/5*n**3 + 0 + 4/5*n**2.
2*n*(n + 1)**2/5
Determine g so that -20 - 72*g + 21*g**3 - 17*g**3 - 21*g**2 + 51*g - 54*g**2 - 78*g = 0.
-1, -1/4, 20
Suppose 0 = -3*r - 2*x + 12, 2*x - 3*x = -r - 1. Suppose -9 = r*k - 31. Let k*v**3 + 2*v - 15*v**2 - 32*v**3 + 4*v = 0. What is v?
-1, 0, 2/7
Let b(y) be the first derivative of 0*y + 0*y**2 + 0*y**3 + 1 + 1/14*y**4. Solve b(n) = 0.
0
Let q = 25 - 18. Suppose 2*u = q - 3. Find z, given that 1 + 1/2*z - 1/2*z**u = 0.
-1, 2
Let g(h) be the second derivative of 4/39*h**3 + 0 + 3*h + 8/39*h**4 - 4/273*h**7 + 0*h**2 + 3/26*h**5 - 4/195*h**6. Let g(t) = 0. Calculate t.
-2, -1/2, 0, 2
Let a(o) be the first derivative of -5*o**6/12 + 5*o**4/4 - 5*o**2/4 - 167. Factor a(f).
-5*f*(f - 1)**2*(f + 1)**2/2
Let p(g) be the first derivative of -55*g**3 - 95/2*g**2 - 55 - 4*g**5 - 15*g - 105/4*g**4. Suppose p(y) = 0. What is y?
-3, -1, -1/4
Let y(b) = b**3 + 6*b**2 - b - 4. Let v be y(-6). Factor 6*l**2 - 16*l**v + 14*l**2 - 16.
4*(l - 2)*(l + 2)
Factor 0 - 2*a**2 - 8/3*a + 2/3*a**3.
2*a*(a - 4)*(a + 1)/3
Suppose 16 = -10*i - 14. Let c(x) = 4*x**3 - 2*x**2 + 4*x + 2. Let z(j) = 4*j + 4*j**3 - j + 0*j - 3*j**2 + 2. Let t(s) = i*c(s) + 4*z(s). Solve t(o) = 0.
-1/2, 1
Let l be (-6)/3 + 3 + 1. Let k(f) = -3*f**3 + 6*f**2 + f. Let g be k(l). Solve 6/5*q**3 + 0*q - 2/5*q**4 + 0 - 4/5*q**g = 0 for q.
0, 1, 2
Let j(v) be the second derivative of -8*v**4/3 - 14*v**3/3 + 2*v**2 + 405*v. Factor j(d).
-4*(d + 1)*(8*d - 1)
Let d be 34/493 + (-328)/(-290). Let 0 - 9/5*y**2 + 12*y**3 - d*y = 0. What is y?
-1/4, 0, 2/5
Let h(f) be the first derivative of 1/8*f**4 + 1/15*f**5 - 1/3*f**2 + 5 - 2/9*f**3 + 0*f - 1/36*f**6. Factor h(x).
-x*(x - 2)**2*(x + 1)**2/6
Let m(u) be the first derivative of -u**6/1980 + u**5/33 - 25*u**4/33 + 6*u**3 + 28. Let i(d) be the third derivative of m(d). Let i(c) = 0. Calculate c.
10
Let s(v) = 19*v**2 - 119*v + 66. Let p(l) = 170*l**2 - 1070*l + 595. Let h be 143/4 + 30/(-40). Let j(k) = h*s(k) - 4*p(k). Suppose j(z) = 0. What is z?
2/3, 7
Determine s, given that 32/11*s + 2/11*s**2 + 10 = 0.
-11, -5
Let h(u) be the first derivative of -u**4/42 - u**3/7 - 2*u**2/7 - 6*u - 4. Let m(g) be the first derivative of h(g). Find w, given that m(w) = 0.
-2, -1
Let s(r) = -r**2 + 37*r - 31. Let a be s(36). Let b(f) be the second derivative of 1/18*f**3 + 0*f**2 - 2*f - 1/24*f**4 + 0 + 0*f**a + 1/180*f**6. Factor b(m).
m*(m - 1)**2*(m + 2)/6
Factor 35/4*y + 0 + 5/4*y**3 - 10*y**2.
5*y*(y - 7)*(y - 1)/4
Factor 13/2 + 11/2*k**2 + 25/2*k - 1/2*k**3.
-(k - 13)*(k + 1)**2/2
Let c(k) be the second derivative of k**7/294 + k**6/70 - k**5/140 - k**4/28 + 21*k + 3. Suppose c(f) = 0. What is f?
