*w**5 + 0 + w**2 + 0*w**3 - 1/84*w**4 + 0*w. Factor h(v).
2*v*(4*v - 1)/7
Let i(m) be the second derivative of -m**7/84 + m**6/60 + m**5/8 + m**4/8 - 24*m. Factor i(b).
-b**2*(b - 3)*(b + 1)**2/2
Let p = 53/6 - 17/2. Suppose 16/3*t**2 + 64/3*t**3 - 4/3*t - p = 0. Calculate t.
-1/4, 1/4
Let n(g) be the third derivative of g**7/13860 - g**6/1980 + g**4/6 + 3*g**2. Let c(l) be the second derivative of n(l). Factor c(u).
2*u*(u - 2)/11
Let s(r) be the second derivative of r**4/66 + 2*r**3/33 + r**2/11 + 10*r. Factor s(i).
2*(i + 1)**2/11
Factor 8*k + 15*k**2 - 21 + 4*k + 3*k**3 - 6 - 3*k.
3*(k - 1)*(k + 3)**2
Let -2/9 - 2/3*t**2 + 2/3*t + 2/9*t**3 = 0. What is t?
1
Let j(q) be the first derivative of -5 - 2/9*q - 1/9*q**4 + 2/15*q**5 + 1/3*q**2 - 4/27*q**3 - 1/27*q**6. Suppose j(a) = 0. Calculate a.
-1, 1
Solve -48*y**5 + 45*y**3 - 25*y**2 + 53*y**5 - 25*y**4 - 10*y**2 + 5*y + 5*y = 0.
0, 1, 2
Let v = 6 - 3. Let u = v - 1. What is d in -7*d - d**u + 6*d + 2*d**2 = 0?
0, 1
Let q(j) be the first derivative of 2*j**5/15 - j**4/3 - 2*j**3/9 + 2*j**2/3 + 8. Factor q(i).
2*i*(i - 2)*(i - 1)*(i + 1)/3
Let -1 - 1/3*c**2 + 4/3*c = 0. Calculate c.
1, 3
Factor 0 - 2/11*d**3 - 2/11*d**2 + 4/11*d.
-2*d*(d - 1)*(d + 2)/11
Determine y so that 5*y**2 - 8 + 15*y + 2 - 14 = 0.
-4, 1
Suppose -9/4*z**2 - 3/8*z**4 + 3/2*z**3 - 3/8 + 3/2*z = 0. Calculate z.
1
Let l(j) = -2*j**4 + 22*j**3 - 30*j**2 + 16*j + 2. Let y(o) = 7*o**4 - 89*o**3 + 119*o**2 - 64*o - 9. Let m(n) = 9*l(n) + 2*y(n). Find r, given that m(r) = 0.
0, 1, 2
Let c(f) = f - 1. Let b(i) = -15*i**2 + 40*i + 17. Let p(g) = -b(g) + c(g). What is m in p(m) = 0?
-2/5, 3
Let v be 22/6 - 6/9. What is a in -3 + a - a + 0*a + v*a + 6*a**2 = 0?
-1, 1/2
Let s(k) be the third derivative of k**6/30 + 2*k**5/15 - 7*k**4/6 + 8*k**3/3 - 14*k**2 - k. Factor s(u).
4*(u - 1)**2*(u + 4)
Suppose t - m + 15 = -4*m, 5*m = -4*t - 25. Factor t*w - 2/7*w**5 + 0 + 2/7*w**3 + 2/7*w**4 - 2/7*w**2.
-2*w**2*(w - 1)**2*(w + 1)/7
Factor 0*q - 4/11*q**4 + 2/11*q**3 + 0 + 2/11*q**5 + 0*q**2.
2*q**3*(q - 1)**2/11
Let h(m) be the first derivative of 3/2*m**2 - m**4 - 4 + 2/3*m**3 + 1/6*m**6 - 2*m + 0*m**5. Suppose h(n) = 0. Calculate n.
-2, -1, 1
Let u(t) = t**3 + t**2 + t. Let v(s) = -2*s**4 + 4*s**3 + 12*s**2 + 16*s. Let n(a) = -20*u(a) + 2*v(a). Factor n(h).
-4*h*(h - 1)*(h + 1)*(h + 3)
Determine t so that -2/3*t + 4/3*t**5 + 0 - 3*t**4 - 2/3*t**3 + 3*t**2 = 0.
-1, 0, 1/4, 1, 2
Solve 6/13*x**3 + 0 - 2/13*x**2 + 0*x = 0 for x.
0, 1/3
Let y = -287/4 - -72. Let y*o + 0 + 3/4*o**3 - o**2 = 0. Calculate o.
0, 1/3, 1
Let n = -112 + 112. Let f(s) be the second derivative of -9/10*s**5 + s**4 + 3*s - 1/14*s**7 + 0*s**2 + 2/5*s**6 + n - 1/2*s**3. Find j, given that f(j) = 0.
