+ j**7/1440 - j**6/480 + 3*j**4/8 - 16*j**2. Let h(x) be the second derivative of k(x). Factor h(c).
-c*(c - 2)*(c - 1)*(c + 3)/4
Let w be 0*1*(-2)/(-4). Let j(y) be the second derivative of 3*y + w - 81/140*y**5 + 3/2*y**4 + 3/7*y**2 - 17/14*y**3. Determine o, given that j(o) = 0.
2/9, 1/3, 1
Let t = -7 - -20. Suppose g - 11 = -4*i, 5*i - t = -0*i - g. Factor z**2 + 8 + z**2 + 2*z - 8*z - 4*z**i.
-2*(z - 1)*(z + 4)
Let g = 9294 - 9288. Let f be (-3)/(39/(-12) - -1). Suppose -28/3*x**3 - 2/3*x**5 + f - g*x + 4*x**4 + 32/3*x**2 = 0. Calculate x.
1, 2
Let u = -69 + 109. Factor 305 - 6*z**2 - 93 + 8*z**4 + 140*z - u*z**3 - 114.
2*(z + 1)**2*(2*z - 7)**2
Let j(o) be the third derivative of -o**5/210 + 8*o**4/21 + 11*o**3/7 - 4*o**2 + 1. Factor j(u).
-2*(u - 33)*(u + 1)/7
Let x(q) be the first derivative of 0*q - 4/9*q**3 + 11 + 1/6*q**4 + 1/3*q**2. Determine a, given that x(a) = 0.
0, 1
Let n(f) = -9*f + 29. Let z be n(3). Suppose 1/4*t**z - 5/4*t**4 - 1/4*t**3 + 0*t + 0 - 3/4*t**5 = 0. What is t?
-1, 0, 1/3
Let w(q) = 9*q**3 - 26*q**2. Let x(v) = -3*v**3 + 9*v**2. Let g(f) = -3*w(f) - 8*x(f). Factor g(n).
-3*n**2*(n - 2)
Factor -3/7*m**2 - 12/7 - 12/7*m.
-3*(m + 2)**2/7
Factor 0*g - 2/7*g**2 + 1/7*g**5 + 5/7*g**3 - 4/7*g**4 + 0.
g**2*(g - 2)*(g - 1)**2/7
Let t be (-19)/38 + (-90)/(-4). Determine o, given that -10*o**3 + 4 + 44*o**3 + 12*o + 20*o**2 + 10*o + 10*o**4 + t*o**2 = 0.
-1, -2/5
Let t(z) = z**3 + z**2. Suppose 0 = 3*p - 0 - 3. Let u be t(p). Factor -4 + a + 3*a + 2*a**4 - a**4 + 3*a**u - a**3 - 3*a**3.
(a - 2)**2*(a - 1)*(a + 1)
Let p(l) be the third derivative of 10*l**2 - 5/12*l**4 + 0*l + 0 - 1/12*l**5 + 1/42*l**7 - 5/336*l**8 + 0*l**3 + 1/8*l**6. Determine j so that p(j) = 0.
-1, 0, 1, 2
Let c be 10/(-4)*3/(-30)*28. Find w, given that -45*w**2 + 18*w - w - c*w = 0.
0, 2/9
Let y = -34/3 + 2/3. Let k = 5/6 - y. Determine t, given that 10*t**2 + k*t**3 + 0 + 7/2*t**4 + 2*t = 0.
-2, -1, -2/7, 0
Let z be (-76)/(-22) + 174/319. Suppose 4/5 + 13/5*r**2 + 1/5*r**z - 12/5*r - 6/5*r**3 = 0. Calculate r.
1, 2
Let q be (7/1323)/(3/((-3537)/(-15))). Let r = q + -1/63. Let r*o**2 + 0 - 2/5*o**4 + 2/5*o**5 + 0*o - 2/5*o**3 = 0. Calculate o.
-1, 0, 1
Let -1740/7*w + 450/7 - 8/7*w**3 - 34*w**2 = 0. Calculate w.
-15, 1/4
Let u be (8/(-6))/((-36)/54). Let l(j) be the second derivative of 5*j + 1/48*j**4 + 0 - 1/4*j**u - 1/24*j**3. Solve l(v) = 0.
-1, 2
Let g(f) = -4*f**4 + 11*f**3 - 148*f**2 - 511*f + 2359. Let t(z) = -3*z**4 + 12*z**3 - 147*z**2 - 510*z + 2358. Let q(v) = -6*g(v) + 7*t(v). Factor q(n).
3*(n - 4)**2*(n + 7)**2
Let y(b) be the first derivative of -3*b**4/4 + 3*b**2/2 - 120. Find c, given that y(c) = 0.
