 that w(u) = 0.
0, 1/4, 1
Let b = -3 - -5. Suppose 3*p - 12 = -k, -4*p + 3*k = -b - 1. Factor -3*u**4 + u**4 + 7*u**4 - 2*u**4 - p*u**5.
-3*u**4*(u - 1)
Let j(v) be the first derivative of 4*v**5 - 85*v**4/4 + 85*v**2/2 - 20*v + 20. What is l in j(l) = 0?
-1, 1/4, 1, 4
Let j be 1 - (168/4 + -2). Let u = 196/5 + j. Factor -2/5*a - 1/5*a**2 - u.
-(a + 1)**2/5
Let g(m) = -m + 1. Suppose f - 4*d = -5, 0*d - 4 = 2*f - 2*d. Let h be g(f). Determine k so that 6*k**2 - k**3 + 11 - 14*k - 3 + h*k = 0.
2
Let i = 9 + -13. Let c = i - -6. Solve 0*f - 2/7 + 2/7*f**c = 0 for f.
-1, 1
Suppose -u - 53 = -53. Let o(s) be the third derivative of 0*s**4 - 1/330*s**5 + u*s + 0 + 1/33*s**3 - s**2. Suppose o(b) = 0. What is b?
-1, 1
Let l(k) = -2*k**2 + 4*k - 2. Let q be l(1). Determine w, given that -1/2*w**2 - 1/4*w + q - 1/4*w**3 = 0.
-1, 0
Suppose y = -2 + 8. Let j be 20/y + 4/6. Let -2*w + 2*w**5 - j*w**5 + w**2 - 9*w**2 - 12*w**3 - 8*w**4 = 0. Calculate w.
-1, 0
Factor -5/3*o**3 + 0*o + 0 + 5/3*o**5 - 5/3*o**2 + 5/3*o**4.
5*o**2*(o - 1)*(o + 1)**2/3
Let w(q) be the third derivative of q**6/330 + q**5/66 + q**4/132 - 2*q**3/33 + 20*q**2. Solve w(i) = 0.
-2, -1, 1/2
Let i = 3 - -1. Let w(b) be the third derivative of -1/168*b**8 + 0*b + 0*b**6 + 1/12*b**i + 0 - 2*b**2 + 1/15*b**5 - 2/105*b**7 + 0*b**3. Factor w(p).
-2*p*(p - 1)*(p + 1)**3
Let v(m) be the first derivative of -m**6/36 + m**5/10 - m**4/12 - m**3/9 + m**2/4 - m/6 - 4. Suppose v(x) = 0. Calculate x.
-1, 1
Let x = 25 + -49/2. Solve -3/4*g**4 + 1/4 + 3/4*g + 1/2*g**2 - 1/4*g**5 - x*g**3 = 0.
-1, 1
Let y be -5 - (25/(-3) + 2). Factor 0 - 2/9*n + 8/9*n**2 - 2/9*n**5 + 8/9*n**4 - y*n**3.
-2*n*(n - 1)**4/9
Suppose 0*a + 4*a = 2*i - 8, a + 20 = -4*i. Let p be (-6)/(-27) - i/(-18). Factor o**4 + o**5 - 2*o**3 + 1 + p + 0*o**2 + o - 2*o**2.
(o - 1)**2*(o + 1)**3
Suppose -b = -5*c - 21, -3*b + 15 = -2*c - c. Let g be (2/c)/((-6)/96). Factor -18*h + 54*h**2 - 13*h**3 - 14*h**3 + g - 18*h.
-(3*h - 2)**3
Suppose -r - i - 1 = -4*r, -5*r + 3*i = 5. Factor -2*b + 2/3 - 2/3*b**3 + r*b**2.
-2*(b - 1)**3/3
Let c(p) be the third derivative of p**7/210 + p**6/120 - p**5/20 - p**4/24 + p**3/3 + 23*p**2. Let c(d) = 0. Calculate d.
-2, -1, 1
Let c = 10 - 8. Factor -d**3 - d**3 - d**4 + 4*d - d**c - 4*d.
-d**2*(d + 1)**2
Suppose p - 15 = -56*x + 59*x, 3*x = -2*p - 15. Factor 1/3*t**4 + 0 - 1/3*t**3 + p*t + 0*t**2.
t**3*(t - 1)/3
Suppose 55 = 5*r + 2*x, r - 3*x - 55 = -4*r. Let b = r - 8. Factor d**2 - 4*d**b + 3*d**4 + d**2 - d**4.
2*d**2*(d - 1)**2
Suppose 0 = h - 2*y - 4, h - 4 = -0*y - 3*y. Let v(j) be the first derivative of 2/3*j**3 + j**2 - 2*j - 1/2*j**h - 2. Factor v(d).