-3, -1, 0, 1
Let i(z) be the second derivative of z**4/6 + 320*z**3/3 + 25600*z**2 + 54*z - 2. Factor i(y).
2*(y + 160)**2
Let j(u) be the second derivative of -12*u + 0 - 1/10*u**4 + 2/5*u**3 + 12/5*u**2 - 3/100*u**5. Find d, given that j(d) = 0.
-2, 2
Suppose 4*f - 3*f = 0. Suppose 3*d - 4*t + 4 = f, 5 = 2*d + 3*t + 2. Factor -8/5 + d*x + 2/5*x**2.
2*(x - 2)*(x + 2)/5
Factor 0 - 3*o**2 + 6*o + 1/3*o**4 - 2/3*o**3.
o*(o - 3)*(o - 2)*(o + 3)/3
Let m(b) be the first derivative of b**6/9 - 2*b**5/3 + b**4/2 + 10*b**3/9 - 4*b**2/3 + 203. Suppose m(u) = 0. What is u?
-1, 0, 1, 4
Let w(n) be the first derivative of n**6/12 + 31*n**5/10 + 151*n**4/4 + 457*n**3/3 + 273*n**2/4 - 1521*n/2 + 639. Suppose w(c) = 0. Calculate c.
-13, -3, 1
Suppose 44*x - 46*x = 14. Let o be -4*9/(-42)*x/(-5). Factor 12/5*w + o*w**3 - 3/5 - 3*w**2.
3*(w - 1)**2*(2*w - 1)/5
Factor -8*h**2 + 17355*h**3 + 15 - 10*h + 4*h**2 - 11*h**2 - 17335*h**3 - 10*h**2.
5*(h - 1)**2*(4*h + 3)
Suppose 0 = -5*d - 0*d + 90. Suppose -n + 3*x = -2, x = -4*n + d + 3. Factor -l**n - 2*l**5 - 7*l**4 + 4*l**4.
-3*l**4*(l + 1)
Suppose -247 = 7*t - 268. Suppose g - 2*z = 7, 4*z = t*z - 2. Determine u so that 15/2*u - 9 - 39/2*u**g + 33/2*u**2 + 9/2*u**4 = 0.
-2/3, 1, 3
Let z = 514 - 509. Let y(a) be the third derivative of 0*a**3 + 0*a**z - 1/112*a**8 + 1/40*a**6 + 0*a + 0*a**7 + 0 + 0*a**4 + 8*a**2. Factor y(q).
-3*q**3*(q - 1)*(q + 1)
Let f(b) be the first derivative of -b**7/42 - 2*b**6/15 - b**5/5 - 3*b - 1. Let w(l) be the first derivative of f(l). Let w(d) = 0. What is d?
-2, 0
Let v(u) = -3*u**2 + 6*u - 1. Let b(z) be the first derivative of -2*z**3/3 + 3*z**2/2 - z - 21. Let i(d) = 5*b(d) - 3*v(d). Find y, given that i(y) = 0.
-2, -1
Let l(w) be the first derivative of 0*w**2 + 15 + 5/3*w**3 + 0*w - w**5 + 0*w**4. Solve l(c) = 0 for c.
-1, 0, 1
Let p(c) be the second derivative of -c**6/210 - c**5/14 - 11*c**4/28 - 20*c**3/21 - 8*c**2/7 - 180*c + 1. Factor p(a).
-(a + 1)**2*(a + 4)**2/7
Suppose 4 = 2*o - 4*i, -2*o + i - 1 = 2*i. Let p(v) be the first derivative of 0*v + 0*v**3 + 5 + 1/7*v**4 + 8/21*v**6 + o*v**2 - 4/7*v**5. Factor p(l).
4*l**3*(l - 1)*(4*l - 1)/7
Let m = -802 + 4813/6. Let h(o) be the second derivative of 1/15*o**3 + 2/25*o**5 + 4*o + 0 + m*o**4 + 0*o**2. Find y such that h(y) = 0.
-1, -1/4, 0
Suppose -48/19 + 28/19*s - 2/19*s**2 = 0. What is s?
2, 12
Let m(o) = -3*o**2 - 3*o - 1. Let b(z) = 2*z**2 + 1. Let x(a) = 4*b(a) + 4*m(a). Determine y, given that x(y) = 0.
-3, 0
Determine g, given that -6/7*g**5 + 24/7*g - 54/7*g**3 - 16/7 + 20/7*g**2 + 32/7*g**4 = 0.
-2/3, 1, 2
Let z(h) be the second derivative of 0*h**2 - 2/27*h**3 + 1/189*h**7 + 1/90*h**5 + 0 - 11*h + 1/18*h**4 - 1/45*h**6. Let z(l) = 0. Calculate l.
