et h(a) be the second derivative of 0 - a - 1/42*a**4 + d*a**2 - 1/70*a**5 + 1/105*a**6 + 1/21*a**3. Determine o so that h(o) = 0.
-1, 0, 1
Determine k so that 56*k**2 - 2*k + 0*k + 5*k - 53*k**2 = 0.
-1, 0
Let l(w) be the third derivative of 0*w**3 - 1/20*w**5 - 2*w**2 + 0 + 0*w**4 - 1/40*w**6 + 0*w. Determine r so that l(r) = 0.
-1, 0
Suppose -2*t + 0 = -10. Suppose 2*l - 3 - 3 + 7*l + 2*l**2 - t*l**2 = 0. Calculate l.
1, 2
Let g be (-1 - 0) + (-9)/(-9). Suppose -2*s + 3*s - 2 = g. Let 2*c**3 + 0 - 16/5*c**s - 8/5*c = 0. What is c?
-2/5, 0, 2
Factor 2/9 - 4/9*m + 2/9*m**2.
2*(m - 1)**2/9
Let v = -9 + 12. Suppose 0 = -r + v*r. Factor 0*o**3 + r*o - 4/7*o**2 + 2/7*o**4 + 2/7.
2*(o - 1)**2*(o + 1)**2/7
Let l(b) = -4*b**4 + 8*b**3 + 9*b**2 - 19*b - 19. Let f(p) = -4*p**4 + 8*p**3 + 8*p**2 - 20*p - 20. Let c(t) = -3*f(t) + 4*l(t). Factor c(o).
-4*(o - 2)**2*(o + 1)**2
Let a(j) = -j**2 - 7*j - 3. Let s be a(-3). Suppose b = s - 4. Factor -2/7*k**b + 0*k**3 + 4/7*k**4 + 0 + 2/7*k - 4/7*k**2.
-2*k*(k - 1)**3*(k + 1)/7
Solve 8/3*k**2 + 0 + 2/3*k = 0 for k.
-1/4, 0
What is n in 2/11*n**3 - 2/11*n + 0*n**2 + 0 = 0?
-1, 0, 1
Let d(y) = -y**2 + 3*y + 2. Let v be d(3). Factor -6*i - i**3 - 3*i + 2*i**v + 8*i.
-i*(i - 1)**2
Factor -20 + 184*n - 224*n + 8*n**2 - 33*n**2 - 5*n**3.
-5*(n + 1)*(n + 2)**2
Let y be (-3)/((-18)/(-28))*(-201)/268. Factor -1/2*l**3 - y*l + 5/2*l**2 + 3/2.
-(l - 3)*(l - 1)**2/2
Factor -2/3 - 2/3*f**3 - 2*f**2 - 2*f.
-2*(f + 1)**3/3
Let h = 61 - 35. Factor 3*n + 6*n**3 - 3*n**3 + h*n**2 - 32*n**2.
3*n*(n - 1)**2
Let p be (-6)/(-2)*4/6. Let q be 3/(-2) + (-2709)/(-630). Factor q*j**p + 0 + 4/5*j + 6/5*j**3.
2*j*(j + 2)*(3*j + 1)/5
Let o(i) be the first derivative of -2*i**3/15 - 4*i**2/5 - 6*i/5 - 4. What is g in o(g) = 0?
-3, -1
Let w(g) be the second derivative of g**4/4 - 2*g**3 + 22*g. Factor w(u).
3*u*(u - 4)
Let i(t) = 1 + t**3 - t + 0*t**3 - 2*t**2 + 1 - 6. Let b be i(3). Solve -b*g - g + 6*g - 2*g**2 - g**2 = 0.
0, 1
Factor -4/9*a + 2/9 + 2/9*a**2.
2*(a - 1)**2/9
Let d(b) be the first derivative of b**6/120 - b**4/24 - 3*b**2/2 + 1. Let s(u) be the second derivative of d(u). Let s(t) = 0. What is t?
