(c) = 0. What is c?
1
Suppose -b + 6*b = 10. Let z(g) be the first derivative of 1/3*g**3 + 3/2*g**2 - 1 + b*g. Find y, given that z(y) = 0.
-2, -1
Let q(w) be the third derivative of w**5/480 + w**4/96 + w**3/48 - 3*w**2. Find c, given that q(c) = 0.
-1
Let u(x) = -x**5 - x**3 + x**2 + 1. Suppose b + 10 - 8 = 0. Let s(q) = -2*q**4 - 6*q**3 + 2*q**2 + 2. Let d(l) = b*u(l) + s(l). What is i in d(i) = 0?
-1, 0, 2
Let s(a) be the second derivative of 1/6*a**2 - 1/90*a**6 + 0*a**4 + 1/30*a**5 - 1/9*a**3 + 0 - 2*a. Determine c so that s(c) = 0.
-1, 1
Solve -39/5*z**4 + 12/5 + 27/5*z**2 + 9/5*z**5 - 8*z + 31/5*z**3 = 0 for z.
-1, 2/3, 1, 3
Let k(s) be the second derivative of -s**10/20160 + s**9/5040 - s**8/4480 + s**4/6 + 5*s. Let a(w) be the third derivative of k(w). Factor a(t).
-3*t**3*(t - 1)**2/2
Factor 0 - 2/13*q - 12/13*q**3 - 8/13*q**4 - 2/13*q**5 - 8/13*q**2.
-2*q*(q + 1)**4/13
Let q(a) be the second derivative of -a**7/147 + 3*a**6/70 - 13*a**5/140 + 5*a**4/84 + a**3/14 - a**2/7 + 2*a. Determine y so that q(y) = 0.
-1/2, 1, 2
Let h be (-64)/36 + 6 + -4. Find v, given that -8/9*v**3 - 8/9*v + h*v**4 + 4/3*v**2 + 2/9 = 0.
1
Let p(t) = 8*t**3 - 45*t**2 + 72*t + 128. Let q(r) = 95*r**3 - 540*r**2 + 865*r + 1535. Let j(d) = -35*p(d) + 3*q(d). Factor j(m).
5*(m - 5)**2*(m + 1)
Let m(f) be the first derivative of 1/8*f**4 + 0*f**2 + 1/6*f**3 + 0*f - 3. Factor m(r).
r**2*(r + 1)/2
Factor 0*q + 0 - 1/2*q**3 + 1/2*q**2.
-q**2*(q - 1)/2
Let m(k) = k**4 + k**3 - 2*k**2 + 1. Let o(b) = -b**3 + b**2 - 1. Let w = -22 + 21. Let g(i) = w*o(i) - m(i). What is t in g(t) = 0?
-1, 0, 1
Let j be (7 + 65)*(-2)/(-3). Let i be (j/32)/((-6)/(-16)). Determine x so that x**i + 0 - 1/2*x**5 + 0*x**3 + 1/2*x - x**2 = 0.
-1, 0, 1
Let h be 2*2/((-12)/(-915)). Let k = 625/2 - h. Suppose 0 + k*r**2 + r - 14*r**5 - 15/2*r**4 + 13*r**3 = 0. Calculate r.
-1, -2/7, -1/4, 0, 1
Let y be (0 + 1 - 1)/2. Suppose 3*c + 2*c = y. What is z in 0*z**3 + 0*z**4 + 0 + c*z + 0*z**2 - 1/4*z**5 = 0?
0
Let d = -9 + 12. Let s be d/9 + (-1)/(-3). Suppose 0 + 0*l + s*l**2 - 2/3*l**3 = 0. Calculate l.
0, 1
Let d(o) be the third derivative of 0*o**3 + 1/8*o**4 + 0*o + 7*o**2 + 0 + 0*o**5 - 1/40*o**6. Find m, given that d(m) = 0.
-1, 0, 1
Factor 132*q**3 - 69*q**3 - 68*q**3 - 10 + 5*q + 10*q**2.
-5*(q - 2)*(q - 1)*(q + 1)
Factor 0*w + 1/3*w**2 + 0 + 1/3*w**3.
w**2*(w + 1)/3
Suppose 140*f - 135*f - 20 = 0. Let o(s) be the third derivative of f*s**2 + 0*s + 1/6*s**4 + 0 - 1/60*s**5 - 2/3*s**3. Factor o(j).
-(j - 2)**2
Let w be (18/(-6))/((-3)/5). What is i in 4*i**2 - 5*i**4 - 4*i**3 + 2 - 6*i**4 - 2*i**w + 5*i**4 + 6*i = 0?
-1, 1
Let l be (-200)/(-35) + -4 + (-4)/(-14). Factor 4/7*t**4 + 0 + 0*t**3 - 4/7*t**l - 2/7*t**5 + 2/7*t.
-2*t*(t - 1)**3*(t + 1)/7
Factor -4/5 - 2/5*c**2 + 6/5*c.