-2*(d - 1)**2*(d + 1)
Let n(g) = -g**2 + g - 1. Let d(k) = -6*k**2 - 6. Let y = 3 + -1. Let v = y + -6. Let q(w) = v*n(w) + d(w). Factor q(r).
-2*(r + 1)**2
Let l(v) be the second derivative of 7*v**5/5 - 4*v**4 + 2*v**3 + 4*v**2 - 3*v. Factor l(r).
4*(r - 1)**2*(7*r + 2)
Let u = 13 - 13. Let s(a) be the first derivative of 2 - 2/3*a**3 - 2*a**2 + u*a. Factor s(o).
-2*o*(o + 2)
Suppose 2*g - 28 = -4*v, -26 = -3*g - g - 2*v. Suppose 4*j - g*y = 0, j = 2*j - 2*y + 3. Let 1/5*a - 2/5*a**2 + 0 + 1/5*a**j = 0. What is a?
0, 1
Let h(l) be the third derivative of -l**8/672 - l**7/280 + l**5/240 - 5*l**2. Factor h(v).
-v**2*(v + 1)**2*(2*v - 1)/4
Let z(c) = c**3 + c**2 - 3*c - 3. Let q be z(-2). Let u be -3*(2 + -1)/q. Let 2*n**5 - 17*n + 17*n - u*n**5 = 0. What is n?
0
Suppose -2*h - 17 = -5*f, h + 10 = 3*f - 0*h. Suppose f*r - 6 = 0, -4*m + 2 = -r + 4. Factor 0*x + m - 4/5*x**5 + 2/5*x**2 - 6/5*x**4 + 0*x**3.
-2*x**2*(x + 1)**2*(2*x - 1)/5
Suppose -21*o = -14 - 28. Factor 0 + 0*u - 1/4*u**o.
-u**2/4
Let u(k) = 5*k**2 + 14*k + 7. Let o(h) = -11*h**2 - 27*h - 15. Let q(x) = -6*o(x) - 15*u(x). Suppose q(m) = 0. What is m?
-5, -1/3
Let k = 1397 - 37715/27. Let r(b) be the third derivative of 0 - 2*b**2 + 0*b + k*b**3 + 1/270*b**5 - 1/27*b**4. Factor r(y).
2*(y - 2)**2/9
Factor -3/7*w**2 + 1/7*w**3 + 0 - 1/7*w + 3/7*w**4.
w*(w - 1)*(w + 1)*(3*w + 1)/7
Let b(y) = -y**3 - 7*y**2 - 3*y + 3. Let s be b(-6). Let t be 26/10 - 6/s. Suppose -3*h + 2*h**2 - h**2 + 3*h - h**t = 0. What is h?
0, 1
Let p(u) = u**2 + 2*u + 1. Let q be p(-1). Suppose q*k = -4*k + 52. Find s, given that 6*s + k*s**2 - 49*s**2 - 15*s**3 - 14*s - 6 - 19*s = 0.
-1, -2/5
Let u(s) be the third derivative of s**7/140 - s**6/160 - s**5/80 - 4*s**2. Determine m so that u(m) = 0.
-1/2, 0, 1
Let c(f) be the third derivative of -f**6/12 + 2*f**5/5 + 11*f**4/12 - 2*f**3 + 14*f**2. Find q, given that c(q) = 0.
-1, 2/5, 3
Let p(b) = 2*b**3 + 5*b**2 + b - 2. Let x(s) = s**2 + s. Let i(l) = p(l) - 3*x(l). Factor i(y).
2*(y - 1)*(y + 1)**2
Let a be (-9 + 6)/(0 - 1). Find u, given that -34*u**5 - 100*u**4 - 2 + 24*u**2 - 2 - 52*u**a + 10*u + 4*u - 8*u**5 = 0.
-1, 2/7, 1/3
Let s = -4 - -7. Determine m, given that -7*m + 6*m - m**4 - 11*m**s - 3*m**4 + 1 - 2*m**2 - 7*m**2 = 0.
-1, 1/4
Let 3/4*q**4 + 0 - 1/4*q + 5/4*q**3 - 3/4*q**2 - q**5 = 0. What is q?
-1, -1/4, 0, 1
Let d(t) be the first derivative of 1/2*t**3 - 6 + 0*t + 1/2*t**2 + 1/8*t**4. Factor d(z).
z*(z + 1)*(z + 2)/2
Suppose -4*q**4 - q**4 + q**4 + 4*q**3 = 0. What is q?
0, 1
Let v = 13/4 + 0. Let h = 15/4 - v. Factor 0*d**2 - h*d**5 + 0 + 1/4*d**3 + 0*d + 1/4*d**4.
-d**3*(d - 1)*(2*d + 1)/4
Let j(n) be the first derivative of 5*n**3/3 - 33. Factor j(b).
