of o(x). Solve r(m) = 0.
0, 2
Let v(m) = 8*m**5 - 16*m**4 + 24*m**3 - 12*m**2 - 4*m. Let i(q) = -7*q**5 + 16*q**4 - 23*q**3 + 11*q**2 + 3*q. Let b(w) = -4*i(w) - 3*v(w). Factor b(g).
4*g**2*(g - 2)*(g - 1)**2
Let y(u) be the first derivative of -4*u**5/25 + 3*u**4/5 + 26. What is v in y(v) = 0?
0, 3
Suppose -3*c = -3 - 3. Let o(w) be the third derivative of -2/105*w**7 - 2*w**c + 1/15*w**5 + 0*w**6 + 0 + 0*w + 1/12*w**4 - 1/168*w**8 + 0*w**3. Factor o(k).
-2*k*(k - 1)*(k + 1)**3
Let p(a) be the second derivative of 1/24*a**4 + 0*a**2 + 1/12*a**3 + 3*a + 0 - 1/40*a**5 - 1/60*a**6. Factor p(c).
-c*(c - 1)*(c + 1)**2/2
Let f(d) be the third derivative of d**8/2016 - d**6/180 + d**5/180 + d**4/48 - d**3/18 + 4*d**2. Factor f(i).
(i - 1)**3*(i + 1)*(i + 2)/6
Let z be 0 + 5 + 1*(-2)/2. Factor 0*a**3 + 4/5*a - 6/5*a**2 + 0 + 2/5*a**z.
2*a*(a - 1)**2*(a + 2)/5
Let m(c) be the second derivative of -1/30*c**6 - 6*c + 2/105*c**7 + 0 + 1/100*c**5 + 0*c**4 + 0*c**2 + 0*c**3. Factor m(t).
t**3*(t - 1)*(4*t - 1)/5
Let i(y) be the second derivative of 2*y**7/7 - 7*y**6/5 + 219*y**5/80 - 43*y**4/16 + 11*y**3/8 - 3*y**2/8 - 5*y. Factor i(q).
3*(q - 1)**3*(4*q - 1)**2/4
Let a = -9 - -10. Let r(l) = 3*l**4 + 9*l**3 - 9*l**2 + 9*l. Let f(v) = v**4 + v. Let x(i) = a*r(i) - 6*f(i). Factor x(h).
-3*h*(h - 1)**3
Let d(z) be the third derivative of z**8/13440 - z**7/1680 + z**6/720 + z**4/12 - 2*z**2. Let n(u) be the second derivative of d(u). Factor n(y).
y*(y - 2)*(y - 1)/2
Let s(b) be the third derivative of b**8/10080 + b**7/1260 + b**6/360 - b**5/60 - b**2. Let j(u) be the third derivative of s(u). Determine q so that j(q) = 0.
-1
Let k(w) be the first derivative of -4*w**4 + 20*w**3/3 - 2*w**2 - 5. Suppose k(s) = 0. Calculate s.
0, 1/4, 1
Let z be (-8)/(-198) - 14/(-77). Solve -z*a - 4/9 + 2/9*a**2 = 0 for a.
-1, 2
Let h(w) be the third derivative of -w**5/60 + w**4/48 + w**3/12 - 4*w**2. Solve h(l) = 0 for l.
-1/2, 1
Let y(t) be the third derivative of -t**6/180 + t**4/9 + 9*t**2. Factor y(i).
-2*i*(i - 2)*(i + 2)/3
Let d(h) be the second derivative of -h**7/2016 + h**6/1440 + h**4/6 + 5*h. Let t(k) be the third derivative of d(k). What is z in t(z) = 0?
0, 2/5
Suppose 8 = 3*d - 4. Let f(q) be the second derivative of -2/15*q**6 - 1/3*q**d - 3/10*q**5 - 1/42*q**7 + 0*q**2 + 0 - 3*q - 1/6*q**3. Factor f(i).
-i*(i + 1)**4
Let q(v) be the third derivative of -v**6/160 + v**5/20 + 5*v**4/32 - 39*v**2. Factor q(n).
-3*n*(n - 5)*(n + 1)/4
Let a(n) be the first derivative of -n**3/5 - 9*n**2/10 - 6*n/5 - 1. What is m in a(m) = 0?
-2, -1
Let x(s) be the first derivative of 1/5*s**2 + 2/15*s**3 + 3 - 4/5*s. Determine u, given that x(u) = 0.
-2, 1
Let c(i) = -19*i - 112. Let j be c(-6). Factor 0 + 0*u - 2/3*u**j + 1/3*u**4 + 1/3*u**3.
u**2*(u - 1)*(u + 2)/3
Let s be 15/4 + 76 + -78. Factor -s*r - 1/2*r**3 + 2*r**2 + 1/2 + 1/4*r**5 - 1/2*r**4.
