15/2*k**2.
k*(k + 1)*(k + 3)**2/2
Let b(k) be the second derivative of -6 + 0*k**2 + 0*k**3 + 2*k - 1/21*k**4 - 3/140*k**5 + 1/210*k**6. Determine n so that b(n) = 0.
-1, 0, 4
Let q(b) = 4*b**4 - 13*b**2 - 3*b - 3. Suppose 2 - 3 = -h - 2*m, 3*h + 4*m - 1 = 0. Let v(d) = -d**2 + d + 1. Let a(u) = h*q(u) - 3*v(u). Factor a(z).
-4*z**2*(z - 2)*(z + 2)
Suppose 5*h**4 + 9 - 3*h**4 - 190*h - 12*h**3 + 0*h**4 + 15 - 6*h**2 + 222*h = 0. Calculate h.
-1, 2, 6
Let 2/3*n**4 + 0 + 4/5*n + 16/15*n**3 - 38/15*n**2 = 0. Calculate n.
-3, 0, 2/5, 1
Suppose -10*l = -8*l - 6. Factor -5*q - q + 2 - 24*q - 18*q**2 + 48 - 2*q**l.
-2*(q - 1)*(q + 5)**2
Let c be 4*(-11)/(-132)*0. Let b(w) be the third derivative of 5*w**2 + c + 0*w + 1/60*w**5 + 0*w**4 - 1/6*w**3. Find t, given that b(t) = 0.
-1, 1
Let i = 35 - 33. Factor -5*t**2 - t**4 + i*t**4 - t**5 - 30*t + 3*t**3 + 32*t.
-t*(t - 1)**3*(t + 2)
Let j(v) be the first derivative of 273*v**4/20 + 74*v**3/3 + 99*v**2/10 + 2*v/5 - 415. Let j(c) = 0. Calculate c.
-1, -1/3, -2/91
Let x(c) be the first derivative of -c**2/2 - 8*c - 1. Let w be x(-11). Factor -23*i**5 + 17*i**5 - 2*i**4 + 6*i**w - 7*i**4.
-3*i**3*(i + 2)*(2*i - 1)
Determine z so that 26 - 34 + z**2 + 19*z + 18 + 8 = 0.
-18, -1
Let k(t) be the second derivative of t**4/48 - 13*t**3/24 + 5*t**2 + t + 114. Factor k(y).
(y - 8)*(y - 5)/4
Suppose -5*u + 35 = 4*f, -4*u + 3*u = -5*f + 22. Determine p so that -3 + u*p + 6 + 3 - 3*p**2 = 0.
-1, 2
Suppose 82*j - 85*j = -5*h - 12, h = -4*j + 39. Determine g so that 2/3*g**h + 28/3*g + 14/3*g**2 + 16/3 = 0.
-4, -2, -1
Let z(j) = -j**4 - j**2 - 2*j - 2. Let y(d) = d**2 - 13*d - 6. Let n be y(13). Let i(v) = v**2 + v + 1. Let a(m) = n*i(m) - 3*z(m). Let a(h) = 0. What is h?
-1, 0, 1
Let x(g) = 6*g + 82. Let q be x(-13). Suppose -2*j + 2*d - 6 = 4*d, -12 = j + q*d. Factor 1/7 + j*l - 1/7*l**2.
-(l - 1)*(l + 1)/7
Suppose 0 = -10*y + 3*y + 14. Factor 445*v**2 + 2*v**3 - 2*v - 445*v**y.
2*v*(v - 1)*(v + 1)
Let f(g) be the first derivative of 11*g**4/4 - 35*g**3/3 + 14*g**2 - 4*g - 26. Factor f(w).
(w - 2)*(w - 1)*(11*w - 2)
Find c such that -20/9 + 2*c + 2/9*c**2 = 0.
-10, 1
Let z(p) = -p**3 + p**2. Let s(o) = -9*o**3 + 112*o**2 - 900*o - 648. Let w(b) = -s(b) + 6*z(b). Factor w(c).
(c - 18)**2*(3*c + 2)
Let g be 1/(-7)*22/(-264)*42. Solve 0 - g*v - 1/6*v**2 = 0.
-3, 0
Let y be 4 + -1 + (-12)/4. Suppose y = -4*k - 0 + 20. Factor -7*t**4 - 3*t**3 + 2 + 14*t - 6*t**3 - 5*t + k*t**2.
-(t - 1)*(t + 1)**2*(7*t + 2)
Let h(f) be the first derivative of f**6/360 - f**4/72 + 11*f**2/2 + 8. Let i(g) be the second derivative of h(g). Factor i(s).
s*(s - 1)*(s + 1)/3
Suppose 3*z + z = -16. Let s be z/10 - (-1164)/60. Factor -s*q + 10*q + 5*q - 4*q**2.