-2*(c - 2)*(c - 1)/5
Determine x so that 2/3 + 1/3*x - 1/3*x**2 = 0.
-1, 2
Let d(m) = m**3 - 4*m**2 + 2. Let t be d(4). Let f(r) be the first derivative of 2 - 1/2*r**4 + 0*r**t + 0*r + 2/3*r**3. Suppose f(p) = 0. What is p?
0, 1
Let q(f) be the third derivative of f**9/60480 + f**5/15 - 4*f**2. Let c(b) be the third derivative of q(b). Let c(s) = 0. What is s?
0
Solve 0*b**4 + 18*b**2 - 9*b**2 + b**4 - 6*b**3 = 0.
0, 3
Let p = -7 - -11. Find a, given that -4*a + 4 - a**p - 6*a**2 + 3 + 1 + 5*a**3 = 0.
-1, 2
Factor -5*c - 8*c**3 + 7*c**3 + c**2 - 2 - 5*c**2.
-(c + 1)**2*(c + 2)
Find a, given that 72 - 4*a**5 - 4*a**4 - 72 = 0.
-1, 0
Let c(b) be the second derivative of -b**9/6048 + b**8/1680 - b**7/1680 - b**3/2 + 3*b. Let n(r) be the second derivative of c(r). Solve n(f) = 0.
0, 1
Let s = -1/156 - -8/65. Let z(c) be the third derivative of 0 - 5/12*c**4 + 2/105*c**7 - s*c**6 - c**2 + 3/10*c**5 + 1/3*c**3 + 0*c. Factor z(d).
2*(d - 1)**3*(2*d - 1)
Let n(p) be the third derivative of 9/16*p**4 + 1/240*p**6 - 3/40*p**5 - 9/4*p**3 + p**2 + 0*p + 0. Factor n(b).
(b - 3)**3/2
Let j(k) = -3*k**2 - 4*k - 2. Let h(b) = -b**3 - b**2 - b. Let q(y) = -5*h(y) - 5*j(y). Factor q(c).
5*(c + 1)**2*(c + 2)
Let m(b) = 26*b**4 + 20*b**3 - 20*b - 26. Let q(i) = -5*i**4 - 4*i**3 + 4*i + 5. Let g(n) = 3*m(n) + 16*q(n). Factor g(p).
-2*(p - 1)*(p + 1)**3
Let i(p) = p**4 - 1. Let o(j) = 15*j**4 - 24*j**3 + 54*j**2 - 93. Let u(c) = -12*i(c) + o(c). Factor u(b).
3*(b - 3)**3*(b + 1)
Let u(y) be the first derivative of 4*y**6/21 - 18*y**5/35 + y**4/7 + 16*y**3/21 - 6*y**2/7 + 2*y/7 - 26. Suppose u(x) = 0. What is x?
-1, 1/4, 1
Suppose -24 = 3*h - 9*h. Let y = -1 + h. Factor 8/7*m**2 - 16/7*m**y - 2/7*m**5 + 10/7*m**4 + 0 + 0*m.
-2*m**2*(m - 2)**2*(m - 1)/7
Let d(w) = -12*w**4 + 9*w**3 + 15*w**2 + 6*w - 3. Let j(p) = p**2 - p**4 - 9*p**3 + 6*p**3 + 4*p**3. Let k(g) = d(g) - 15*j(g). Factor k(z).
3*(z - 1)**3*(z + 1)
Let o = -4 - -10. Suppose -2*w - 5*w**2 - 2*w**4 + 0*w**2 - w**2 + 0*w**2 - o*w**3 = 0. What is w?
-1, 0
Let h(x) be the second derivative of -x**4/3 + 4*x**3/3 + 31*x. Find i, given that h(i) = 0.
0, 2
Factor -4/3*w**2 + 4*w + 0.
-4*w*(w - 3)/3
Let j(r) be the third derivative of 3*r**2 + 0*r - 1/12*r**4 + 1/30*r**5 - 1/105*r**7 + 0 + 0*r**3 + 1/60*r**6. Let j(b) = 0. Calculate b.
-1, 0, 1
Let l = 23817 + -7145093/300. Let u(q) be the third derivative of 7/60*q**4 + 0*q - 1/50*q**5 + 0 + q**2 + 1/105*q**7 - l*q**6 - 2/15*q**3. Solve u(x) = 0.
-1, 2/5, 1
Factor 64/3 - 12*n**2 - 11/3*n**3 - 1/3*n**4 - 16/3*n.
-(n - 1)*(n + 4)**3/3
Factor -2*g**3 - 16*g**2 - 37*g + 25*g + 18 - 2*g**4 + 14*g**3.
-2*(g - 3)**2*(g - 1)*(g + 1)
Let o(q) = -1 + 4 + 3*q - 4*q. Let t be o(3). Factor 2*a - 4*a + 4*a**2 + 4*a**3 + t*a**5 - 2*a**4 - 2 - 2*a**5.
