). Suppose 4*t - 11 + 3 = d. Let 2*b**3 - 2*b**4 - b - 4 + 6*b**2 + t*b - 3*b = 0. Calculate b.
-1, 1, 2
Let t = 377/5 - 75. Let k be 11/4 + (54/24 - 3). Determine a so that 0*a + 2/5*a**3 + 0 - 2/5*a**k + t*a**4 - 2/5*a**5 = 0.
-1, 0, 1
Let k(h) = -8*h**3 + 13*h**2 + 3*h + 4. Let c(q) = 1 + 26 - 53*q**3 + 21*q - 4*q**3 + 90*q**2. Let y(g) = 4*c(g) - 27*k(g). Determine n so that y(n) = 0.
-1/4, 0, 1
Let m be (1 + -1)*2/4. Suppose t + t + 2*d - 4 = m, 0 = 5*t + d - 14. Factor 0*p + t*p + p**2 - 3*p.
p**2
Let b(v) be the first derivative of v**3/7 - 6*v**2/7 - 29. Find s, given that b(s) = 0.
0, 4
Let h(t) be the first derivative of -27*t**6/2 + 234*t**5/5 - 105*t**4/2 + 12*t**3 + 27*t**2/2 - 6*t - 2. Find q, given that h(q) = 0.
-1/3, 2/9, 1
Let l = 2 - -8. Factor -32*t**2 - l*t**5 - 44*t**4 - 4 - 76*t**3 - 32*t**2 - 25*t - t.
-2*(t + 1)**4*(5*t + 2)
Let m be (4/(-3))/(12 - 16). Let d(a) be the second derivative of -1/10*a**5 + m*a**4 + a + 0*a**2 + 0 - 1/3*a**3. Factor d(z).
-2*z*(z - 1)**2
Suppose 0 = -13*n + 6*n + 14. Solve 1/3*c + 2/3*c**n - 2/3*c**4 - 1/3*c**5 + 0 + 0*c**3 = 0.
-1, 0, 1
Suppose -8*n - 5 = -3*n - 4*y, -3*n - 5*y = -34. Suppose 2*w**3 - w - 2*w - 2*w**n - 6*w**2 - 3*w**3 = 0. What is w?
-1, 0
Let g(p) be the first derivative of -4*p**5/5 + 68*p**3/3 - 72*p**2 + 80*p + 27. Factor g(w).
-4*(w - 2)**2*(w - 1)*(w + 5)
Let r(s) = -s**3 + 6*s**2 - s + 3. Let h be r(6). Let x be 3/h - 8/(-2). Find d such that -4/7*d - 8/7*d**x + 2*d**2 - 2/7 = 0.
-1/4, 1
Let g = -79 - -81. Let b(l) be the first derivative of -3/2*l**g + 3/4*l**4 + 5/2*l**3 - 3/2*l**5 + 2 + 0*l. Solve b(w) = 0.
-1, 0, 2/5, 1
Let k = 122 - 120. Let g(b) be the first derivative of 0*b**3 - 3/10*b**4 + 1 + 1/5*b**k + 4/25*b**5 + 0*b. Factor g(n).
2*n*(n - 1)**2*(2*n + 1)/5
Let d(a) be the second derivative of -a**7/63 + 2*a**6/45 + a**5/15 - 2*a**4/9 - a**3/9 + 2*a**2/3 - 7*a. Find w, given that d(w) = 0.
-1, 1, 2
Let p(h) be the second derivative of -h**8/560 + h**7/70 - h**6/20 + h**5/10 - h**4/8 - 5*h**3/6 + 10*h. Let w(d) be the second derivative of p(d). Factor w(m).
-3*(m - 1)**4
Let p(v) be the third derivative of 0 + 0*v - 1/150*v**5 - 1/15*v**3 - v**2 - 1/30*v**4. Find w such that p(w) = 0.
-1
Let g(n) be the third derivative of n**7/315 - n**6/36 + n**5/10 - 7*n**4/36 + 2*n**3/9 - 11*n**2. Factor g(w).
2*(w - 2)*(w - 1)**3/3
Let b be 6/(-27)*3*-6. Let o(p) be the second derivative of 1/3*p**3 - p + 0 - 1/6*p**b + 0*p**2. Factor o(r).
-2*r*(r - 1)
Suppose -2*w - 1 + 5 = 0. Suppose n = w*n. Factor n*b + 0 - 2/5*b**2 - 6/5*b**3.
-2*b**2*(3*b + 1)/5
Let a = 613/2 - 3459/10. Let x = a + 40. Solve 6/5 - 3/5*m**2 + x*m = 0 for m.
-1, 2
Let k(y) = -y**2 - 8*y - 4. Let r be k(-7). Factor 7*l + 0*l**4 - 4*l**3 + 2*l**r + 5*l**2 - 5*l**4 - 5*l.
