(d).
d*(d + 1)**2*(d + 2)/8
Let j(r) = -r**3 + 6*r**2 + 8*r - 7. Let g be j(7). Suppose g = 3*n - 5*a - 22, -n - 2 = -0*n + 3*a. Let 92*k**n + 2*k**2 - 95*k**4 + k**2 = 0. What is k?
-1, 0, 1
Let l = 29 - 29. Let w(t) be the second derivative of 0 + l*t**2 + 1/168*t**7 + 0*t**3 + 1/80*t**5 - 4*t + 1/60*t**6 + 0*t**4. What is j in w(j) = 0?
-1, 0
Factor 0 - 87/4*d - 3/4*d**2.
-3*d*(d + 29)/4
Let p(a) be the third derivative of -a**5/15 + 9*a**4 - 486*a**3 + 15*a**2. Factor p(u).
-4*(u - 27)**2
Suppose -25 = -4*d - 21. Let w(p) be the first derivative of 1/3*p**6 + 0*p**4 + 0*p**2 - d + 0*p + 2/5*p**5 + 0*p**3. Let w(n) = 0. Calculate n.
-1, 0
Let l(b) be the first derivative of -3*b**4/8 - 4*b**3 - 57*b**2/4 - 18*b + 262. Factor l(d).
-3*(d + 1)*(d + 3)*(d + 4)/2
Let o be (-2)/(-5) + 78/(-325). Let u(a) be the first derivative of -o*a**5 + 1 + 0*a**2 + 1/4*a**4 + 1/30*a**6 - 2/15*a**3 + 0*a. Factor u(g).
g**2*(g - 2)*(g - 1)**2/5
Let n(d) be the third derivative of -d**4/8 - 5*d**3/3 + d**2. Let y be n(-4). Factor -c + 6*c + 2*c**y + 2*c - 3*c.
2*c*(c + 2)
Let s be (700/(-875))/(2/(-10)). Let 2/5*p**5 - 4/5*p**3 + 0*p**2 + 0 + 2/5*p + 0*p**s = 0. Calculate p.
-1, 0, 1
Factor 0*c**2 - 3/5*c**5 + 0 + 6/5*c**4 - 3/5*c**3 + 0*c.
-3*c**3*(c - 1)**2/5
Let g(d) = d**2 + 22*d + 23. Let w be g(-21). Factor 5*n**3 - 21*n**2 - 5*n + 21*n**w.
5*n*(n - 1)*(n + 1)
Let v(q) be the second derivative of 0 - 3/20*q**5 + 11/4*q**4 + 6*q**2 + 1/14*q**7 - 6*q**3 - 21*q - 3/10*q**6. Solve v(u) = 0.
-2, 1, 2
Let j = -45 - -27. Let d be j/(-5) - 14/(-35). Suppose -1/4 + 0*p**3 + 1/2*p**2 - 1/4*p**d + 0*p = 0. What is p?
-1, 1
Let z(u) be the first derivative of 3*u**5/5 - 3*u**4/2 - 24*u**3 + 27*u**2 + 405*u - 47. Find c, given that z(c) = 0.
-3, 3, 5
Let c be 7/5 - (1 + 6/(-10)). Let d be ((c + -1)/(-1))/(15 - 16). Find v such that -1/5*v**3 + 0*v + 1/5*v**4 + d - 2/5*v**2 = 0.
-1, 0, 2
Let k(s) be the third derivative of s**6/360 + s**5/180 - 7*s**4/36 - 4*s**3/3 - 638*s**2. Factor k(d).
(d - 4)*(d + 2)*(d + 3)/3
Let w(z) be the second derivative of z**5/15 + 14*z**4/9 + 98*z**3/9 + 5*z - 6. Factor w(l).
4*l*(l + 7)**2/3
Let m(u) be the second derivative of 0*u**5 - 1/3*u**3 + 0*u**2 + 2/15*u**6 - 29*u + 0 + 1/21*u**7 - 1/3*u**4. Factor m(b).
2*b*(b - 1)*(b + 1)**3
Let s(f) = -5*f**2 - f. Let y be s(1). Let a be (-183)/(-6) - y/4. Factor 14*v**2 - 4*v**3 - a*v**2 - 24*v + 2 - 10.
-2*(v + 2)**2*(2*v + 1)
Let n = -50 + 55. Suppose -22 = b + 5*i, -n*b - 3*i = -0*i. Suppose 3/2*c**b + 0 + 3/4*c**2 + 3/4*c**4 + 0*c = 0. Calculate c.
-1, 0
Suppose -3*z - 10 + 10 = 0. Let g(v) be the first derivative of z*v + 0*v**2 - 2/9*v**3 - 7. Factor g(p).
-2*p**2/3
Let w(x) be the third derivative of 0*x + 4/21*x**3 + 0 + 0*x**4 - 1/70*x**5 + 11*x**2 + 1/420*x**6. Factor w(y).