-4*q*(q + 1)
Let y(w) = w**2 - 16*w - 1. Let x(h) = h + 1. Let k(s) = 2*x(s) + 2*y(s). Factor k(v).
2*v*(v - 15)
Let z(a) be the first derivative of -2*a**3/69 + 10*a**2/23 - 32*a/23 + 90. Factor z(i).
-2*(i - 8)*(i - 2)/23
Suppose 16*q - 32955 = 13*q. Factor -9*y**3 + 4*y**3 + q - 2535*y + 169*y**2 + 26*y**2.
-5*(y - 13)**3
Determine g so that 72/7*g**2 - 2*g**3 + 74/7*g - 12/7 = 0.
-1, 1/7, 6
Let a(p) be the third derivative of -p**8/168 - 4*p**7/315 + p**6/36 + p**5/45 + 37*p**2. What is j in a(j) = 0?
-2, -1/3, 0, 1
Let -3*f**2 + 338 - 177 + 24*f - 182 = 0. What is f?
1, 7
Let l be ((-48)/(-30))/((2/(-5))/1). Let d be (l + -2)/6*4/(-10). Factor d*y**2 - 2/5*y - 4/5.
2*(y - 2)*(y + 1)/5
Let f(c) = -c**3 - 6*c**2 - 2*c - 10. Let u be (1 - 8) + (12/(-3) - -5). Let q be f(u). Factor -4/7 - 6/7*n - 2/7*n**q.
-2*(n + 1)*(n + 2)/7
Suppose 0 = -50*g + 48*g. Determine d so that 2/3*d**3 + g - 4/3*d - 2/3*d**2 = 0.
-1, 0, 2
Let r = -20 - -23. Suppose r + 42 = 5*x. Solve -f - 2*f**2 + 3*f + x*f + f - 18 = 0 for f.
3
Let q(v) be the third derivative of -v**6/32 + 13*v**5/48 + 5*v**4/3 - 5*v**3/2 + 340*v**2. Let q(j) = 0. Calculate j.
-2, 1/3, 6
Suppose 4*j - 5 = 3. Factor 15*w**j + 0*w**2 - 557 + 563 - 21*w.
3*(w - 1)*(5*w - 2)
Let a(y) = 4*y + 2*y**2 + 0*y**2 - 12*y + 6*y. Let u(q) = 2*q**2 - 3*q. Let t(h) = -6*a(h) + 4*u(h). Solve t(i) = 0 for i.
0
Let h(i) be the second derivative of -i**4/42 + 16*i**3/21 - 15*i**2/7 - 7*i. Solve h(c) = 0 for c.
1, 15
Let l be 2944/(-3864) - (-20)/14 - (2 - 6). Factor 4*a - l*a**2 - 2/9*a**4 + 0 + 16/9*a**3.
-2*a*(a - 3)**2*(a - 2)/9
Let p(l) = -l**2 - 13*l + 2. Let d be p(-13). Find j, given that -4*j**4 - 2*j + 10*j**2 + d*j**2 + 5*j + 5*j = 0.
-1, 0, 2
Let p(h) be the first derivative of h**4/4 - 2*h**3 + 11*h**2/2 - 6*h + 63. Solve p(r) = 0 for r.
1, 2, 3
Let u(i) be the first derivative of i**4/48 - i**3/4 - 7*i**2/8 + 44*i + 40. Let k(s) be the first derivative of u(s). Solve k(p) = 0.
-1, 7
Let r = -1045/3 + 355. Let g = r + -6. Factor -2/3*m**2 + 2/3*m - 2/3*m**3 + g.
-2*(m - 1)*(m + 1)**2/3
Let t be -5*(16/10 - 2). Suppose -3*w + 28 - t = 5*i, -5*w + 22 = 3*i. Determine c so that 3*c**4 + c**5 + 0*c**5 + c**i + 2*c**3 + c**5 = 0.
-1, 0
Suppose -102*y = 86 - 80 - 210. Determine m, given that 28/5 + 24/5*m - 4/5*m**y = 0.
-1, 7
Suppose 0 = 7*v - 5*z + 12, -v = -5*z + 6 + 30. Factor -14*m - 10/3 - 2/3*m**5 - 52/3*m**3 - 6*m**v - 68/3*m**2.
-2*(m + 1)**4*(m + 5)/3
Suppose -3*a + 2*p = -2, 0*p = 3*a + p - 8. Factor 4*g**a + g + 172 - 15*g + 84 - 50*g.
4*(g - 8)**2
Let h be (-14)/14 - (1 + -11). Let x be (h + -11)*(-3)/2. Find g, given that 11*g + 6 - 10*g + x*g**2 - 10*g = 0.