-1, 0, 1, 2
Determine n so that 12*n**3 + 27/2*n**2 + 0 - 3/2*n**4 + 0*n = 0.
-1, 0, 9
Let b be (-7 - -8)/((-609)/309 + 2). Let d = -33 + b. Factor 0*f**2 + 2/3*f**3 - 2*f + d.
2*(f - 1)**2*(f + 2)/3
Solve 4/7*b**2 + 144/7 - 80/7*b = 0.
2, 18
Let a(s) = -s**2 - 3*s + 9. Let c be a(3). Let p be (c - (1 - 2))*30/(-540). Determine q so that -2/9*q**2 - p - 2/3*q = 0.
-2, -1
Let u(l) be the third derivative of -l**5/75 + 5*l**4/48 - l**3/20 + 187*l**2 + 1. Solve u(k) = 0.
1/8, 3
Let t = 160/51 - -4337/357. Let p = t - 15. Find m, given that 0 + 4/7*m + p*m**2 = 0.
-2, 0
Let l(k) = 3*k**2 - 3*k - 23. Let v be l(7). Factor 18*z**2 + v*z - z**2 - 83*z - 5*z**2 + 8.
4*(z + 1)*(3*z + 2)
Suppose -9*c = -4*c - 130. Let t be (-2)/6 - c/(-6). Find a such that 2*a - 3 - 18*a**2 - 3*a**t + 9*a - a**3 + 13*a**3 + a = 0.
1
Let v(g) be the third derivative of 0 - g**3 - 5*g + 3*g**2 - 1/8*g**4 + 1/20*g**5. Factor v(r).
3*(r - 2)*(r + 1)
Let f be (27/54)/(-1)*0/(-2). Suppose 2/3*w**2 + 4/3*w + f = 0. What is w?
-2, 0
Let o = -217 - -220. Suppose o*r = 63 - 57. Factor -4/11*a + 2/11*a**r + 2/11.
2*(a - 1)**2/11
Suppose 3*n = -4*o + 92, 4*o = 3 + 5. Let l be -4 - (n/(-16) + -3). Factor 3/2 + l*d - 3/4*d**2.
-3*(d - 2)*(d + 1)/4
Let j = 1025/1542 + 1/514. Let u(i) be the third derivative of -5*i**2 - 16/3*i**3 - 1/30*i**5 + 0*i + j*i**4 + 0. Factor u(x).
-2*(x - 4)**2
Let w(f) = 2*f**3 + 119*f**2 - 65*f - 298. Let d be w(-60). Let -4*k + 6 + 1/2*k**d = 0. Calculate k.
2, 6
Factor 0 + 11/8*z**3 + 1/4*z**2 + 0*z + 9/8*z**4.
z**2*(z + 1)*(9*z + 2)/8
Let f(i) be the third derivative of -i**7/15120 + i**6/1080 - i**5/180 - 25*i**4/24 + 16*i**2. Let c(h) be the second derivative of f(h). Factor c(x).
-(x - 2)**2/6
Let q(c) be the second derivative of 4*c**4/3 - 10*c**3/3 + 25*c**2/8 - 139*c. Factor q(w).
(8*w - 5)**2/4
Let z(s) be the first derivative of -2*s**5/45 + 5*s**4/9 - 8*s**3/3 + 6*s**2 - 6*s - 59. What is a in z(a) = 0?
1, 3
Let b(n) = -n**3 + 5*n**2 + n. Let v be b(5). Let x(g) be the first derivative of 12/5*g**v + 4 + 9/4*g**4 + 0*g + 0*g**2 - g**3. Factor x(h).
3*h**2*(h + 1)*(4*h - 1)
Let q(f) be the third derivative of f**8/720 - f**7/504 - f**6/540 + 3*f**3/2 - 7*f**2. Let k(w) be the first derivative of q(w). Solve k(b) = 0 for b.
-2/7, 0, 1
Suppose 0 = -3*k + 14 + 22. Suppose 0*w = -4*w + k. Factor 6*g**2 - 3*g + g - 5*g**2 + g**w.
g*(g - 1)*(g + 2)
Let p(o) be the second derivative of o**6/1260 - o**5/84 + o**4/21 + 31*o**3/6 - 10*o. Let t(u) be the second derivative of p(u). Suppose t(w) = 0. What is w?
1, 4
Let q(d) be the third derivative of d**6/160 - 3*d**5/10 + 45*d**4/32 - 11*d**3/4 + 101*d**2. Determine r, given that q(r) = 0.
1, 22
Let x = -16 - -3. Let m(k) = k**2 + 14*k + 16. Let y be m(x). Factor -14*g - g**y + 5*g**3 - 2*g**5 + 12*g.
-2*g*(g - 1)**2