2*(y - 2)**2*(y + 1)/7
Suppose 2/11*g**5 - 4/11*g**2 - 32/11*g**3 - 12/11*g**4 + 30/11*g + 16/11 = 0. What is g?
-1, 1, 8
Let c = 111 + -108. Let y be ((-69)/92)/(c/(-2)). Solve 1/2 - y*p**2 + 1/2*p - 1/2*p**3 = 0 for p.
-1, 1
Let s(g) be the second derivative of g**6/24 - 5*g**4/24 - g**2/2 + 11*g. Let i(w) be the first derivative of s(w). Factor i(d).
5*d*(d - 1)*(d + 1)
Let s(j) be the third derivative of -2*j**7/105 + j**6/5 - 4*j**5/15 - j**4 + 10*j**3/3 - 22*j**2 - 8*j. Find i such that s(i) = 0.
-1, 1, 5
Let d(t) be the third derivative of 0 + 0*t**3 + 1/18*t**4 + 0*t + 1/180*t**6 - 1/30*t**5 + 2*t**2. Factor d(k).
2*k*(k - 2)*(k - 1)/3
Let a = -14 + 18. Suppose 3 - 11 = -a*p. Factor -3*b + 3*b**p + 3 - 2 - 2*b**3 + 0*b + b**3.
-(b - 1)**3
Let t(q) = q**2 - 8*q + 10. Let z be t(7). Suppose 5*d - 7 = z. Determine k so that d*k**3 - 8*k**2 + 2*k**3 - 10*k**3 + 2*k**3 = 0.
-2, 0
Find g such that 2/3*g**5 - 4/3 - 14/9*g + 20/3*g**2 - 8/3*g**3 - 16/9*g**4 = 0.
-2, -1/3, 1, 3
Let l(y) be the third derivative of y**7/105 + y**6/10 + 11*y**5/30 + y**4/2 - 54*y**2. Suppose l(v) = 0. What is v?
-3, -2, -1, 0
Let b(u) = 12*u**2 + 83*u - 5. Let k be b(-7). Determine n so that -4/3*n + 2/3*n**5 - 10/3*n**k + 2/3*n**4 - 2*n**3 + 0 = 0.
-1, 0, 2
Let t be 4/(-12) - 7/(-3). Suppose 5*m - t*c - 22 = 0, 3*m = 4*m - 3*c - 7. Suppose -4/3*f + 0 + 14/3*f**m - 14/3*f**2 + 4/3*f**3 = 0. What is f?
-1, -2/7, 0, 1
Let u = -23/172 + 1583/1548. Factor -8/9*q + 2/9*q**3 + u - 2/9*q**2.
2*(q - 2)*(q - 1)*(q + 2)/9
Let y(n) = -2*n**3 + 4*n**2 - 4*n + 3. Let m be y(2). Let z = 10 + m. Suppose -8 - 8 + 5*x**2 + 16 + z*x = 0. What is x?
-1, 0
Find z such that -4*z - 2/7*z**3 - 18/7*z**2 + 0 = 0.
-7, -2, 0
Suppose -v = -5*v + 20. Suppose -4*d - 2 = -v*d. What is m in 16*m**5 + 7*m**2 + 48*m**4 + 5*m**5 + 33*m**3 + 0*m**d - m**2 = 0?
-1, -2/7, 0
Let d = 8 + -7. Let 2 - 3*h**2 + d + 6*h + 6 = 0. What is h?
-1, 3
Suppose -139 = 4*p - 3*f + 16, 3*f = 3*p + 120. Let l = -30 - p. Let 2*x**3 + 0*x**5 + 0*x**l - 2*x**5 = 0. What is x?
-1, 0, 1
Suppose -2*f + h + 2 = -11, h = -5*f + 15. Suppose -f*y**3 + 0*y**2 - 15*y**2 - 10*y - y**3 = 0. Calculate y.
-2, -1, 0
Let h(l) be the third derivative of 0 + 0*l - 1/24*l**4 + 30*l**2 - 1/20*l**5 + 1/120*l**6 + 1/210*l**7 + 1/3*l**3. Factor h(v).
(v - 1)**2*(v + 1)*(v + 2)
Let u = 32639/4 + -8159. Factor -1/2 + 5/4*b + u*b**2.
(b + 2)*(3*b - 1)/4
Let 245*b**3 - 3046*b**2 - 1554*b + 6250 - 2071*b + 181*b**2 - 5*b**4 = 0. Calculate b.
-2, 1, 25
Let p(n) be the first derivative of -2 + 1/14*n**4 - 4/21*n**3 + 16/7*n - 4/7*n**2. Factor p(u).
2*(u - 2)**2*(u + 2)/7
Let j(l) = -l**2 + 6*l + 2. Let r be j(7). Let w be r/3*36/(-16). What is v in -9/4*v + w*v**2 - 3/2 = 0?