0, 1
Factor 3*i**2 - 91 - 10*i + 109 - 5*i.
3*(i - 3)*(i - 2)
Suppose 0 = -3*o + 4*o - 5. Suppose 2*s**2 + 6*s**3 + 4*s**o + s**5 + 9*s**4 - 3*s**5 - 3*s**4 = 0. Calculate s.
-1, 0
Let v(b) be the first derivative of -b**3/2 - 21*b**2/4 + 12*b + 18. What is j in v(j) = 0?
-8, 1
Factor 16/5 - 2/5*q**2 - 4/5*q.
-2*(q - 2)*(q + 4)/5
Let p(o) = -3*o**4 - 7*o**2 + 6*o + 4. Let t(x) = -x**4 - x**2 + x + 1. Let l(f) = p(f) - 4*t(f). Suppose l(j) = 0. Calculate j.
-2, 0, 1
Let d be ((-65)/(-15) - 0) + -4. Let a(f) be the first derivative of -3 - 1/15*f**5 + d*f**2 - 1/6*f**4 + 1/3*f + 0*f**3. Factor a(u).
-(u - 1)*(u + 1)**3/3
Let o(c) be the third derivative of c**10/75600 - c**9/15120 - 7*c**5/60 - 6*c**2. Let q(x) be the third derivative of o(x). Factor q(y).
2*y**3*(y - 2)
Let g(l) be the first derivative of -l**7/189 - l**6/135 + 3*l + 3. Let m(r) be the first derivative of g(r). What is y in m(y) = 0?
-1, 0
Let d(l) be the third derivative of -l**5/30 - l**4/3 - 8*l**2. Factor d(t).
-2*t*(t + 4)
Let g(s) be the second derivative of s**4/12 + s**3/3 + s**2/2 - 4*s. Factor g(u).
(u + 1)**2
Let p(u) = -2*u - 8. Let c be p(-6). Let a(q) be the first derivative of -4/3*q**3 + 1/2*q**c + q**2 + 0*q - 1. Solve a(s) = 0.
0, 1
Let m = -30 - -1261/42. Let d(k) be the second derivative of -1/3*k**4 - 2/15*k**6 - 3/10*k**5 + 3*k + 0 + 0*k**2 - 1/6*k**3 - m*k**7. Factor d(b).
-b*(b + 1)**4
Let p(y) = 3*y**2 + 2. Let a(c) = c + 7. Let j be a(-5). Let h(g) = 3*g - g + g**j - 3*g + 1 + 0*g. Let b(u) = -2*h(u) + p(u). Determine o, given that b(o) = 0.
-2, 0
Factor 3*j - 6*j**3 + 62*j**4 - 3*j**2 - 60*j**4 + 21*j - 16 - j**2.
2*(j - 2)**2*(j - 1)*(j + 2)
Let o(d) be the third derivative of -5/21*d**7 + 2*d**2 - 2/3*d**4 + 0*d**3 + 0 + 0*d - 7/6*d**6 - 22/15*d**5. Find f, given that o(f) = 0.
-2, -2/5, 0
Let y(j) be the first derivative of -3*j**5/5 + 3*j**4/4 - 8. Suppose y(a) = 0. Calculate a.
0, 1
Let t(o) = o + 1. Let i(c) = 2*c**3 + 2*c**2 - 2*c - 2. Let s(x) = i(x) + 2*t(x). What is u in s(u) = 0?
-1, 0
Suppose -58*j**2 - 1 + 1 + 61*j**2 = 0. Calculate j.
0
Factor -1/2*n**2 - 1 - 3/2*n.
-(n + 1)*(n + 2)/2
Let x(q) = -5*q**3 - 55*q**2 - 181*q - 119. Let v(z) = 20*z**3 + 220*z**2 + 725*z + 475. Let f(g) = -6*v(g) - 25*x(g). Factor f(c).
5*(c + 1)*(c + 5)**2
Let r(i) be the second derivative of -i**10/90720 + i**8/20160 - i**4/6 + 2*i. Let b(t) be the third derivative of r(t). Factor b(y).
-y**3*(y - 1)*(y + 1)/3
Let r(l) = -6*l**4 + 11*l**3 + 5*l. Suppose 19 = 5*v - 6. Let m(q) = -9*q**4 + 16*q**3 + 7*q. Let n(j) = v*m(j) - 7*r(j). Suppose n(a) = 0. Calculate a.
0, 1
Let n(t) be the first derivative of -t**3/9 - 2*t**2/3 - 4*t/3 + 5. Factor n(i).
-(i + 2)**2/3
Let t(l) be the first derivative of -l**4/16 + l**2/8 + 4. Determine r so that t(r) = 0.
