+ n - 2*n**2.
4*n*(n + 1)
Let r(u) be the second derivative of u**7/210 - 2*u**6/45 - u**5/10 + 3*u**4 + 5*u**3/2 - 2*u + 5. Let h(x) be the second derivative of r(x). Factor h(k).
4*(k - 3)**2*(k + 2)
Let o(q) be the second derivative of q**7/16380 - q**4/12 + 5*q. Let l(k) be the third derivative of o(k). Factor l(r).
2*r**2/13
Let u(f) be the third derivative of 0 + 1/45*f**4 + 4/45*f**3 - 13*f**2 + 1/450*f**5 + 0*f. Factor u(s).
2*(s + 2)**2/15
Let o(j) be the second derivative of -j**5/75 - j**4/3 - 6*j**3/5 + 11*j**2 + 25*j. Let q(c) be the first derivative of o(c). Factor q(p).
-4*(p + 1)*(p + 9)/5
Find c such that 0*c + 0 - 8/7*c**2 + 8/7*c**3 - 2/7*c**4 = 0.
0, 2
Let z(w) be the second derivative of 2/27*w**3 + 6*w + 0*w**2 + 0 + 1/54*w**4. Solve z(h) = 0 for h.
-2, 0
Let q be (-2 - -3) + (-4)/(1 + -5). Suppose 0 = 3*r - q*m - 0 - 5, -4*r = -2*m - 8. Solve -9/8*a**2 - 3/8*a**r + 3/8*a**4 + 3/8*a + 3/4 = 0.
-1, 1, 2
Let z(l) be the second derivative of 3*l**5/100 - 18*l**3/5 - 744*l. What is k in z(k) = 0?
-6, 0, 6
Let g(s) be the third derivative of -5*s**8/2184 - 19*s**7/1365 + s**6/195 + 532*s**2. Factor g(m).
-2*m**3*(m + 4)*(5*m - 1)/13
Suppose 4*k = -0*k. Suppose 5*t - 25 = -a - 10, -5*t + 2*a = k. What is z in 3*z**3 - 4*z**2 + z**t - 3*z**2 + 3*z = 0?
0, 1
Let f(n) be the first derivative of -2*n**7/105 - 2*n**6/15 - 4*n**5/15 + 5*n**2 - 14. Let t(y) be the second derivative of f(y). Factor t(p).
-4*p**2*(p + 2)**2
Determine r, given that -3*r**4 - 60*r**3 + 216*r**2 - 4*r**4 + 3*r**4 - 206 - 16*r - 82 = 0.
-18, -1, 2
Suppose -3/4*n**2 + 1/4*n**4 - 23/4*n - 7/2 + 7/4*n**3 = 0. Calculate n.
-7, -1, 2
Solve -15 - 5*u**2 + 25*u**3 + u**2 + 19*u**2 - 25*u = 0.
-1, -3/5, 1
Let g(v) be the first derivative of 0*v + 1/480*v**6 - 4/3*v**3 + 1/16*v**4 + 0*v**2 + 3/160*v**5 + 2. Let o(s) be the third derivative of g(s). Factor o(j).
3*(j + 1)*(j + 2)/4
Let k(i) be the third derivative of -i**6/135 - 533*i**5/270 - 661*i**4/108 - 44*i**3/9 + 433*i**2 - 2. Let k(p) = 0. Calculate p.
-132, -1, -1/4
Let y(g) be the third derivative of g**5/30 + 11*g**4/24 - 5*g**3/6 + 19*g**2. Let a(b) = 2*b**2 + 12*b - 6. Let z(f) = -5*a(f) + 6*y(f). Factor z(m).
2*m*(m + 3)
Factor 9*v**3 + 180*v + 11*v**2 + 192*v**4 - 35*v**2 - 96 - 189*v**4 - 72*v**2.
3*(v - 2)**2*(v - 1)*(v + 8)
Let u(g) be the first derivative of 0*g + 7 + 1/3*g**3 - 5/24*g**4 + 1/30*g**5 + 5/2*g**2. Let i(r) be the second derivative of u(r). Solve i(o) = 0.
1/2, 2
Suppose -3*s - 4 = -2*n, 23*s - 5*n = 49*s - 10. Solve 2*r**2 + s + 2/5*r**5 - 2/5*r**4 - 4/5*r - 6/5*r**3 = 0.
-2, 0, 1
Let r(g) = -5*g + 80. Let d be r(16). Let i(m) be the third derivative of -11/6*m**4 + d*m + 2*m**3 + 0 - 8*m**2 - 4/15*m**5. Determine v so that i(v) = 0.
-3, 1/4
Let u(w) = w**3 + 5*w**2 - 25*w - 112. Let p be u(-6). Find q such that 8/5*q - 2/5*q**p - 8/5 = 0.