-1, 0, 1
Let f(s) be the first derivative of 5*s**7/42 - s**6/3 - s**5/6 + 5*s**4/3 - 5*s**3/2 - s**2 + 6. Let j(l) be the second derivative of f(l). Factor j(b).
5*(b - 1)**2*(b + 1)*(5*b - 3)
Suppose 1 = -5*w + 4*y - 0*y, -5*w + 11 = -y. Suppose -8*r**2 + w*r**2 + r**2 + 12*r = 0. Calculate r.
0, 3
Let i = 143 - 138. Let y be i + -5 + (-4)/(-14). Factor -6/7*g + 0*g**2 - 4/7 + y*g**3.
2*(g - 2)*(g + 1)**2/7
Let h be 1 - 2*(-4)/2. Suppose -2*x = -h*l - 7*x + 35, 4*x = -5*l + 30. Let -5 + 2 + 3 + l*m**2 - 4*m = 0. Calculate m.
0, 2
Let b(p) be the first derivative of 2/5*p + 17 + 1/10*p**2 - 1/5*p**3. Determine f so that b(f) = 0.
-2/3, 1
Let r = -7/467 - -955/1401. Factor r*c**3 + 0 + 0*c + 0*c**4 + 4/9*c**2 - 2/9*c**5.
-2*c**2*(c - 2)*(c + 1)**2/9
Let v(y) be the third derivative of 0*y**4 + 0*y + 2/15*y**3 - 1/300*y**5 + 0 - 6*y**2. Factor v(a).
-(a - 2)*(a + 2)/5
Let m(q) be the third derivative of -q**5/330 - 37*q**4/66 + 25*q**3/11 - 3*q**2 - 71. Factor m(k).
-2*(k - 1)*(k + 75)/11
Let d(w) be the third derivative of w**6/720 + w**5/60 + w**4/18 - 94*w**2. Suppose d(h) = 0. Calculate h.
-4, -2, 0
Determine q so that 3/4*q**2 - 9/2*q - 12 = 0.
-2, 8
Let r(a) = a**2 - a + 13. Let b = -14 - -2. Let y(d) = 18. Let w(x) = 7. Let m(p) = b*w(p) + 5*y(p). Let k(q) = 5*m(q) - 2*r(q). Factor k(i).
-2*(i - 2)*(i + 1)
Let a(p) be the third derivative of 1/21*p**4 + 0*p - 6*p**2 + 1/245*p**7 + 0*p**3 + 1/420*p**6 + 0 - 4/105*p**5. Determine b, given that a(b) = 0.
-2, 0, 2/3, 1
Let q(k) = 59*k + 7. Let h be q(-2). Let f = h + 779/7. Factor -f*d**2 + 2/7*d + 2/7*d**4 + 0 - 2/7*d**3.
2*d*(d - 1)**2*(d + 1)/7
Suppose 180 = 4*t + 168. Factor 5/6*u**2 + 1/6*u**4 - 2/3*u**t + 0 - 1/3*u.
u*(u - 2)*(u - 1)**2/6
Factor 176/7 + 174/7*z - 2/7*z**2.
-2*(z - 88)*(z + 1)/7
Let w be 4 + (-8)/(4/1). Determine l so that 0 + 21*l + 4 + 2*l**3 - w - 15*l + 6*l**2 = 0.
-1
Let d(y) be the second derivative of 3*y**5/160 + 11*y**4/96 + y**3/4 + y**2/4 - 2*y - 120. Factor d(a).
(a + 1)*(a + 2)*(3*a + 2)/8
Let l = -821 - -824. Factor -4/5*x**2 + 0*x + 4/5*x**l + 0.
4*x**2*(x - 1)/5
Let f(o) be the second derivative of o**6/420 - o**5/105 - o**4/84 + 2*o**3/21 - 4*o**2 - 12*o. Let k(g) be the first derivative of f(g). What is j in k(j) = 0?
-1, 1, 2
Let g(j) = j**3 - 9*j**2 - 9. Let n(m) = m**2 + 1. Let a be 294/8 + 6/(-8). Let d(o) = a*n(o) + 4*g(o). Factor d(f).
4*f**3
Let s(f) be the second derivative of -5*f**4/32 - f**3/4 + 3*f**2/16 + 3*f + 3. Determine n, given that s(n) = 0.
-1, 1/5
Find z, given that 32/3*z + 2/9*z**2 + 128 = 0.
-24
Find l, given that -52 + 10*l**2 + 2*l - 35*l**3 + 33*l**3 + 42 = 0.
-1, 1, 5
Let d = -3/877 - -2652/6139. Suppose 0*q + 0*q**2 - d*q**4 + 3/7*q**3 + 0 = 0. What is q?
0, 1
Find w, given that -130/19*w**2 + 46/19*w + 16/19*w**5 + 154/19*w**3 - 4/19 - 82/19*w**4 = 0.
