 a.
1, 2
Let n = 161 + -643/4. Find v such that -1/4*v**2 + 0 - 1/4*v + 1/4*v**3 + n*v**4 = 0.
-1, 0, 1
Let m(a) be the third derivative of -a**6/1260 + a**5/210 - a**4/84 - a**3/2 - 2*a**2. Let v(w) be the first derivative of m(w). Factor v(j).
-2*(j - 1)**2/7
Let s(g) be the first derivative of -g**4/2 + 2*g**3/3 - 26. Let s(o) = 0. Calculate o.
0, 1
Let p(n) be the second derivative of -n**7/63 + n**6/30 + n**5/60 - n**4/12 + n**3/18 - 8*n. Determine o, given that p(o) = 0.
-1, 0, 1/2, 1
Let w(d) be the first derivative of -6*d**5/65 - d**4/26 + 2*d**3/13 + d**2/13 - 18. Suppose w(a) = 0. What is a?
-1, -1/3, 0, 1
Let s be (-16)/8*(0 + -1). Let u(d) be the second derivative of 0 + s*d + 1/15*d**3 + 0*d**2 + 3/50*d**5 + 2/15*d**4. Suppose u(p) = 0. Calculate p.
-1, -1/3, 0
Suppose -s - 4 = -2*p, 3*p = -0*s - 2*s + 6. Suppose s = 2*r + 3*r. Factor -2/7*a**4 + 0*a + 2/7*a**2 + 0 + r*a**3.
-2*a**2*(a - 1)*(a + 1)/7
Let n(x) be the third derivative of x**6/360 - x**5/90 - 7*x**2. Factor n(y).
y**2*(y - 2)/3
What is i in 0 + 6/7*i**2 + 0*i**3 + 4/7*i - 2/7*i**4 = 0?
-1, 0, 2
Let y(v) = 3*v. Let o be y(5). Suppose -2*u = 3*u - o. Let 5*w**2 - 5*w**3 + 0*w**4 + 4*w**4 - 3*w**u - w = 0. What is w?
0, 1/2, 1
Let n(p) be the first derivative of 0*p**4 + 4/15*p**3 - 2/25*p**5 - 2 - 2/5*p + 0*p**2. Suppose n(u) = 0. Calculate u.
-1, 1
Let k(g) be the second derivative of g**5/5 + 2*g**4/3 - 5*g. Factor k(n).
4*n**2*(n + 2)
Let m(c) be the first derivative of 3*c**4/8 + c**3 + 3*c**2/4 + 1. Factor m(z).
3*z*(z + 1)**2/2
Let z = 8 + -3. Determine w, given that -12/7*w**3 - 2/7*w**z - 2/7*w + 0 - 8/7*w**4 - 8/7*w**2 = 0.
-1, 0
Let t(w) = -8*w + 64. Let q be t(8). Factor 3/5*v**2 - 3/5*v + q.
3*v*(v - 1)/5
Factor -3*c**2 + 2*c**3 + 17*c**2 + 0*c**3 + 10*c + 2*c.
2*c*(c + 1)*(c + 6)
Let b(v) be the third derivative of v**6/360 + v**5/36 + 7*v**4/72 + v**3/6 + 10*v**2. Let b(g) = 0. Calculate g.
-3, -1
Let m(q) = -2*q - 1. Let h be m(-1). Let v be -6*(6/(-4) + h). Let -7 + 110*l**4 - 1 - 58*l + 18*l + 70*l**v + 42*l**5 - 30*l**2 = 0. Calculate l.
-1, -2/7, 2/3
Let g(x) be the second derivative of x**6/150 - 3*x**5/50 + x**4/60 + 4*x**3/5 + 8*x**2/5 + 7*x. What is j in g(j) = 0?
-1, 4
Factor -3/5*b**5 + 2/5*b**3 + 0*b + 1/5*b**4 + 0 + 0*b**2.
-b**3*(b - 1)*(3*b + 2)/5
Let p(s) be the first derivative of s**7/189 - s**6/45 + s**5/30 - s**4/54 - s - 7. Let w(j) be the first derivative of p(j). Factor w(i).
2*i**2*(i - 1)**3/9
Suppose a + 6 - 9 = 0. Let 71*u**4 - 12*u**5 - 64*u**a + 4*u**2 + 8*u**2 + 4*u**2 - 19*u**4 = 0. Calculate u.
0, 1/3, 2
Let p be 5/(-20) - (3 - (-42)/(-8)). Let j = 5/18 - 1/18. Suppose -4/9*m**3 - 2/9 - j*m**5 + 2/3*m**4 + 2/3*m - 4/9*m**p = 0. What is m?