-2/5, 1
Factor -20*c**4 - 15*c**3 + 28*c**3 + 5*c**5 - 6*c**2 + 55*c - 73*c**3 - 4*c**2 + 30.
5*(c - 6)*(c - 1)*(c + 1)**3
Let g(a) be the third derivative of a**7/630 - a**6/30 + 23*a**5/90 - 5*a**4/6 + 25*a**3/18 - 579*a**2. Factor g(s).
(s - 5)**2*(s - 1)**2/3
Let z = -61 - -63. Let 0*u**3 - 5*u**2 - u**4 + 6*u**3 + 2*u - z*u**3 + 0*u**3 = 0. Calculate u.
0, 1, 2
Let c = 37 + -35. Let w(j) = j**3 - 2*j**2 + 2. Let r be w(c). What is h in 7/4*h**r + 0 + 1/2*h = 0?
-2/7, 0
Let l(v) be the first derivative of -8*v**6/15 - 12*v**5/25 + 13*v**4/5 + 4*v**3/15 - 18*v**2/5 + 8*v/5 - 79. Determine q so that l(q) = 0.
-2, -1, 1/4, 1
Suppose -60 = -17*g - 3*g. Let q be (-4)/((-10)/15*g). Suppose -14/17*r**q + 4/17 + 10/17*r = 0. What is r?
-2/7, 1
Let c = 472 - 469. Let i(v) be the first derivative of 1/3*v**c + 4 + 9*v + 3*v**2. Determine n, given that i(n) = 0.
-3
Let c = -880 + 880. Let d(j) be the third derivative of -1/480*j**6 - 1/12*j**3 + 0*j + 0*j**5 + 1/32*j**4 + 3*j**2 + c. Factor d(r).
-(r - 1)**2*(r + 2)/4
Suppose -k + 11 = 4*r, 4*r - 147 + 124 = -5*k. Factor 0 - 2/7*w**k + 0*w - 2/7*w**2.
-2*w**2*(w + 1)/7
Let r = 43931/55 - 8784/11. Find a, given that 2/5*a - r*a**2 - 1/5 = 0.
1
Let w = 32 + -40. Let b be (8 - 3)/(-20) - 2/w. Factor 0*c + b + 8/9*c**3 + 2/9*c**4 + 8/9*c**2.
2*c**2*(c + 2)**2/9
Let s(f) = -3*f + 63. Let q be s(21). Factor 3/2*r**2 + 1/2*r**3 + 0 + q*r.
r**2*(r + 3)/2
Let p be (-65)/(-15) + 0 + -5 + 1. Let w(u) be the first derivative of -u**6 + 0*u + 4/3*u**4 + 6 - 4/3*u**3 + 4/5*u**5 + p*u**2. Determine k so that w(k) = 0.
-1, 0, 1/3, 1
Let g be 100/36 - (112/21 - 3). Let n(z) = 2*z**3 + z**2 - z. Let o be n(1). Find r, given that -g*r**o + 0*r + 2/9*r**3 + 0 = 0.
0, 2
Let l = -1293 - -1296. Let h(t) be the first derivative of 5 - 27/5*t**5 - 6*t**2 - 16*t**l + 0*t - 63/4*t**4. Factor h(i).
-3*i*(i + 1)*(3*i + 2)**2
Suppose -7*y + 1/3*y**3 + 0 - 20/3*y**2 = 0. What is y?
-1, 0, 21
Factor -14/3 + 1/6*p**2 + 1/2*p.
(p - 4)*(p + 7)/6
Suppose -102*o - 114 = -318. Factor 2 - 8*l + 2*l**3 - 1/2*l**o.
(l - 2)*(l + 2)*(4*l - 1)/2
Let p = -2461/3 - -821. Let q(l) be the second derivative of 2/3*l**4 - 4*l**2 - 1/5*l**5 + 6*l + p*l**3 + 0. Let q(g) = 0. What is g?
-1, 1, 2
Let g(n) be the third derivative of 1/15*n**5 + 5/6*n**3 + 0 + 19/48*n**4 - 1/240*n**6 - 8*n + n**2. Factor g(b).
-(b - 10)*(b + 1)**2/2
Solve -7*p**2 - 14*p**2 + 0*p**3 - 34*p**3 - 6*p - 3*p**5 + 0*p**5 + 7*p**3 - 15*p**4 = 0.
-2, -1, 0
Let j(g) = 6*g**2 - 440*g - 9691. Let k(l) = l**2 - 88*l - 1938. Let n(t) = 4*j(t) - 22*k(t). Find h such that n(h) = 0.
-44
Let v(c) = -c + 5. Let k be v(2). Factor -3*d + 8*d**2 - 11 + 6*d + k + d - 4*d**3.
-4*(d - 2)*(d -