-1, 0, 1
Let s = -3 + 5. Factor -b + s*b**2 + 8*b - 3*b.
2*b*(b + 2)
Let h(d) = d**2 - 5*d + 7. Let u be h(4). Suppose 2/9*p + 2/9 - 2/9*p**2 - 2/9*p**u = 0. What is p?
-1, 1
Let j = -627 + 627. Factor 4/3*g + j + 2/3*g**2.
2*g*(g + 2)/3
Let j(t) be the second derivative of 0*t**2 + 4*t - 1/42*t**4 + 0 - 1/21*t**3. Factor j(d).
-2*d*(d + 1)/7
Let l(n) be the first derivative of -1/3*n**3 + 1/4*n**2 + n - 2 - 1/8*n**4. Find o such that l(o) = 0.
-2, -1, 1
Let x(j) be the first derivative of -j**4/4 - j**3/3 + 5*j**2/2 - 3*j + 27. Factor x(p).
-(p - 1)**2*(p + 3)
Factor -4/5*c**2 + 0 + 0*c - 11/5*c**3 + 3/5*c**4.
c**2*(c - 4)*(3*c + 1)/5
Solve 10/3*w - 2/3*w**2 - 8/3 = 0.
1, 4
Let v(t) = t**5 - t**4 + t**2 - t + 1. Let y(o) = 5*o**5 - 8*o**4 + 8*o**2 - 5*o + 2. Let k(f) = -2*v(f) + y(f). Determine x, given that k(x) = 0.
-1, 0, 1
Let c(k) = -15*k**2 + 15*k + 5. Let m(x) = -8*x**2 + 7*x + 3. Let z(l) = 3*c(l) - 5*m(l). Let z(p) = 0. Calculate p.
0, 2
Let 4*u**4 + 1 + 47*u**5 - 43*u**5 - 1 = 0. Calculate u.
-1, 0
Let b(p) = p - 8. Let y be b(8). Factor 0*f**2 + 0*f**4 - 1/4*f**3 + y*f + 1/4*f**5 + 0.
f**3*(f - 1)*(f + 1)/4
Let t(x) be the second derivative of -x**8/2240 - x**7/560 - x**6/480 + x**3/6 + x. Let j(m) be the second derivative of t(m). Factor j(k).
-3*k**2*(k + 1)**2/4
Suppose -r = 3*s - 3, -4*r + r - 3*s = -27. Let t be (4/15)/(r/30). Factor -4/3*f - t - 2/3*f**2.
-2*(f + 1)**2/3
Factor 0 - 2/3*b**3 + 0*b + 0*b**2 - 2/3*b**4.
-2*b**3*(b + 1)/3
Let k(c) be the third derivative of 0*c**4 + 0 - c**2 + 0*c + 0*c**3 - 1/30*c**5 + 1/120*c**6. Find b such that k(b) = 0.
0, 2
Let d(c) = -2*c**4 - 8*c**2 - 2. Let r(i) = i**4 + i**2 + 1. Let s(n) = d(n) + 4*r(n). Determine q, given that s(q) = 0.
-1, 1
Suppose 4*s = 5*t + 6, 0 = -t - 0*t + 4*s - 14. Solve 2/3*n**3 + 0*n + 2*n**t - 8/3 = 0 for n.
-2, 1
Suppose -k - 10 = k. Let x be (2/20)/((-2)/k). Factor 1/2*r + 0 + x*r**2.
r*(r + 2)/4
Let y = 6 + -6. Let v be (15/5)/(y + 1). Factor 2/9*s + 2/9*s**v + 4/9*s**2 + 0.
2*s*(s + 1)**2/9
Let r be ((-1 + 2)*4)/2. Factor -5*h + 6*h + 2*h**2 - h**r.
h*(h + 1)
Let a be 52/(-780)*(1 + -26). Let p = -18/13 + 106/39. Solve -8/3*l + p - a*l**2 = 0 for l.
-2, 2/5
Suppose -3*w + 8 = w. Let y = w + 0. Let -z + 6*z**y + 13*z + 8 + 4*z = 0. Calculate z.
-2, -2/3
Let c(j) be the first derivative of 7*j**6/6 + j**5/20 - 15*j**4/8 - j**3/12 + j**2/4 + 1. Suppose c(a) = 0. What is a?
-1, -2/7, 0, 1/4, 1
Let d be (-2)/(((-2)/(-4))/(-1)). Let l be d/(-14) - (-120)/28. Factor 6*s**2 + 15*s**3 + 0 + 12*s**4 - 6*s**l + 0.
3*s**2*(s + 2)*(2*s + 1)
Let f(m) be the first derivative of 3*m**5/10 + 5*m**4/6 + 2*m**3/3 + 2*m + 3. Let r(d) be the first derivative of f(d). Factor r(