-1, 1
Let c(t) = -5*t - 4*t**2 + 7*t**2 + 0*t. Let l(k) = -k**2 + 2*k. Let w(v) = 4*c(v) + 10*l(v). Let w(o) = 0. Calculate o.
0
Let v = 25 + -21. Let -4*q**4 + 31*q**v - 9*q**3 - 12*q**5 + 3*q**2 - 9*q**3 = 0. What is q?
0, 1/4, 1
Let g(l) = l**3 + 8*l**2 - 9*l + 1. Let w be g(-9). Let f be (8/6)/(2/6). Factor -1/2*a**3 - a + w + 5/4*a**f - 15/4*a**2.
(a - 2)*(a + 1)**2*(5*a - 2)/4
Solve 0 + i + 0*i**2 - 1/4*i**3 = 0 for i.
-2, 0, 2
Let n = -151 + 607/4. Factor 0 + 3/4*k**2 - n*k.
3*k*(k - 1)/4
Let d(b) be the third derivative of b**8/26880 + b**4/24 - 6*b**2. Let q(i) be the second derivative of d(i). Factor q(s).
s**3/4
Solve -3/7*h**2 + 0 + 0*h + 6/7*h**3 - 3/7*h**4 = 0 for h.
0, 1
Let c = 49/104 + 3/104. Factor 0*x - x**4 + 0 + 1/2*x**5 + 0*x**2 + c*x**3.
x**3*(x - 1)**2/2
Suppose 3*i - 8 = j, 2*j = -4*i + 4*j + 8. Suppose i*f - 2 = 4*y - 10, -5*f - 10 = 0. Factor 4/5*o**3 + 2/5*o**2 + y + 2/5*o**4 + 0*o.
2*o**2*(o + 1)**2/5
Let i = 3/35 - -61/105. Let o(w) be the first derivative of 1/2*w**4 + i*w**3 + 0*w + 1 + 0*w**2. Factor o(n).
2*n**2*(n + 1)
Let i be (20/6)/((-18)/(-27)). Factor -n**4 - n**2 + 0 + 1/4*n + 1/4*n**i + 3/2*n**3.
n*(n - 1)**4/4
Factor 47*n**4 - 12*n**4 + 25*n**4 + 5*n**3 + 15*n**3 + 25*n**5.
5*n**3*(n + 2)*(5*n + 2)
Find i such that 0 - 2*i**3 - 2/3*i**4 + 2/3*i**5 + 10/3*i**2 - 4/3*i = 0.
-2, 0, 1
Let g = 690 + -686. Factor -1/2*a - 1/2*a**5 - a**2 + 1/2*a**g + 1/2 + a**3.
-(a - 1)**3*(a + 1)**2/2
Let -19*d**3 - 12*d + 17*d - 34*d**2 + 7*d**4 - 2*d - 11*d = 0. What is d?
-1, -2/7, 0, 4
Let l(h) be the second derivative of -21/10*h**5 + 3/5*h**6 - 9/2*h**3 + 3*h**2 + 4*h**4 - 1/14*h**7 + 0 - 5*h. Factor l(o).
-3*(o - 2)*(o - 1)**4
Factor 2*v**3 + 8/3*v**2 - 4/3 - 2/3*v.
2*(v + 1)**2*(3*v - 2)/3
Let c(w) be the third derivative of -2*w**7/105 + 2*w**6/15 - 2*w**5/5 + 2*w**4/3 - 2*w**3/3 + 3*w**2. Let c(v) = 0. What is v?
1
Let m(l) be the first derivative of -l**6/36 - l**5/30 + l**4/12 + l**3/9 - l**2/12 - l/6 + 8. Suppose m(d) = 0. What is d?
-1, 1
Let m be (21/252)/(2/36). Suppose -3/2*o**5 - 9*o**3 + 0 - m*o - 6*o**4 - 6*o**2 = 0. What is o?
-1, 0
Let j(t) be the first derivative of t**4/4 + 2*t**3/3 - 5*t**2/2 - 6*t - 40. Factor j(h).
(h - 2)*(h + 1)*(h + 3)
Let u = -77/4 + 20. Let g(w) be the first derivative of 1/2*w**2 + 1/5*w**5 + w**3 + 0*w - 5 + u*w**4. Factor g(a).
a*(a + 1)**3
Suppose 2*n + 4*j = 12, 10 = n - 4*j + 4. Let f be (12/18)/(14/n). Find o such that 0 - 4/7*o**4 + 4/7*o**2 - 2/7*o + f*o**5 + 0*o**3 = 0.
-1, 0, 1
Suppose 4*d + 1 - 9 = 0, d = 5*u + 2. Factor u*v - 2/5 + 2/5*v**2.
2*(v - 1)*(v + 1)/5
Find h, given that 0 - 4/7*h**3 + 0*h - 4/7*h**2 = 0.
