 a(j).
(j + 1)**2*(j + 2)/3
Let w be 57/21 + 4/14. Suppose -3*g + x = -27 + 11, 2 = g + w*x. Solve -g*r**2 + r**5 - 2 - 2*r**4 + r - 2*r**3 + 4*r**2 + 5*r**2 = 0.
-1, 1, 2
Let q(r) be the first derivative of -2*r**5/15 - r**4/2 + 4*r**3/9 + 4*r**2 + 16*r/3 - 19. Suppose q(n) = 0. Calculate n.
-2, -1, 2
Determine w, given that -37*w**3 - 17*w**3 - 329*w**2 + 20*w**4 + 140 - 440*w - 136*w**2 - 11*w**3 = 0.
-2, 1/4, 7
Suppose -5*d = 2*o + 19, 5 = 12*d - 13*d. Find n, given that o + 15/4*n**2 - 27/4*n**4 - 9*n + 9*n**3 = 0.
-1, 2/3, 1
Let b(k) be the third derivative of k**5/60 + k**4/2 + 10*k**3/3 + 11*k**2 - 3. Factor b(h).
(h + 2)*(h + 10)
Suppose -12 = -3*p, -10*v - 24 = -12*v - 3*p. Let r(u) be the third derivative of -8*u**2 + 0*u - 1/50*u**5 + 1/40*u**4 + 1/200*u**v + 0 + 0*u**3. Factor r(t).
3*t*(t - 1)**2/5
Let t(k) be the first derivative of -k**5/4 + 5*k**4/16 + 5*k**3/4 - 25*k**2/8 + 5*k/2 + 585. Solve t(n) = 0 for n.
-2, 1
Let m = -200/27 + 40009/5400. Let w(i) be the third derivative of 0*i - 1/15*i**3 - 3*i**2 - 1/40*i**4 + m*i**6 + 0*i**5 + 0. Factor w(u).
(u - 2)*(u + 1)**2/5
Let f be (14/(-21))/((-2)/9). Factor -5*t**3 + t**3 + 8*t + 0*t**f - 4*t.
-4*t*(t - 1)*(t + 1)
Let l be 13 - (-2 + 16) - -3. Suppose -1/2*g**l + 0 - 1/2*g = 0. Calculate g.
-1, 0
Let a(c) = 2*c**4 - c**3 + c**2 + c. Let r(x) = 22*x**4 - 22*x**3 + 8*x**2 + 22*x. Let p(n) = 10*a(n) - r(n). Find i, given that p(i) = 0.
-1, 0, 1, 6
Let d be 40*(0 + 1) + 4. Factor 5*g + 7*g**3 - 4 + d - 12*g**3 - 40*g**2.
-5*(g - 1)*(g + 1)*(g + 8)
Let h(n) be the first derivative of -4*n**3/3 - 2*n**2 + 80*n + 182. Factor h(q).
-4*(q - 4)*(q + 5)
Let y(l) be the second derivative of 3*l**7/56 + 4*l**6/5 + 21*l**5/8 + 3*l**4 - l**3/8 - 3*l**2 - 84*l. Determine v, given that y(v) = 0.
-8, -1, 1/3
Let q(h) be the first derivative of h**4/4 + 17*h**3/3 - 17*h**2/2 + 21*h - 9. Let p be q(-18). Let 17*u - 8 + 3*u**p + 14 - 9 - 9*u**2 - 8*u = 0. What is u?
1
Suppose -31*h - 155*h + 0 = -0. Let x(r) = -r**3 + 3*r**2 + 5*r - 1. Let q be x(4). Let -1/6*l + h*l**q + 1/3*l**4 + 1/6*l**5 - 1/3*l**2 + 0 = 0. What is l?
-1, 0, 1
Let v = 102817/2 - 51407. Find j, given that -v*j**3 + 3/2*j - j**2 - 1/4*j**4 + 5/4 = 0.
-5, -1, 1
Let b(n) = 12*n**4 + 12*n**3 - 20*n**2 - 24*n + 4. Let u(a) = -26*a**4 - 24*a**3 + 39*a**2 + 46*a - 9. Let w(c) = -9*b(c) - 4*u(c). Factor w(t).
-4*t*(t - 2)*(t + 1)*(t + 4)
Let z(k) be the second derivative of -3*k**5/20 - 18*k**4 - 864*k**3 - 20736*k**2 - 86*k - 2. Suppose z(w) = 0. What is w?
-24
Find s, given that -36*s**2 + 119*s**4 - 8*s - 39*s**3 - 4*s - 3*s**5 - 137*s**4 = 0.
-2, -1, 0
Let s(u) be the second derivative of u**5/15 - u**4/3 - 4*u**3/3 + 16*u**2/3 + 4*u - 7. Suppose s(w) = 0. Calculate w.