-2*(a - 1)**2*(a + 1)**3
Factor 2*x**3 - 20*x**2 + 16*x + 6*x**2 - 7 - 3 + 6*x.
2*(x - 5)*(x - 1)**2
Factor -1/4*o**2 + 0*o + 1/4*o**4 + 0*o**3 + 0.
o**2*(o - 1)*(o + 1)/4
Suppose 3*q - 3*r + 65 = 5*q, 4*r = -5*q + 159. Let x = q - 27. Factor -3/2*c - 3/2*c**x + 3*c**3 - 3/2 - 3/2*c**5 + 3*c**2.
-3*(c - 1)**2*(c + 1)**3/2
Let s(j) be the third derivative of -j**4/24 + 13*j**3/6 + j**2. Let c be s(13). Let 2/5*m**2 + c*m - 2/5 = 0. Calculate m.
-1, 1
Suppose 5*u - 3*k = -k - 103, -4*k = 3*u + 67. Let q be -4 + ((-576)/u)/6. Find z such that 4/7 + q*z**3 + 2*z**2 + 2*z = 0.
-2, -1, -1/2
What is h in -9*h**2 + 3*h**4 + 6*h + 9*h**3 - 5*h**2 - 3*h**5 - h**2 = 0?
-2, 0, 1
Let o be (2 - 0)*(-5)/(-15). Let j(g) be the first derivative of o*g**3 + 3 - 1/2*g**2 + 0*g - 1/4*g**4. Factor j(f).
-f*(f - 1)**2
Suppose -3*m - 5*o + 16 = 0, -2*m - 3*m + 20 = 5*o. Suppose y - 9 = -m*y. Factor -20*j - 9*j**4 + 6*j**3 - 22*j**y - 37*j**2 - 4 - 14*j**3.
-(j + 1)**2*(3*j + 2)**2
Determine n, given that n + 17*n**2 - n**3 - 17*n**2 = 0.
-1, 0, 1
Let q(y) be the third derivative of -3*y**6/80 + y**5/4 - 9*y**4/16 + y**3/2 - 14*y**2. Find i such that q(i) = 0.
1/3, 1, 2
Let h = 127/738 - 2/369. Factor 0*v + 1/3*v**2 + h*v**3 + 0.
v**2*(v + 2)/6
Let x = 82/33 + -20/11. Solve -2/3*r**2 - 4/3*r - x = 0 for r.
-1
Let x(a) be the second derivative of -a**7/840 + a**6/360 + 2*a**3/3 - 2*a. Let z(r) be the second derivative of x(r). Factor z(m).
-m**2*(m - 1)
Let f(z) be the third derivative of 1/40*z**5 + 0*z - 1/2*z**3 + 0 + 1/16*z**4 - z**2. What is n in f(n) = 0?
-2, 1
Let v = -1 + -2. Let b be 1/((-15)/v)*2. Factor -2/5*r**2 + b*r + 0.
-2*r*(r - 1)/5
Factor -6 + 2 + 5*c - 13*c - 4*c**2.
-4*(c + 1)**2
Factor -16 + 55*l + 18*l**2 + 13*l**3 + l**3 - 2*l**4 - 15*l - 54*l**2.
-2*(l - 2)**3*(l - 1)
Suppose 0 = -0*y + 3*y - 33. Solve -y*o**3 - 4*o**2 - 5*o**4 + 0*o**4 + 4*o - 2*o**3 = 0 for o.
-2, -1, 0, 2/5
Let x(n) be the second derivative of -9/20*n**5 + 3/2*n**3 + 3*n**2 + 3*n + 0 - 1/2*n**4. Factor x(h).
-3*(h - 1)*(h + 1)*(3*h + 2)
Let h(u) = 5*u**3 - 4*u**2 + u - 2. Let b(p) = -11*p**3 + 9*p**2 - 2*p + 4. Let d(i) = 6*b(i) + 13*h(i). Factor d(w).
-(w - 2)*(w - 1)*(w + 1)
Suppose -5*s**4 - 4*s**2 - 99*s**5 + 5*s**3 + 9*s**2 + 94*s**5 = 0. Calculate s.
-1, 0, 1
Let -1 - 60*t**2 + 33*t**2 + 28*t**2 = 0. Calculate t.
-1, 1
Suppose 8*b = 5*b. Suppose 2*k + 0*k + t - 5 = b, k - 20 = -4*t. Factor -1/2*n + 1/2*n**3 + 1/2*n**4 + k - 1/2*n**2.
n*(n - 1)*(n + 1)**2/2
Let r = 242/265 - 6/53. Suppose 3*v - 3 = i + 8, -3*i - 18 = -4*v. Find h such that -r*h + 4/5*h**v + 2*h**4 + 0 - 2*h**2 = 0.
-1, -2/5, 0, 1
Let z(r) = 26*r**2 + 26*r - 