(r - 1)**4*(r + 2)/4
Let m(x) be the first derivative of 7*x**6/12 - 8*x**5/5 + 11*x**4/8 - x**3/3 + 9. Factor m(o).
o**2*(o - 1)**2*(7*o - 2)/2
Let d(r) be the third derivative of -r**6/6 - r**5/3 + 35*r**4/24 - 5*r**3/3 + 27*r**2. Factor d(t).
-5*(t + 2)*(2*t - 1)**2
Suppose 0 = -n + 3. Let r(u) = u. Let i be r(1). Factor i - n*z**2 - z**3 + 2*z**2 + 0 + z.
-(z - 1)*(z + 1)**2
Let p(w) = -w + 1. Let t be p(-1). Factor -2/9*r**t - 2/9*r + 0.
-2*r*(r + 1)/9
Suppose -2*u - 3*i + 13 = 0, -5*i + 0 + 20 = 3*u. Suppose 1/3*p**u - 1/3*p**3 - p**4 + 7/3*p**2 - 4/3 + 0*p = 0. What is p?
-1, 1, 2
Let w(o) = o**2 + 18*o - 16. Let r be w(-18). Let y = r + 16. Solve 2/7*u + 2/7*u**3 + y - 4/7*u**2 = 0 for u.
0, 1
Let g(s) be the third derivative of -s**6/120 + s**5/10 - 5*s**4/24 + s**3/3 - 2*s**2. Let o be g(5). Solve -2 - o*d**2 + 4 + 0 = 0 for d.
-1, 1
Find c such that -38 + 2*c**2 - c**2 + 34 + 0*c**2 = 0.
-2, 2
Let v(z) be the third derivative of z**8/11200 - z**6/1200 - z**4/24 - 4*z**2. Let f(t) be the second derivative of v(t). Suppose f(o) = 0. What is o?
-1, 0, 1
Suppose -f = -3*a + 10, -9 = -2*a - 1. Let m(d) be the first derivative of d**f + 1/10*d**4 + 4/5*d + 8/15*d**3 + 1. Factor m(u).
2*(u + 1)**2*(u + 2)/5
Suppose -4/15 + 2/15*v + 2/15*v**2 = 0. What is v?
-2, 1
Let k(s) = -4*s + 18. Let g be k(4). Let z(c) be the third derivative of 1/3*c**3 - 1/15*c**6 + 0*c + 1/5*c**5 + 0 + 1/105*c**7 + c**g - 1/3*c**4. Factor z(n).
2*(n - 1)**4
Let h(b) = -8*b + b**3 - 8*b**2 - 5 + 0*b - 4. Let f be h(9). Solve -3/2*s**3 + 0 + f*s**2 + 1/2*s**4 + 2*s = 0 for s.
-1, 0, 2
Let l(o) = -o**2 - 12*o - 10. Let f be l(-11). Let a(w) be the first derivative of -f + 1/9*w**3 + 1/3*w + 1/3*w**2. Factor a(n).
(n + 1)**2/3
Let q = 2 - 16. Let j = q - -14. Let -3*y + j + 3/2*y**2 = 0. What is y?
0, 2
Let j(p) be the third derivative of -p**8/588 + 4*p**7/245 - 13*p**6/210 + 4*p**5/35 - 2*p**4/21 - 14*p**2. Factor j(h).
-4*h*(h - 2)**2*(h - 1)**2/7
Let s = -3 - -1. Let w be s/(-8) - (-33)/60. Factor 0*p + 6/5*p**3 + w*p**2 - 24/5*p**4 + 0 + 14/5*p**5.
2*p**2*(p - 1)**2*(7*p + 2)/5
Let j be (-4)/(72/(-21) + 2). Let y(s) be the first derivative of -2 - 5/3*s**6 + 0*s**2 + 0*s**3 - s**4 + j*s**5 + 0*s. Factor y(d).
-2*d**3*(d - 1)*(5*d - 2)
Let c(o) be the third derivative of 5*o**8/336 - o**7/21 + o**5/6 - 5*o**4/24 + 20*o**2. Factor c(k).
5*k*(k - 1)**3*(k + 1)
Factor 0*g**2 + 0 + 0*g + 1/4*g**3.
g**3/4
Let x(z) be the third derivative of z**5/570 - z**4/228 - 2*z**3/57 + 26*z**2. Suppose x(m) = 0. Calculate m.
-1, 2
Let g(l) = l**3 - 11*l**2 + 10*l. Suppose -w + 10 = -0*w. Let k be g(w). Factor 2/11 - 2/11*r**2 + k*r.