1, 2
Let -35/2 + 17/4*v - 1/4*v**2 = 0. Calculate v.
7, 10
Let s(p) be the second derivative of -8*p**7/21 + 4*p**6/15 + 7*p**5/20 + p**4/12 + 2*p - 6. Let s(a) = 0. What is a?
-1/4, 0, 1
Let g(m) be the third derivative of -5*m**8/336 + 11*m**7/42 - 5*m**6/12 - 53*m**5/6 - 665*m**4/24 - 245*m**3/6 + m**2 + m. Factor g(u).
-5*(u - 7)**2*(u + 1)**3
Let t be 6/(-8) + 589/124. Suppose t*n = 20, -3*v + 0*n + 1 = -n. Factor -8/13*p - 2/13*p**v - 8/13.
-2*(p + 2)**2/13
Let i(v) be the second derivative of -4/3*v**3 - 18*v + 0 - 2/3*v**4 - 1/10*v**5 + 0*v**2. Find j, given that i(j) = 0.
-2, 0
Let v(r) be the third derivative of r**6/1080 + r**5/180 - r**4/24 + 7*r**3/3 - 3*r**2. Let w(h) be the first derivative of v(h). Factor w(f).
(f - 1)*(f + 3)/3
Let y be (2 - -8) + -64 + 54. Factor 2/13*p**2 + y*p + 4/13*p**3 + 0 + 2/13*p**4.
2*p**2*(p + 1)**2/13
Factor -5*k + 0 + 5/4*k**3 + 15/4*k**2.
5*k*(k - 1)*(k + 4)/4
Let u(t) be the first derivative of 21*t**5/40 - 9*t**4/4 - 19*t**3/8 + 9*t**2/4 - 57. What is x in u(x) = 0?
-1, 0, 3/7, 4
Let i(p) be the second derivative of -p**9/3024 - p**8/280 - 3*p**7/280 - p**3 - 7*p. Let w(x) be the second derivative of i(x). Suppose w(v) = 0. What is v?
-3, 0
Let j(g) = -5*g + 2*g**2 + 2*g**2 - 4 - 5*g**2. Let c be j(-3). What is w in w**3 - 8*w**c - w**2 + 3*w**4 + 15*w - 4*w**3 - 6 + 0*w**4 = 0?
-2, 1
Let o(c) be the third derivative of 0*c**4 + 0*c**3 + 0 + 1/120*c**6 - 11*c**2 + 0*c - 7/60*c**5. Factor o(j).
j**2*(j - 7)
Let l(c) be the first derivative of 1/3*c**6 + 0*c - 27 + 9/10*c**4 - 2/5*c**2 - 2/15*c**3 + 26/25*c**5. Determine z so that l(z) = 0.
-1, 0, 2/5
Let s(f) be the first derivative of f**4/6 - 10*f**3/9 + 2*f**2 + 20. Find u such that s(u) = 0.
0, 2, 3
Let b = -10856 - -10860. Factor -6*p + 8/3 + 2/3*p**5 + 16/3*p**3 - b*p**4 + 4/3*p**2.
2*(p - 4)*(p - 1)**3*(p + 1)/3
Let d be -1 - 8/48*-6. Let b(f) be the first derivative of -2/9*f**3 + 10 - 2/15*f**5 + 1/4*f**4 + 1/12*f**2 + d*f + 1/36*f**6. Find x such that b(x) = 0.
0, 1
Let k(c) be the second derivative of -1/120*c**6 + 2/3*c**3 - 5*c - 3/20*c**5 + 0 - 9/8*c**4 + 0*c**2. Let q(m) be the second derivative of k(m). Factor q(w).
-3*(w + 3)**2
Suppose -61 = -31*v + 63. Let z(h) be the second derivative of 8*h + 0 + 0*h**2 - 1/15*h**5 + 0*h**3 + 2/9*h**v. Factor z(k).
-4*k**2*(k - 2)/3
Let m(f) be the first derivative of -f**6/21 + 2*f**4/7 + 4*f**3/21 - 3*f**2/7 - 4*f/7 - 61. Let m(h) = 0. Calculate h.
-1, 1, 2
Let u(k) be the second derivative of k**7/210 - k**5/60 - 3*k**2/2 + 18*k. Let b(f) be the first derivative of u(f). Factor b(n).
n**2*(n - 1)*(n + 1)
Let p be (2*(-3)/(-15))/((-7 - -17)/10). What is l in -2/15*l**3 - 2/15 - p*l**2 - 2/5*l = 0?
-1
Let n = 6652 + -6650. Factor 156/7 + 1035/7*g**n + 75/7*g**3 + 792/7*g.
3*(g + 13)*(5*g + 2)**2/7
Let f(r) be the first derivati