1/8, 1, 2
Let z(n) be the second derivative of -2*n**7/63 + 2*n**6/9 - n**5/3 - 5*n**4/9 + 4*n**3/3 + 3*n + 7. Find c, given that z(c) = 0.
-1, 0, 1, 2, 3
Let z(t) = -t**2 - 6*t. Let c(j) = 6*j. Let m(h) = -21*h. Let k(l) = -22*c(l) - 6*m(l). Let i(s) = -2*k(s) + 3*z(s). Solve i(w) = 0.
-2, 0
Let q be 826/(-714) - (-7)/3. Factor -2/17*k**3 - q*k**2 - 50/17*k + 0.
-2*k*(k + 5)**2/17
Let y be 16/7 + (4 + -13 - -7). Let d(u) be the first derivative of 1/14*u**4 + 6 + 2/21*u**3 - y*u - 1/7*u**2. Factor d(n).
2*(n - 1)*(n + 1)**2/7
Suppose -3*t + 3*y + 6 = 6*y, 5*t + 10 = 5*y. Factor 1/3*p**3 + t - 2/3*p - 1/3*p**2.
p*(p - 2)*(p + 1)/3
Factor 5*l**5 - 267*l**3 + 581*l**4 - 358*l**3 + 16790*l + 109760 + 2810*l - 3325*l**2 - 556*l**4.
5*(l - 8)**2*(l + 7)**3
Let h be 424/(-88) - 15/(-3). Factor -2/11*x**3 - 6/11*x**2 - 6/11*x - h.
-2*(x + 1)**3/11
Let b(p) be the second derivative of 20*p + 1/9*p**3 - 1/30*p**5 - 1/18*p**4 + 1/3*p**2 + 0. Let b(k) = 0. Calculate k.
-1, 1
Let w = 87 - 87. Let i(l) be the second derivative of 5*l + 0 + w*l**3 - 1/20*l**5 + 0*l**2 + 1/30*l**6 + 0*l**4. Determine g so that i(g) = 0.
0, 1
Let x(i) = i**4 - 2. Let c(q) = 9*q**3 + 20*q**2 + 12*q + 2. Let a(g) = -c(g) - x(g). Factor a(o).
-o*(o + 1)*(o + 2)*(o + 6)
Let w(c) = 10*c**4 + 80*c**3 - 170*c**2 - 260*c - 55. Let x(o) = -o**4 - 9*o**3 + 19*o**2 + 29*o + 6. Let k(d) = -4*w(d) - 35*x(d). Solve k(a) = 0 for a.
-1, 2
Let r be -1*3*1/(-3). Factor -r + 8*p - 3*p**2 - p**3 + 4*p + 13 - 2*p**3.
-3*(p - 2)*(p + 1)*(p + 2)
Find d such that -54/11*d**2 - 338/11 - 2/11*d**3 - 390/11*d = 0.
-13, -1
Let m(k) = k**3 - 4*k**2 - 21*k. Let h be m(7). Let t(s) be the second derivative of -1/24*s**4 + h + 0*s**3 + 1/4*s**2 + 2*s. Factor t(f).
-(f - 1)*(f + 1)/2
Factor -9*s - 3/7*s**2 - 60/7.
-3*(s + 1)*(s + 20)/7
Let d(p) be the first derivative of p**6/14 + 6*p**5/7 + 18*p**4/7 - 10*p**3/7 - 75*p**2/14 + 1028. Suppose d(j) = 0. What is j?
-5, -1, 0, 1
Let y(r) be the first derivative of 0*r + 1/28*r**4 - 2/21*r**3 + 1/14*r**2 - 27. Factor y(c).
c*(c - 1)**2/7
Suppose 0 = -5*n - 5*v + 30, 4*n + n - 33 = -2*v. Let g be 5/(-45)*3 - n/(-3). Find a, given that 4/7*a**3 - 2/7*a**4 + 0*a + 0 - 2/7*a**g = 0.
0, 1
Let g = 7 + -4. Suppose -3*p - 3*h + 4*h + 5 = 0, -3*p = -3*h - 15. Factor 5*v**5 - 2*v**3 + 4*v**4 - 4*v**5 + p*v**g - 3*v**4.
v**3*(v - 1)*(v + 2)
Let t be 22/150 - (-59)/(-885). Let o(r) be the second derivative of 13*r + 0*r**4 + 4/15*r**3 + 2/5*r**2 + 0 - 2/75*r**6 - t*r**5. Factor o(k).
-4*(k - 1)*(k + 1)**3/5
Factor -45*q**2 + 2*q**3 + 141*q**2 + 507*q + 645*q.
2*q*(q + 24)**2
Let n be 8 - ((-12)/(-15))/(4/10). What is c in -n + 2*c**2 + 6 - 10*c + 12 = 0?
2, 3
Let c(r) be the third derivative of -r