4/9*n**3 - 2/9 - 2/3*n**u + 8/9*n**2 = 0?
-1, -1/3, 1
Let j(w) be the third derivative of -w**11/166320 + w**9/30240 + w**5/60 + 2*w**2. Let p(r) be the third derivative of j(r). Determine t, given that p(t) = 0.
-1, 0, 1
Factor -1/8*a**2 + 1/8*a + 1/4.
-(a - 2)*(a + 1)/8
Let x(t) = -t**3 - t**2 + 2*t. Let d(l) = 60*l**3 - 56*l**2 - 32*l. Let o(j) = -d(j) - 24*x(j). Suppose o(w) = 0. What is w?
0, 2/9, 2
Let n(t) = t + 4. Let v be n(0). Let u(h) be the third derivative of -1/180*h**5 + 0*h**v - 2*h**2 + 0 + 0*h + 1/18*h**3. Determine s so that u(s) = 0.
-1, 1
Let v(f) be the first derivative of -f**6/60 + f**5/10 - f**4/4 + f**3/3 - f**2/4 - f + 2. Let z(o) be the first derivative of v(o). Let z(q) = 0. Calculate q.
1
Factor 0*a + 0 - 1/3*a**3 - 1/3*a**4 + 0*a**2.
-a**3*(a + 1)/3
Let v = 1318 - 1318. Determine s, given that -48/7*s**4 - 32/7*s**5 - 2/7*s**3 + v - 2/7*s + 12/7*s**2 = 0.
-1, 0, 1/4
Determine k so that -5*k**5 - 6*k**5 - k**4 + 10*k**5 = 0.
-1, 0
Suppose -25 = -2*u - 3. Let x = u - 6. Let d(j) = j**2 - 2*j - 3. Let s(w) = -2*w**2 + 5*w + 7. Let c(l) = x*d(l) + 2*s(l). Let c(o) = 0. What is o?
-1, 1
What is t in -14*t**2 - 20*t - 5*t**3 - 3*t**2 - 5*t**2 + 2*t**2 = 0?
-2, 0
Suppose 0 = r - 1 - 1. Find d such that -4*d + 3*d + 5*d**r - 2*d**2 = 0.
0, 1/3
Let r(p) be the second derivative of -p**6/210 + p**5/35 - p**4/14 + 2*p**3/21 - p**2/14 + 2*p. Determine z so that r(z) = 0.
1
Let z = 41 + -18. Suppose 4*m + 2*x = -3*x + z, 3*m - 2*x = 0. Suppose 8/9*j - 2/3*j**3 + 8/9*j**m + 0 = 0. What is j?
-2/3, 0, 2
Let m(f) = f + 2. Let l be m(2). Let q(x) = 3*x + 0*x + 3*x - l*x**2. Let a(y) = -1. Let g(s) = 4*a(s) - q(s). Factor g(p).
2*(p - 2)*(2*p + 1)
Let b(f) be the third derivative of -f**8/504 + 4*f**7/945 - f**6/540 - 6*f**2. Factor b(q).
-2*q**3*(q - 1)*(3*q - 1)/9
Let j = 11 - 8. Let y be (-25)/(-60) - j/12. What is w in 1/6 + 1/3*w + y*w**2 = 0?
-1
Let -76/3*n**2 - 52/9*n**3 - 200/9 - 4/9*n**4 - 380/9*n = 0. What is n?
-5, -2, -1
Let r(k) be the first derivative of 2/9*k**3 + 1 - 1/3*k + 1/6*k**2. Factor r(l).
(l + 1)*(2*l - 1)/3
Suppose 3*l + 2*r - 6 = 0, r + 2*r + 17 = 2*l. Let f(j) be the second derivative of 0*j**2 - 1/12*j**l + 0 + 1/6*j**3 + 3*j. Factor f(c).
-c*(c - 1)
Factor 4/3*g**4 - 8/3*g**3 + 8/3*g + 0 - 4/3*g**2.
4*g*(g - 2)*(g - 1)*(g + 1)/3
Let x(j) = 3*j**3 + 11*j**2 + 8*j + 2. Let q(k) = 3*k**3 + 12*k**2 + 9*k + 3. Suppose -f - 2 = -2*f. Let b(a) = f*q(a) - 3*x(a). Factor b(d).
-3*d*(d + 1)*(d + 2)
Let y = 23 + -17. Let f(n) be the third derivative of 2*n**2 + 2/75*n**5 + 0*n + 1/60*n**4 + 0 + 0*n**3 + 1/100*n**y. Factor f(p).
2*p*(p + 1)*(3*p + 1)/5
Let x(a) be the second derivative of a + 0*a**2 + 0*a**3 + 1/12*a**4 + 0. Find w such that x(w) = 0.