2
Let r(i) be the third derivative of i**7/1050 + i**6/60 + 2*i**5/25 + 11*i**4/60 + 7*i**3/30 - 30*i**2. Factor r(o).
(o + 1)**3*(o + 7)/5
Let g(n) be the third derivative of 0*n**4 + 1/180*n**5 - 1/1080*n**6 + 0*n - 1/3*n**3 + 0 - n**2. Let r(p) be the first derivative of g(p). Factor r(u).
-u*(u - 2)/3
Suppose 0 = -6*r + 1 + 23. Determine h so that 4*h - 7*h + 15*h + 4 + h**r + 28*h**2 + 6*h**3 - 15*h**2 = 0.
-2, -1
Let y(m) = -10*m**3 - 28*m**2 - 10*m + 6. Let p(c) = 10*c**3 + 29*c**2 + 11*c - 5. Let f(d) = 2*p(d) + 3*y(d). Factor f(n).
-2*(n + 1)*(n + 2)*(5*n - 2)
Let u be 6*6/(-378)*154/(-33). What is c in u - 2/9*c**4 - 10/9*c + 2/9*c**3 + 2/3*c**2 = 0?
-2, 1
Let n = 196 + -196. Let x(y) be the third derivative of 5/12*y**4 + 0*y - 7/30*y**5 - 5*y**2 + 2/3*y**3 + n. Factor x(a).
-2*(a - 1)*(7*a + 2)
Suppose 13*n + 20*n = 10*n. Let q(s) be the third derivative of 1/144*s**4 + 1/12*s**3 + 0*s - 1/120*s**5 - 1/720*s**6 + n - 8*s**2. Factor q(g).
-(g - 1)*(g + 1)*(g + 3)/6
Suppose -4*b + 20 = 5*r, -6 = -b + 4*r - 22. Solve -12/19*m**4 + 0 + b*m + 0*m**2 - 2/19*m**5 - 18/19*m**3 = 0.
-3, 0
Let z(k) = -k**4 - k**3 + 1. Let j(d) = 7*d**4 + 8*d**3 + d**2 - 6. Let n be 286/(-55) - (-3)/15. Let g(b) = n*j(b) - 30*z(b). Determine i so that g(i) = 0.
-1, 0
Suppose -3*s = -p - 10, p + 4*p = 2*s + 15. Suppose 0 = s*o - 10*o + 5*h - 5, -2*o - 4*h = -4. Factor 0*u - 1/7*u**3 + 1/7*u**2 + o.
-u**2*(u - 1)/7
Let r(c) be the second derivative of 7/3*c**3 + 47*c - 1/6*c**4 + 0 - 10*c**2. Let r(g) = 0. Calculate g.
2, 5
Suppose -4*i + 36 = 2*i. Let m(c) be the third derivative of 0*c**3 - 9*c**2 + 0 + 1/1050*c**7 + 0*c**5 + 1/1680*c**8 + 0*c**4 + 0*c**i + 0*c. Factor m(z).
z**4*(z + 1)/5
Let w = -19 + 34. Solve -8*z**2 + z**4 - 5*z**4 - 3*z**3 + w*z**3 = 0 for z.
0, 1, 2
Let u(l) be the second derivative of l**6/15 + l**5/2 - 131*l**4/24 + 19*l**3/2 - 27*l**2/4 - 343*l - 1. Factor u(s).
(s - 3)*(s + 9)*(2*s - 1)**2/2
Let x = -27 + 34. Solve -6*i - i**2 + x*i + 3*i + 3 + 2*i**2 = 0.
-3, -1
Let l be ((-30)/9)/(2/6). Let j be 5/l*(-6)/1. Let -3*i**j + i**3 + 46*i - 44*i = 0. Calculate i.
-1, 0, 1
Let t = 19489/28 - 696. Let w(l) be the first derivative of 6 + 0*l - 1/14*l**2 + 0*l**3 + t*l**4. Solve w(r) = 0.
-1, 0, 1
Let t(d) = 201*d**2 - 199*d - 2. Let m(y) = 2210*y**2 - 2190*y - 20. Let i(c) = -4*m(c) + 45*t(c). Let i(o) = 0. Calculate o.
-2/41, 1
Let h be 6/21 + 410/35. Let v be 18/h*(-2 + (-7)/(-3)). Factor -v*n**3 + 0*n + 1/2*n**5 + 0 + 1/2*n**2 - 1/2*n**4.
n**2*(n - 1)**2*(n + 1)/2
Let y(r) be the first derivative of r**4/2 + 4*r**3/3 + 2*r**2 - r + 10. Let v(o) = o**3 + o**2 + o. Let m(a) = -3*v(a) + y(a). Solve m(x) = 0 for x.