5*b**2
Let q(n) be the second derivative of n**5/10 - n**4/2 + n**3 - n**2 + 6*n. Solve q(i) = 0 for i.
1
Let z(s) be the third derivative of s**8/10080 + s**7/420 + s**6/40 + s**5/20 + 2*s**2. Let l(d) be the third derivative of z(d). Solve l(i) = 0 for i.
-3
Let r(n) be the third derivative of 0*n + 1/40*n**6 + 0*n**5 - 2*n**2 + 1/4*n**3 - 1/140*n**7 - 1/8*n**4 + 0. Factor r(l).
-3*(l - 1)**3*(l + 1)/2
Suppose 2*k + 8 = 4*k. Let z(c) be the second derivative of 0 - 1/48*c**k - 1/12*c**3 + c - 1/8*c**2. Solve z(d) = 0 for d.
-1
Let k(h) = -h**3 + 4*h**2 - 2*h - 7. Let u(o) = -4*o**2 + 2*o + 6. Let z(d) = -2*k(d) - 3*u(d). Determine b, given that z(b) = 0.
-2, -1, 1
Let x(o) be the third derivative of -o**7/12600 + o**5/600 - o**4/8 + 4*o**2. Let g(i) be the second derivative of x(i). Find a, given that g(a) = 0.
-1, 1
Let b(k) = -3*k**2 + k - 2. Let z be b(2). Let q be ((-3)/(-6))/((-8)/z). Let 5/4*h**3 + q*h**2 - 1/4*h + 1/2*h**4 - 1/4 = 0. What is h?
-1, 1/2
Factor -x**5 + 5*x**2 - 2*x**2 + 2*x**3 - 3*x**2 - x**4.
-x**3*(x - 1)*(x + 2)
Let n(g) be the third derivative of g**7/210 - g**6/150 - g**5/50 + g**4/30 + g**3/30 + 28*g**2. Find a such that n(a) = 0.
-1, -1/5, 1
Let l(g) be the third derivative of 0 + 3/10*g**5 + 7/60*g**6 + 1/6*g**4 + 0*g + 6*g**2 + 0*g**3. What is s in l(s) = 0?
-1, -2/7, 0
Let i(u) be the third derivative of -2*u**7/35 - 7*u**6/30 - u**5/5 + u**4/2 + 4*u**3/3 + 9*u**2. Factor i(d).
-4*(d + 1)**3*(3*d - 2)
Suppose -7*q = -0*q. Suppose q = -b + 6*b - 15. Let -54/5*w**4 + 14/5*w + 4/5 - 102/5*w**b - 38/5*w**2 = 0. What is w?
-1, -2/9, 1/3
Let l be -2 + (0 - -7) + -1. Factor -1 - 2*r**4 + 0*r**2 + 4*r**2 - 2*r - 2*r**5 + l*r**3 - 1.
-2*(r - 1)**2*(r + 1)**3
Let j(t) be the second derivative of t**4/54 - 25*t. Factor j(i).
2*i**2/9
Let o(l) = -l**3 + 7*l**2 - 5*l - 3. Let j be o(6). Let x(i) be the first derivative of i + j - 1/6*i**3 - 1/4*i**2. Factor x(y).
-(y - 1)*(y + 2)/2
Let w be ((-6)/12)/(22/(-4)). Let k(b) be the first derivative of 2/11*b**3 - 4 + 0*b + 2/55*b**5 - 3/22*b**4 - w*b**2. Factor k(o).
2*o*(o - 1)**3/11
Suppose -4*g + 4*q - 32 = 0, 0 = -4*g + 3*g + 4*q - 23. Let v = g + 5. Factor -162*o**2 + 0*o**4 - 2*o**4 - 243 - o**4 + v*o**3 - 38*o**3 - 324*o.
-3*(o + 3)**4
Let f(y) = -y + 8. Let b be f(5). Suppose 2*i = -b*i + 20. Suppose -40/3*z**2 - 7/3*z**5 - 5*z - 10*z**i - 2/3 - 50/3*z**3 = 0. What is z?
-1, -2/7
Let m(c) be the first derivative of -5*c**4/4 + 10*c**3 + 35*c**2/2 - 26. Solve m(n) = 0.
-1, 0, 7
Let a(t) = -t**3 - 7*t**2. Let o(d) = -d**3 - 6*d**2 - d. Let q(j) = -4*a(j) + 6*o(j). Determine r so that q(r) = 0.
-3, -1, 0
Solve -8/7*o - 4/7*o**3 - 2/7 - 10/7*o**2 = 0.
-1, -1/2
Let c(o) be the first derivative of -o**5/5 - o**4 - 4*o**3/3 + 2. Let c(n) = 0. What is n?
-2, 0
Let x be (2 + -12)*12/(-10). Let u = x - 10. Factor 4*s**2 - 12*s**3 - 