-1, 0
Let j(m) be the third derivative of m**5/90 + m**4/18 + m**3/9 + 3*m**2. Factor j(l).
2*(l + 1)**2/3
Let x = 1/244 + 4381/2684. Let q = 76/33 - x. Factor 2/3*g - q*g**2 + 0.
-2*g*(g - 1)/3
What is g in -6*g - 3/2*g**2 + 6*g**3 + 3/2 = 0?
-1, 1/4, 1
Let c(x) = 6*x**3 + 2*x**2 + 4*x. Let t(w) = 7*w**3 + w**2 + 4*w. Let l(y) = -5*c(y) + 4*t(y). Determine d, given that l(d) = 0.
-2, -1, 0
Let k be 4 + (1 - 2) + 2. Let x(s) be the second derivative of -1/6*s**3 - 1/60*s**k + 0 + 1/12*s**4 + 2*s + 1/6*s**2. Determine q so that x(q) = 0.
1
Let y(b) = -2*b**3 + 7*b**2 + 5*b + 5. Let r = 2 - 3. Let c(k) = -k**2 + 0*k**2 + 2 - k + k**3 - 3. Let p(x) = r*y(x) - 5*c(x). Factor p(j).
-j**2*(3*j + 2)
Let d(r) = -r**3 - r**2 - r. Let u(h) = h**4 - 4*h**3 - 8*h**2 - 6*h. Let z(p) = -15*d(p) + 5*u(p). Factor z(q).
5*q*(q - 3)*(q + 1)**2
Let b(y) be the first derivative of 3*y**4/22 + 8*y**3/11 + 9*y**2/11 + 6. Factor b(p).
6*p*(p + 1)*(p + 3)/11
Suppose 34*w**4 - 84*w**2 + 12*w**3 + 43*w**3 - 39*w**4 - 180*w - 36*w**2 = 0. Calculate w.
-1, 0, 6
Let g = 4 - 12. Let b = -22/3 - g. Find n such that 4/3*n + 2/3 + b*n**2 = 0.
-1
Let z(w) be the third derivative of -w**7/210 - 2*w**6/45 - 2*w**5/15 - w**4/3 + 9*w**2. Let v(i) be the second derivative of z(i). What is c in v(c) = 0?
-2, -2/3
Let o(k) be the first derivative of -1 + 3/8*k**2 - 1/2*k - 1/12*k**3. Factor o(z).
-(z - 2)*(z - 1)/4
Let s(n) be the second derivative of n**6/120 - n**5/80 - n**4/24 - 19*n. Factor s(b).
b**2*(b - 2)*(b + 1)/4
Suppose 14 = -3*z + 20. Let p(t) be the second derivative of 1/70*t**5 + 0 + 0*t**z + 1/105*t**6 - 3*t - 1/42*t**4 - 1/147*t**7 + 0*t**3. Factor p(w).
-2*w**2*(w - 1)**2*(w + 1)/7
Factor 2/5*b**5 + 0 + 2/5*b + 0*b**2 - 4/5*b**3 + 0*b**4.
2*b*(b - 1)**2*(b + 1)**2/5
Factor 3 - 13*k + 16*k**3 + 24*k**2 + 1 + 29*k + 4*k**4.
4*(k + 1)**4
Suppose -2*c = -4*c - 4. Let z be c/(-10) + (-15)/(-25). Factor 2/5*s**4 - 2/5 - 4/5*s**3 + 0*s**2 + z*s.
2*(s - 1)**3*(s + 1)/5
Let r(w) be the first derivative of -w**6/1260 + w**5/420 + w**3/3 + 2. Let t(x) be the third derivative of r(x). Determine a so that t(a) = 0.
0, 1
Let c(g) be the second derivative of 0*g**3 + 0 + 0*g**2 + 3*g - 1/66*g**4 - 1/110*g**5. Determine u, given that c(u) = 0.
-1, 0
Let y(c) be the second derivative of -c**6/285 - c**5/95 - c**4/114 - 17*c. Determine f so that y(f) = 0.
-1, 0
Let v(p) be the first derivative of -25*p**7/63 + 4*p**6/9 - 2*p**5/15 - 2*p + 1. Let g(q) be the first derivative of v(q). Determine z, given that g(z) = 0.
0, 2/5
Let i be -20 - -28 - (4 - 0). Solve 10/11*d**i - 24/11*d - 8/11 - 2/11*d**2 + 24/11*d**3 = 0.
-2, -1, -2/5, 1
Let u(t) be the first derivative of -t**4/2 - 8*t**3 - 36*t**2 + 36. Suppose u(d) = 0. Calculate d.
-6, 0
Let l(u) be the second derivative of 0*u**3 + 0 + 0*u**5 + 0*u**6 + 0*u**4 + 0*u**2 + 1/273*u**7 +