-l*(l - 1)*(l + 1)*(5*l + 2)
Let n(l) be the second derivative of 0*l**4 + 1/3*l**3 + 3*l - 2/3*l**2 + 0 - 1/30*l**5. Determine a, given that n(a) = 0.
-2, 1
Let t(b) = -6*b - 52. Let z be t(-9). Let w(g) be the first derivative of 4/15*g**3 + 1/20*g**4 + 1/2*g**2 - z + 2/5*g. Let w(i) = 0. Calculate i.
-2, -1
Solve -2/5*a**2 + 16/5*a - 32/5 = 0 for a.
4
Let p(a) = 2*a**2 + 70*a - 72. Let s be p(-36). Factor -4/5*k - 2/5*k**2 + s.
-2*k*(k + 2)/5
Let w(b) be the second derivative of 3*b**5/80 - 3*b**3/8 + 3*b**2/4 - 7*b. Let w(m) = 0. Calculate m.
-2, 1
Let f be 0 + (-14)/16 + 1. Let u(h) be the first derivative of 0*h + 0*h**4 - 1/10*h**5 + 2 + 1/6*h**3 + f*h**2 - 1/24*h**6. Factor u(w).
-w*(w - 1)*(w + 1)**3/4
Let y(a) = -4*a**5 + 4*a**4 + 3*a**3 - 2*a**2 - a + 3. Let f(u) = -u**5 + u**4 + u**2 - u + 1. Let t(q) = -3*f(q) + y(q). Factor t(z).
-z*(z - 1)**3*(z + 2)
Let s(t) be the second derivative of 0 + 1/2*t**3 + 5/24*t**4 - 5*t + 1/4*t**2. Let s(c) = 0. What is c?
-1, -1/5
Let v(g) be the second derivative of g**4/12 - 2*g**3/3 + 3*g**2/2 + 16*g. What is o in v(o) = 0?
1, 3
Let z(m) = -5*m**2 - m - 3. Suppose 2*o - 5 = 1. Let t(c) = 26*c**2 + 6*c + 16. Let s(f) = o*t(f) + 16*z(f). Suppose s(d) = 0. What is d?
0, 1
Factor -1/2*c - 7/4*c**2 + 0.
-c*(7*c + 2)/4
Factor 0*l**2 - 3 - 12*l**2 - 21*l - 6 + 0.
-3*(l + 1)*(4*l + 3)
Let g(k) be the second derivative of k**7/1260 - k**6/180 + k**5/60 + 3*k**4/4 + 6*k. Let f(o) be the third derivative of g(o). Factor f(l).
2*(l - 1)**2
Let -75/4 + 3/4*f**3 + 27/4*f**2 + 45/4*f = 0. What is f?
-5, 1
Let b(s) be the second derivative of -s**4/36 + 2*s**3/9 - s**2/2 - 15*s. What is q in b(q) = 0?
1, 3
Let i(o) be the first derivative of -27/5*o**5 - 13*o**3 + 0*o + 3 + 15*o**4 + 3*o**2. Factor i(g).
-3*g*(g - 1)**2*(9*g - 2)
Let t(k) be the first derivative of -k**6/1440 - k**5/120 - k**4/32 - k**3 + 5. Let s(x) be the third derivative of t(x). What is m in s(m) = 0?
-3, -1
Suppose 4*u + 84 = 4*l, -3*l - u + 14 = -37. Suppose 0 = -4*v - 2*n + l, 5*v - 20 = -0*n - 2*n. Solve 0 - 1/2*t + 1/2*t**v = 0 for t.
0, 1
Let s(j) = 2*j - 1. Let g be s(2). Let 4*w**2 + w**4 - 3*w**2 - w**3 - 3*w**g + 2*w**3 = 0. Calculate w.
0, 1
Let v(f) = -f**2 - 6*f + 2. Let w be v(-6). Factor -2*n - 4 + n + 8*n - n - 2*n**w.
-2*(n - 2)*(n - 1)
Let j(v) be the third derivative of -v**7/420 - v**6/80 - v**5/40 - v**4/48 - 9*v**2. Suppose j(a) = 0. What is a?
-1, 0
Suppose -3*o + 12 - 2 = -2*k, 2*k = 5*o - 10. Let x be (-13)/k - 2/(-5). Determine g, given that 0 + 8/3*g**2 - 22/9*g**x - 8/9*g + 2/3*g**4 = 0.
0, 2/3, 1, 2
Let h(f) = f**2 - 9. Let t be h(-3). Factor -1/2*u + 1/4*u**2 + t.
u*(u - 2)/4
Let r be 13/5 - 9/15. Factor n**2 + 2*n**3 - n**3 + 4*n**2 - 4*n**r.
n**2*(n + 1)
Let h(u) be the first derivative of 3*u**4/28 - u**3/7 - 15*u**2/14 - 9*u/7 - 36. What is m in h(m) = 0?