-2*(r - 1)*(r + 1)/11
Let h = -136/9 + 91/6. Let j(u) be the second derivative of -h*u**4 - 2*u + 0 - 1/60*u**5 + 0*u**2 - 1/18*u**3. Suppose j(c) = 0. Calculate c.
-1, 0
Suppose 4*w + 1 = -k + 12, w - 3*k + 7 = 0. Let o(b) be the second derivative of -4*b + 1/2*b**3 - 1/2*b**w - 5/48*b**4 + 0. Factor o(z).
-(z - 2)*(5*z - 2)/4
Let o be -6*3*(-4)/18. Let h be (42/(-9) + o)*-3. Factor -2/3*m**4 - 2/3*m**3 + 2/3*m + 2/3*m**h + 0.
-2*m*(m - 1)*(m + 1)**2/3
Let n(x) be the second derivative of -x**4/21 - 11*x. Factor n(u).
-4*u**2/7
Let s = 39 - 37. Let x(q) be the second derivative of -1/2*q**3 - 1/12*q**4 - q**2 - s*q + 0. Suppose x(d) = 0. What is d?
-2, -1
What is d in -6*d**3 - 2*d**2 + 3*d**4 + 3*d**3 + 3*d - d**2 + 0*d**2 = 0?
-1, 0, 1
Let r be 18/8*4*1. Let y be ((-3)/r)/(3 - 4). Factor -1/3*s**3 + y*s**2 + 1/3*s - 1/3.
-(s - 1)**2*(s + 1)/3
Find x such that 3*x**2 - 35*x**3 + x**2 + 11*x - 4*x**4 + 23*x**3 + x = 0.
-3, -1, 0, 1
Suppose -4 = 4*w - 64. Let b = w + -10. Determine m so that 3/2*m**4 + 3/2*m - 1/2 - 1/2*m**b - m**2 - m**3 = 0.
-1, 1
Factor -1/3*b + 1/6*b**4 + 0*b**3 + 0 - 1/2*b**2.
b*(b - 2)*(b + 1)**2/6
Let a(w) be the second derivative of -w**7/147 + w**6/105 + 3*w**5/70 - w**4/42 - 2*w**3/21 + 4*w. Determine y, given that a(y) = 0.
-1, 0, 1, 2
Factor -14/3*h - 10/3*h**2 - 2/3*h**3 - 2.
-2*(h + 1)**2*(h + 3)/3
Let a(d) be the first derivative of -d**6/4 - d**5/10 + d**4/4 + 11. Suppose a(h) = 0. Calculate h.
-1, 0, 2/3
Suppose 0 = -5*s - 2*t, -4*s - t = -0*t. Let j = 2213/7 - 315. Find k such that -6/7*k**4 + j*k**2 + 0*k**3 - 2/7*k**5 + 0*k + s = 0.
-2, 0, 1
Factor -3/4*h**2 + 1/4*h + 0.
-h*(3*h - 1)/4
Suppose 6*m**4 + 19*m**3 - 3*m**5 - 12*m + 17*m**3 - 12*m**2 - 27*m**3 = 0. Calculate m.
-1, 0, 2
Let o be ((-3)/2)/(4/8). Let r be 38/20 + o/(-5). Factor r*s**3 - 6*s**2 - 1/4 + 25/4*s**4 - 5/2*s.
(s - 1)*(s + 1)*(5*s + 1)**2/4
Factor 14/19*z - 2/19*z**2 - 20/19.
-2*(z - 5)*(z - 2)/19
What is z in 22/5*z**2 + 12/5*z + 14/5*z**5 + 18/5*z**4 + 0 - 66/5*z**3 = 0?
-3, -2/7, 0, 1
Let i(q) be the second derivative of q**6/90 - q**5/10 + q**3/2 - 6*q. Let o(h) be the second derivative of i(h). Solve o(p) = 0.
0, 3
Let w = 345/52 - 83/13. Find g, given that 1/2*g - 1/4*g**2 - w = 0.
1
Let j(h) be the second derivative of h**5/80 - h**4/16 - h**3/24 + 3*h**2/8 + h. Solve j(t) = 0.
-1, 1, 3
Determine h, given that 1/3*h**5 + 2/3 - 4/3*h**2 + 1/3*h - 2/3*h**3 + 2/3*h**4 = 0.
-2, -1, 1
Let r(f) be the third derivative of -f**5/30 + f**4/6 - f**3/3 + 11*f**2. Find h, given that r(h) = 0.
1
Let l(m) be the second derivative of m**9/3024 - m**8/840 - 2*m**3/3 - m. Let o(r) be the second derivative of l(r). Find d such that o(d) = 0.