-2, 1, 4
Suppose 0*j - 5 = -j + 5*t, -2*t = 5*j - 79. Suppose -16*a + 7*a**2 + j*a - 8*a**2 = 0. Calculate a.
-1, 0
Suppose 66*j = 68*j - 10. Factor -2*o - 17*o**3 - 5*o**2 + j*o + 12*o**3 + 7*o.
-5*o*(o - 1)*(o + 2)
Find p, given that -1/3*p - 1/3 + 2/3*p**3 + 2/3*p**2 - 1/3*p**4 - 1/3*p**5 = 0.
-1, 1
Let m(t) be the second derivative of 0 - 13*t - 13/75*t**6 + 1/15*t**3 + 0*t**2 + 4/105*t**7 + 3/10*t**5 - 7/30*t**4. Factor m(z).
2*z*(z - 1)**3*(4*z - 1)/5
Let k(a) = a**3 + 5*a**2 + a + 32. Let j be k(-5). Let h be (j/15)/(12 - 9). Factor 9/5*u - 6/5 - h*u**2.
-3*(u - 2)*(u - 1)/5
Let y(m) be the third derivative of 1/60*m**6 - 2/9*m**3 + 16*m**2 - 13/180*m**5 - 1/630*m**7 + 0 + 1/6*m**4 + 0*m. Factor y(i).
-(i - 2)**2*(i - 1)**2/3
Let m(z) be the first derivative of 2*z**6/3 - 36*z**5/5 + 14*z**4 + 8*z**3/3 - 30*z**2 + 28*z - 83. Factor m(f).
4*(f - 7)*(f - 1)**3*(f + 1)
Let p(h) = -15*h**2 + 318*h - 8427. Let s(k) = 3*k**2. Let j(w) = -p(w) - 4*s(w). Factor j(a).
3*(a - 53)**2
Let q(i) be the third derivative of 2/75*i**5 + 0*i**3 - 9*i**2 + 0 - 2/525*i**7 + 0*i + 0*i**4 + 1/150*i**6. What is d in q(d) = 0?
-1, 0, 2
Let x(n) be the first derivative of -n**4/18 + 2*n**3/3 + 22*n**2/9 + 41. Factor x(h).
-2*h*(h - 11)*(h + 2)/9
Let h(g) = -13*g**2 + 109*g - 7. Let s(l) = -6*l**2 + 54*l - 3. Let x(m) = 3*h(m) - 7*s(m). Factor x(u).
3*u*(u - 17)
Let a(p) = -2*p**3 + 92*p**2 - 174*p. Let h(j) = 2*j**3 - 93*j**2 + 175*j. Let x(c) = -6*a(c) - 4*h(c). Determine w so that x(w) = 0.
0, 2, 43
Let v(r) be the second derivative of -2*r**2 + 1/3*r**3 + 0 - 22*r - 1/15*r**6 + 1/2*r**4 - 1/10*r**5. Factor v(s).
-2*(s - 1)**2*(s + 1)*(s + 2)
Let w(t) be the first derivative of 3*t**4/20 + 57*t**3/5 + 470. Factor w(f).
3*f**2*(f + 57)/5
Suppose -9 = f + x, 26*f + 7*x = 28*f - 81. Let j be (28/3)/(-1 - -3). Factor -16/5*o + 8/15 + j*o**f.
2*(5*o - 2)*(7*o - 2)/15
Factor 7*b**4 - 13*b**4 + 8*b**4 + 2*b**3 - 4*b**2.
2*b**2*(b - 1)*(b + 2)
Let k be (-2)/(-18) - 27/(-1944). Let f(c) be the second derivative of -k*c**2 + 1/12*c**3 + 0 - 4*c - 1/48*c**4. Factor f(d).
-(d - 1)**2/4
Suppose -q + 0*q + 5 = -3*v, v + 1 = 0. Let u(z) be the second derivative of 9/4*z**2 - 3*z + 0 + q*z**3 + 13/24*z**4 + 1/20*z**5. Factor u(t).
(t + 3)**2*(2*t + 1)/2
Let b(o) be the third derivative of o**5/21 - 76*o**4/21 + 40*o**3/7 + 98*o**2. Factor b(t).
4*(t - 30)*(5*t - 2)/7
Let d(o) be the third derivative of 1/7*o**3 + 1/140*o**5 + 0 + 0*o + 12*o**2 - 3/56*o**4. Find l such that d(l) = 0.
1, 2
Let k be (-42)/12 - (0 + -1 - 3). Let t(j) be the first derivative of k*j**4 - 2*j**3 - 2*j + 1 + 3*j**2. Let t(y) = 0. What is y?
1
Determine o so that -17/2*o**3 + 99*o**2 + 1/4*o**4 + 1331/4 - 847/2*o = 0.