0
Let a be (2/(-6))/(1/(-9)). Let s(k) be the third derivative of a*k**2 - 1/24*k**6 - 1/30*k**5 + 5/24*k**4 + 0 + 1/3*k**3 + 0*k. Suppose s(j) = 0. Calculate j.
-1, -2/5, 1
Let c = 1/51 - -31/153. Solve -4/9*b**2 + c*b - 2/9*b**3 + 4/9 = 0.
-2, -1, 1
Let h(z) be the second derivative of -z**7/70 - 3*z**6/20 - 9*z**5/20 + z**2 - 10*z. Let v(n) be the first derivative of h(n). Factor v(u).
-3*u**2*(u + 3)**2
Let n(r) be the first derivative of -r**3/6 + 2*r + 8. Suppose n(b) = 0. What is b?
-2, 2
What is i in 2*i + 344*i**2 - 339*i**2 + 8*i = 0?
-2, 0
Let n be 2/9 + 68/18. Let 27 + n*k + 2*k**2 + 4*k**2 - 22*k - 3*k**2 = 0. Calculate k.
3
Let b be ((-10)/6)/((-1)/3). Suppose -4*s = -o - 7, -o = -b*o + 2*s. Factor -1 + o - h**2 - h**2 - 2*h.
-2*h*(h + 1)
Let p(i) be the second derivative of 4*i**6/5 + 7*i**5/5 + 2*i**4/3 - 10*i. Factor p(k).
4*k**2*(2*k + 1)*(3*k + 2)
Factor 657*o**3 + o**2 - 5*o**5 + 10 - 637*o**3 - 11*o**2 - 15*o.
-5*(o - 1)**3*(o + 1)*(o + 2)
Find x, given that 117/4*x**2 + 6591/4 - 3/4*x**3 - 1521/4*x = 0.
13
Factor 0 - 3/7*b**2 - 3/7*b.
-3*b*(b + 1)/7
Let f(q) be the first derivative of 9/10*q**2 + 3/5*q - 6 + 3/5*q**3 + 3/20*q**4. Suppose f(p) = 0. Calculate p.
-1
Let w(b) = b**3 + b**2 + 1. Let c(s) = -3*s**3 + 52*s**2 - 160*s + 162. Let z(j) = -c(j) + 2*w(j). Solve z(y) = 0 for y.
2, 4
Let k = -2/43 + 92/129. Find g, given that 2/3*g**2 + 2/3*g - k*g**3 - 2/3 = 0.
-1, 1
Suppose -4*z = -3 - 13. Suppose 1 = g + z*y - 15, 4*y - 16 = -3*g. Solve -r**3 + 3*r**3 + g*r - 2*r = 0 for r.
-1, 0, 1
Suppose 7*l - 6*l = 4. Let n(t) be the first derivative of 0*t**2 - 1/10*t**5 + 1 - 1/4*t**l - 1/6*t**3 + 0*t. Factor n(k).
-k**2*(k + 1)**2/2
Suppose 2*p + 4 = 20. Factor x**5 + 0*x**5 + 12*x**3 + 13*x**4 - 5*x**4 + 2*x + p*x**2 + x**5.
2*x*(x + 1)**4
Let i = 33 + -31. Factor 1/4*a**4 + 0*a - 1/4*a**3 + 0 + 1/4*a**5 - 1/4*a**i.
a**2*(a - 1)*(a + 1)**2/4
Factor -8*c**3 - 4*c**3 + 0*c**2 + 5*c**2 + 4*c**4 + 3*c**2.
4*c**2*(c - 2)*(c - 1)
Let d(i) be the second derivative of 0*i**2 + 0 - 1/84*i**4 + 2*i - 1/210*i**5 - 1/1260*i**6 - 1/6*i**3. Let j(x) be the second derivative of d(x). Factor j(h).
-2*(h + 1)**2/7
Let l(f) be the third derivative of -3/8*f**4 + 0*f - f**3 + 4*f**2 - 1/20*f**5 + 0. Factor l(d).
-3*(d + 1)*(d + 2)
Let k(n) = -5*n**2 + 2*n + 7*n**3 - n**2 - 9*n. Let j(l) = -6*l**3 + 5*l**2 + 6*l. Let x(z) = -6*j(z) - 5*k(z). What is a in x(a) = 0?
-1, 0, 1
Let l(s) be the third derivative of 0*s**5 - 1/42*s**4 + 0*s + 1/735*s**7 - 1/21*s**3 + 0 - 3*s**2 + 1/210*s**6. Find g such that l(g) = 0.
-1, 1
Factor 4/3*s + 1/6 - 1/6*s**2 - 4/3*s**3.
-(s - 1)*(s + 1)*(8*s + 1)/6
Let y(o) be the second derivative of 3*o + 21/10*o**5 + 2/3*o**3 + 5/21*o**7 + 0*o**2 + 17/15*o**6 + 11/6*o**4 + 0. Let y(x) = 0. What is x?