-1, 1
Let m(o) be the first derivative of 1/2*o**4 - 2/9*o**3 + 0*o**2 - 11 + 1/9*o**6 + 0*o - 2/5*o**5. Factor m(f).
2*f**2*(f - 1)**3/3
Let i(h) = 6*h**2 - 18*h + 18. Let b be i(1). Let p be b/21 - (23/7 + -3). What is y in 1/4*y**2 + 1/2*y + p = 0?
-2, 0
Find n such that 92*n - 629*n**2 + 672*n**2 + 35*n - 6 = 0.
-3, 2/43
Let l(g) = -g**2 + 2*g + 18. Let u be l(5). Factor -51*r**u + 23*r**3 + 18*r**3 + 10*r + 0*r + 5*r**2 - 5*r**4.
-5*r*(r - 1)*(r + 1)*(r + 2)
Let j = 12178/105 - 488/5. Let x = 138/7 - j. What is f in -2/3 - 5/6*f**2 + x*f + 1/6*f**3 = 0?
1, 2
Let x = -25 - -28. Determine w so that -6*w**3 - w**2 + 5*w**2 + x*w**4 - 4*w**2 = 0.
0, 2
Let y(n) = -2*n. Let r(k) = k**2 - 4*k + 49. Let i(d) = -r(d) - 5*y(d). Find s, given that i(s) = 0.
7
Determine q, given that 36 + 33/2*q + 3/2*q**2 = 0.
-8, -3
Let a(z) be the first derivative of 0*z**4 - 2 - 1/27*z**3 + 3/2*z**2 + 0*z + 1/270*z**5. Let c(h) be the second derivative of a(h). Find m such that c(m) = 0.
-1, 1
Suppose -2*c - 28 = -8. Let z = 14 + c. Determine i, given that -5*i**2 + 3*i**2 + i**2 + z*i**3 - 4*i**5 + i**4 = 0.
-1, 0, 1/4, 1
Let p be 1/(-5) - -1*(-20)/775. Let o = 109/341 - p. Find k such that -2/11 - 2/11*k**3 - o*k**2 - 6/11*k = 0.
-1
Suppose 0 = -7*f + f. Factor -2*a**3 + 3*a**5 + f*a**5 - a**5.
2*a**3*(a - 1)*(a + 1)
Let g(n) be the third derivative of -19*n**5/390 + 11*n**4/78 - n**3/13 - 35*n**2. Factor g(x).
-2*(x - 1)*(19*x - 3)/13
Determine v, given that -1/7*v**2 - 4/7*v + 5/7 = 0.
-5, 1
Let 16 - 2/3*l**4 + 14/3*l**3 - 4/3*l**2 - 56/3*l = 0. What is l?
-2, 1, 2, 6
Let r = -32 - -22. Let p = -7 - r. Suppose 0 + 3 + 14*m**2 + 16*m + 4*m**p + 3 = 0. Calculate m.
-3/2, -1
Let k(d) = -4*d**2 + 240*d - 3612. Let q(x) = -3. Let i(z) = -k(z) + 4*q(z). What is w in i(w) = 0?
30
Let w(l) be the second derivative of 1/42*l**3 + 0*l**2 + 1/28*l**4 + 16*l + 1/140*l**5 - 1/70*l**6 - 1/147*l**7 + 0. Solve w(f) = 0.
-1, -1/2, 0, 1
Let q be ((105/(-28))/5)/((-2)/(-40)). Let m be 65/30 + (q/9 - -1). Find w such that -w**4 + 0*w + 0 + m*w**5 + w**2 - 3/2*w**3 = 0.
-1, 0, 2/3, 1
Let q = 2201 - 2198. Factor -3/2*m**5 + 0*m + 3*m**q + 0 + 3/2*m**4 + 0*m**2.
-3*m**3*(m - 2)*(m + 1)/2
Let r be (-2 - 3/(-2)) + 990/900. What is k in -r*k**2 - 9/5*k + 6/5 - 3/5*k**4 + 9/5*k**3 = 0?
-1, 1, 2
Suppose -4*d = -6*d + 6. Let p be (5 - (d - -3))/(13/(-2)). Solve -2/13*k + 0 + p*k**2 = 0 for k.
0, 1
Suppose -5*m = 3*x - 10*m, 4*m = -11*x. Let z(u) be the second derivative of -11*u + 1/6*u**3 + x - 1/20*u**5 + 1/90*u**6 + 1/36*u**4 - 1/3*u**2. Factor z(k).
(k - 2)*(k - 1)**2*(k + 1)/3
Factor 36/5*n**3 + 26/5*n - 6/5 + 2/5*n**5 - 44/5*n**2 - 14/5*n**4.
2*(n - 3)*(n - 1)**4/5
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