-1, 3
Let i(m) = 2 - 10 + 0*m - m + 2*m. Let r be i(8). Suppose 0*p**2 + r*p**3 + 2/5*p**5 - 2/5*p**4 + 0 + 0*p = 0. Calculate p.
0, 1
Let w(j) be the second derivative of j**6/1260 - j**5/210 - j**3/2 - 3*j. Let m(g) be the second derivative of w(g). Factor m(q).
2*q*(q - 2)/7
Let u(w) = 2*w + 24. Let x be -9 - 8/(-4) - 3. Let k be u(x). Suppose -1/5*b**2 - 2/5*b**3 - 1/5*b**k + 0*b + 0 = 0. Calculate b.
-1, 0
Let n(s) be the second derivative of 2*s**4/3 - 50*s**3/3 + 24*s**2 - 47*s. Factor n(u).
4*(u - 12)*(2*u - 1)
Let b = 1 - 0. Let q be b - ((-12)/(-2))/(-3). Let -3*a**2 + 0*a**2 + 3 - 3*a**3 - q = 0. Calculate a.
-1, 0
Let p(k) = k**3 + k + 1. Let y(s) = 30*s**3 - 5*s**2 + 25*s + 25. Let z(i) = 25*p(i) - y(i). Factor z(d).
-5*d**2*(d - 1)
Let d(r) = 45*r**4 - 24*r**3 - 91*r**2 - 37*r. Let s(p) = 5*p**3 - 9*p**2 - 23*p**4 + 19*p + 7*p**3 + 54*p**2. Let x(w) = -3*d(w) - 5*s(w). Factor x(c).
-4*c*(c - 2)*(c + 1)*(5*c + 2)
Let j(a) = -a - 2. Let w be j(-3). Let d = 9 + -7. Factor -5 - 3*p**d + 3*p + 3 + w + p**3.
(p - 1)**3
Let m be (-6)/8 - 370/40. Let x be ((-12)/m)/((-9)/(-6)). Find w such that -x*w + 2/5 + 2/5*w**2 = 0.
1
Suppose 4*d = -5*f + 3, 0*d - d + 3 = 2*f. Factor 2/7*t**f - 2/7*t + 0*t**2 + 0.
2*t*(t - 1)*(t + 1)/7
Let b(d) = -7*d**2 - 2 + 3*d**2 + 4*d**2 - 2*d - d**2 + d**3. Let g(x) = -4*x**3 + 4*x**2 + 7*x + 7. Let h = -4 - -11. Let p(c) = h*b(c) + 2*g(c). Factor p(r).
-r**2*(r - 1)
Let p(l) = l**2 + 15*l + 16. Let d = -2 + -12. Let f be p(d). Factor -2/7*u**3 - 2/7*u**f + 0 + 4/7*u.
-2*u*(u - 1)*(u + 2)/7
Let r be 8/(-16)*(-2 - (-4 + 2)). Factor 1/4*g + r + 1/4*g**2.
g*(g + 1)/4
Suppose -5*x + 24 = -x. Suppose -x = -2*o - 4. Find q, given that -3*q - q**2 - 2*q**2 + 0*q**3 - o - q**3 = 0.
-1
Let y(w) be the third derivative of -1/60*w**4 - 1/150*w**6 - 1/60*w**5 + 0*w**3 + 0*w + 0 - 1/1050*w**7 - 2*w**2. Factor y(z).
-z*(z + 1)**2*(z + 2)/5
Let i(k) be the third derivative of k**8/16 - 13*k**7/210 - 11*k**6/40 + 17*k**5/60 + k**4/2 - 2*k**3/3 - 4*k**2. Determine y, given that i(y) = 0.
-1, -2/3, 2/7, 1
Suppose 9*k - 10*k = 0. Let f(l) be the third derivative of -1/80*l**6 + 2*l**2 - 1/240*l**5 - 3/280*l**7 + 0 - 1/336*l**8 + 0*l**3 + 0*l**4 + k*l. Factor f(h).
-h**2*(h + 1)**2*(4*h + 1)/4
Let p = -336/5 - -68. Factor -p - 6/5*i - 2/5*i**2.
-2*(i + 1)*(i + 2)/5
Let z(d) be the second derivative of d**5/20 - d**4/4 - 15*d. Factor z(j).
j**2*(j - 3)
Suppose -1/3 + 2/3*y**2 + 1/3*y - 1/3*y**4 - 2/3*y**3 + 1/3*y**5 = 0. Calculate y.
-1, 1
Let d(y) = y - 5. Let a be d(7). Let g(f) be the third derivative of 1/84*f**4 - 2*f*