = 910 - 910. Let j = -37 + 115/3. Factor j*t**2 + k*t**3 - 2/3 - 2/3*t**4 + 0*t.
-2*(t - 1)**2*(t + 1)**2/3
Let z be 9*(-4 - -8 - 8). Let w be z/24 - 4/(-2). Find t, given that -w + 1/2*t + t**2 = 0.
-1, 1/2
Let k = -21 - -23. Let y(g) be the second derivative of -1/30*g**4 + 0*g**3 + 0*g**k + 0 - 2*g. Factor y(s).
-2*s**2/5
Let d(x) = -x**2 - 6*x + 5. Let n be d(-6). Let z be (-2)/(-2) - (0 + -1). Factor -n*p - 3*p**2 + p**2 + 6*p - 5*p - z.
-2*(p + 1)**2
Determine w so that 1/4 + 1/8*w - 1/8*w**2 = 0.
-1, 2
Let o be (30/8)/((-9)/(-120)). Factor 7*c**2 + 14*c**2 + c**2 - 8 - 60*c**3 - o*c**4 + 24*c.
-2*(c + 1)**2*(5*c - 2)**2
Let a(t) be the first derivative of t**5/30 + t**4/12 + t**3/18 - 6. Factor a(z).
z**2*(z + 1)**2/6
Let t(m) be the first derivative of -m**7/945 + m**5/270 + 2*m**2 - 4. Let y(v) be the second derivative of t(v). Factor y(a).
-2*a**2*(a - 1)*(a + 1)/9
Let r(g) = -g**2 - 11*g + 11. Let q be r(-12). Let f be (6/(-18))/(q/2). Factor -f*h**5 + 0*h**2 + 0*h + 0 - 2*h**4 - 4/3*h**3.
-2*h**3*(h + 1)*(h + 2)/3
Solve 0 + 0*m**2 - 2/11*m**4 + 0*m + 4/11*m**3 = 0.
0, 2
Let p be 0/(-3)*2/(-4). Let j(a) be the first derivative of -2/21*a**3 + 2/7*a - 2 + p*a**2. Suppose j(x) = 0. What is x?
-1, 1
Let d(g) = -g**4 - 6*g**2 + g + 3. Let t(m) = 6*m**4 - m**3 + 35*m**2 - 6*m - 17. Let w(l) = -34*d(l) - 6*t(l). Solve w(x) = 0 for x.
0, 1
Factor -3*q**3 - 4*q + 32*q**2 - 5*q**3 - 3 - 12*q**2 - 5.
-4*(q - 2)*(q - 1)*(2*q + 1)
Let b be 1/(-2)*(-3 - 1). Let n be -2 - (6/(-2) - b). Find s such that -s**2 + 11 + s + 2*s**5 - 11 - n*s**3 + s**4 = 0.
-1, 0, 1/2, 1
Let n(o) be the second derivative of 0 + 0*o**4 + 0*o**3 + 2*o - 1/300*o**6 - o**2 + 0*o**5 + 1/525*o**7. Let j(b) be the first derivative of n(b). Factor j(p).
2*p**3*(p - 1)/5
Let b be (12/(-9))/((-6)/117). Suppose -3*p + b = 5*m, 3*m = -2*p + 16 - 0. Let 3/5*d**4 - 21/5*d**3 + 54/5*d**p + 24/5 - 12*d = 0. What is d?
1, 2
Let a(v) = v**3 - 10*v**2 - 12*v + 14. Let w be a(11). Suppose -1/2*r**w + 0*r**2 + 2*r**4 + 0 + 0*r - 3/2*r**5 = 0. Calculate r.
0, 1/3, 1
Let u(q) be the first derivative of -5*q**6/6 - 2*q**5 + 10*q**3/3 + 5*q**2/2 + 6. Determine r, given that u(r) = 0.
-1, 0, 1
Suppose 0 = l - a - 8, 2 = l - 0*a + 2*a. Let f be ((-1)/9)/((-3)/l)