-1, -2/5, 0
Let t(y) be the first derivative of 1/9*y**3 + 1/9*y**4 + 0*y**2 + 1 + 1/30*y**5 - y. Let x(i) be the first derivative of t(i). Factor x(o).
2*o*(o + 1)**2/3
Factor 3*m**2 + 5*m**5 - 3*m**4 + 3*m**3 + 0*m**3 - 2*m**5 - 6*m**3.
3*m**2*(m - 1)**2*(m + 1)
Let u(t) = t**3 - 2*t**2 - 9*t - 1. Let o be u(4). Let d be (1/14)/(o/(-60)). Factor -d*c - 2/7*c**2 - 4/7.
-2*(c + 1)*(c + 2)/7
Suppose 0*k = -k. Let v = 3 - 0. Factor k*f - 2/5*f**2 + 0 + 0*f**v + 2/5*f**4.
2*f**2*(f - 1)*(f + 1)/5
Solve 3/2 - 1/2*y**2 + y = 0 for y.
-1, 3
Let v(b) be the second derivative of -5*b**5/4 - 65*b**4/12 - 10*b**3/3 + 10*b**2 + 3*b. Suppose v(o) = 0. Calculate o.
-2, -1, 2/5
Let u(z) be the first derivative of 1/4*z**3 + 0*z + 4 - 1/16*z**4 - 1/4*z**2. Determine i, given that u(i) = 0.
0, 1, 2
Factor 50*z**5 - 16*z**4 - 2 - 8*z**2 + 20*z**3 + 2 - 46*z**5.
4*z**2*(z - 2)*(z - 1)**2
Let i(d) be the first derivative of -d**8/6720 + d**6/1440 - d**3/3 + 4. Let j(p) be the third derivative of i(p). Factor j(b).
-b**2*(b - 1)*(b + 1)/4
Let z(x) be the first derivative of 2/5*x**5 - 1/6*x**6 + 1/2*x**4 - 2*x + 7/2*x**2 + 6 - 8/3*x**3. Factor z(p).
-(p - 1)**4*(p + 2)
Let h = 2 + -4. Let p(v) = -6*v. Let k(d) = 25*d + d**2 + 11 + 0*d**2 - 11. Let s(r) = h*k(r) - 9*p(r). Factor s(n).
-2*n*(n - 2)
Suppose -v + 8 = 6. Let r(z) be the third derivative of 0*z + 1/96*z**4 + 1/840*z**7 - 1/480*z**6 + 0 - 1/240*z**5 + v*z**2 + 0*z**3. Factor r(n).
n*(n - 1)**2*(n + 1)/4
Solve -4*v**3 - 14 + 7*v**3 + v**4 + 4*v + 6 - 8*v**3 + 6*v**2 = 0.
-1, 2
Let y(w) be the third derivative of -w**6/600 + w**4/120 - 2*w**2. Factor y(d).
-d*(d - 1)*(d + 1)/5
Let s(q) = 11*q**4 + 10*q**3 + 5*q**2 - 6*q + 6. Let y(c) = 12*c**4 + 10*c**3 + 5*c**2 - 7*c + 7. Let w(h) = -7*s(h) + 6*y(h). Suppose w(r) = 0. What is r?
-1, 0
Let f be (-4)/14 + 2216/(-84). Let u = f + 27. Factor 0 - 1/3*l - u*l**3 - 2/3*l**2.
-l*(l + 1)**2/3
Let z(n) = 9*n**4 - 6*n**3 + 3*n**2 + 3*n + 3. Let o(q) = q**5 + 18*q**4 - 11*q**3 + 6*q**2 + 7*q + 7. Let s(i) = 3*o(i) - 7*z(i). Solve s(r) = 0 for r.
0, 1
Suppose -25 = -5*s - 5. Let f(z) be the first derivative of 1/12*z**s + 0*z - 1/6*z**2 - 1/9*z**3 + 2 + 1/15*z**5. Factor f(c).
c*(c - 1)*(c + 1)**2/3
Let f be 30/45 + (-62)/3. Let g = 101/5 + f. Factor g*k + 0 - 1/5*k**2.
-k*(k - 1)/5
Solve 0*d**2 + 0*d**4 + 2/9*d**5 - 4/9*d**3 + 2/9*d + 0 = 0.
-1, 0, 1
Suppose 1531 = 7*q + 1517. Determine k, given that k**q + 1/2*k**3 + 1/2*k + 0 = 0.
-1, 0
Let b(h) be the third derivative of 0 + 0*h**5 - 1/6*h**3 + 1/60*h**6 + 0*h - 3*h**2 + 1/210*h**7 - 1/12*h**4. Factor b(a).
(a - 1)*(a + 1)**3
Let j(z) = z**3 - 10*z**2 + z - 5. Let p be j(10). Suppose 0 = p*l + 2 - 22. Factor -2/