1, 11
Let q(k) be the third derivative of k**7/210 + k**6/120 - k**5/6 + k**4/3 - 2*k**2 + 3*k. Factor q(c).
c*(c - 2)*(c - 1)*(c + 4)
Suppose 2*g + 2*g = 12. Let v(i) = 125*i**2 + 0*i**3 - 109*i**2 - 4*i**3 - 21*i. Let f(w) = -2*w**3 + 8*w**2 - 11*w. Let z(p) = g*v(p) - 5*f(p). Solve z(m) = 0.
0, 2
Suppose 0 = 5*a - 8768 + 8733. Let v(y) be the third derivative of -1/10*y**6 + 0*y - a*y**2 + 0*y**3 + 0 + 1/4*y**5 - 1/8*y**4. Factor v(u).
-3*u*(u - 1)*(4*u - 1)
Suppose -3*a + 2*a = 0. Suppose a*l + 2*l = 10. Factor -3*v**4 - 4*v - v**2 - 4*v**3 - l + 4 + 2*v**4 - 5*v**2.
-(v + 1)**4
Solve 72/17 - 98/17*w + 28/17*w**2 - 2/17*w**3 = 0 for w.
1, 4, 9
Suppose 84500 - 929*c - 371*c - 779886*c**2 + 779891*c**2 = 0. Calculate c.
130
Let k(x) be the second derivative of x**5/130 + 3*x**4/26 + 2*x**3/13 - 16*x**2/13 - 13*x - 1. Factor k(i).
2*(i - 1)*(i + 2)*(i + 8)/13
Let r(x) = 15*x**4 + 73*x**3 - 103*x**2 - 80*x + 95. Let g(j) = -8*j**4 - 36*j**3 + 52*j**2 + 40*j - 48. Let s(n) = 7*g(n) + 4*r(n). Find m such that s(m) = 0.
-11, -1, 1
Let -80/7*s + 2/7*s**2 - 82/7 = 0. Calculate s.
-1, 41
Let g(h) = -15*h**4 - 145*h**3 - 95*h**2 + 35*h. Let v(c) = 2*c**4 + 18*c**3 + 12*c**2 - 4*c. Let n(m) = 3*g(m) + 25*v(m). Factor n(z).
5*z*(z + 1)**3
Let w(r) be the third derivative of -r**7/630 + 7*r**6/360 + r**5/60 - 55*r**4/72 - 25*r**3/9 - 2*r**2 + 2. Factor w(h).
-(h - 5)**2*(h + 1)*(h + 2)/3
Let g(a) be the third derivative of a**6/300 - 13*a**5/600 - 13*a**4/240 + a**3/15 + 104*a**2. Solve g(k) = 0.
-1, 1/4, 4
Let i = -2 + 7. Let p(v) = v - 3. Let s be p(i). Suppose -2*n**3 + 13*n - 2*n**s - 13*n = 0. Calculate n.
-1, 0
Let o(r) be the second derivative of r**7/42 - 11*r**6/15 + 39*r**5/5 - 63*r**4/2 + 81*r**3/2 - 312*r. Factor o(y).
y*(y - 9)**2*(y - 3)*(y - 1)
Suppose r + 5*o - 33 = 0, -5 + 34 = r + 4*o. Let l be ((-1612)/(-48))/r + (-2)/8. Factor -l*x - 3*x**2 - 5/3*x**3 - 1/3*x**4 - 2/3.
-(x + 1)**3*(x + 2)/3
Let g(h) be the first derivative of 2*h**4/5 + 10*h**3/3 + 26*h**2/5 + 2*h + 15. Factor g(s).
2*(s + 1)*(s + 5)*(4*s + 1)/5
Suppose -6*x = -5*h - 3*x + 7, -2*x - 8 = -5*h. Let i = 6 + -4. Factor 6*g**2 + g**h + 2*g - 5*g**i.
2*g*(g + 1)
Let s(m) be the third derivative of m**9/211680 - m**8/70560 + 3*m**5/20 + 8*m**2. Let a(o) be the third derivative of s(o). Factor a(r).
2*r**2*(r - 1)/7
Find k such that 9/7*k + 54/7 - 3/7*k**2 = 0.
-3, 6
Let c = -25819/7 + 3689. Determine l, given that 1/7*l + 0 - c*l**2 = 0.
0, 1/4
Let x(w) be the first derivative of -1/2*w**2 - 19 + 0*w + 2/3*w**3. Find h, given that x(h) = 0.
0, 1/2
Let d(q) = -9*q**3 - 23*q**2 - 11*q + 53. Let r(u) = -4*u**3 - 12*u**2 - 6*u + 26. Let m(o) = 4*d(o) - 10*r(o). Factor m(f).
4*(f - 1)*(f + 2)*(f + 6)
Let a(c) = 5*c**2 - 389*c + 412. Let g(