-1, 0, 1
Factor -32/15 - 2/15*q**2 + 16/15*q.
-2*(q - 4)**2/15
Let b(w) = -w**2 - 4*w + 1. Let o be b(-3). Let -5*c**3 + 2*c**4 + 4*c**2 + 5*c**4 - c - 5*c**o = 0. Calculate c.
0, 1/2, 1
Let t(i) be the second derivative of -3/10*i**5 - 1/9*i**4 + 1/7*i**7 + 0*i**3 + 4*i + 2/45*i**6 + 0*i**2 + 0. Let t(r) = 0. Calculate r.
-1, -2/9, 0, 1
Let l(s) be the second derivative of 2*s**7/7 - s**6/2 - 21*s**5/4 - 35*s**4/4 - 5*s**3/2 + 6*s**2 + 34*s. Factor l(b).
3*(b - 4)*(b + 1)**3*(4*b - 1)
Let c(y) be the second derivative of y**4/20 - 3*y**3/10 + 3*y**2/5 + 2*y - 4. What is p in c(p) = 0?
1, 2
Factor -2/13*d**2 - 2/13*d + 0.
-2*d*(d + 1)/13
Let m be (0 + 2)*(5 - 3). Suppose y = -2*v + 13, -y = 3*y + m*v - 36. Factor -2/3*q**y - 10/3*q**4 - 6*q**3 + 0 - 4/3*q - 14/3*q**2.
-2*q*(q + 1)**3*(q + 2)/3
Factor 0 - 2/15*w**3 - 8/15*w**2 + 2/3*w.
-2*w*(w - 1)*(w + 5)/15
Let a(x) be the second derivative of x**7/273 - 2*x**6/195 + x**4/39 - x**3/39 + 17*x. Factor a(b).
2*b*(b - 1)**3*(b + 1)/13
Let -16/7*m + 2/7*m**5 + 0 - 8/7*m**2 + 10/7*m**4 + 12/7*m**3 = 0. Calculate m.
-2, 0, 1
Let l(n) = -21*n**3 - 89*n**2 - 35*n + 1. Let c(b) = 20*b**3 + 90*b**2 + 36*b - 2. Let y(m) = 4*c(m) + 5*l(m). Factor y(f).
-(f + 3)*(5*f + 1)**2
Let a(r) = 5*r - 4. Let i be a(2). Let g(j) be the second derivative of 0 + 1/60*j**4 - 3*j + 0*j**3 - 1/50*j**5 + 1/150*j**i + 0*j**2. Factor g(x).
x**2*(x - 1)**2/5
Let h(x) be the third derivative of -x**6/45 + x**5/30 + x**4/4 + 2*x**3/9 - 11*x**2. Factor h(i).
-2*(i - 2)*(i + 1)*(4*i + 1)/3
Suppose -3*h + 4*p - 22 = -8*h, 0 = -4*p + 12. Suppose -1/2*r + 1/2*r**4 + 0 + 1/2*r**3 - 1/2*r**h = 0. Calculate r.
-1, 0, 1
Let o = 88 + -86. Factor 2/3*r**4 + 4*r**o + 10/3*r**3 - 8/3*r - 16/3.
2*(r - 1)*(r + 2)**3/3
Factor 10*k**4 + 4*k**2 - 5 + 3*k**2 + 3*k**2 - 15*k**4.
-5*(k - 1)**2*(k + 1)**2
Determine h, given that -2/3*h**3 + 0 + 4/3*h**2 + 0*h - 2/3*h**4 = 0.
-2, 0, 1
Factor -12 - 23*p**2 + 2*p**2 + 32 + 6*p**2 - 5*p**3.
-5*(p - 1)*(p + 2)**2
What is o in 3/7*o**4 - 12/7 - 9*o**5 + 9/7*o**2 - 48/7*o + 111/7*o**3 = 0?
-1, -2/3, -2/7, 1
Factor 9*x**3 + x**2 + 2*x**2 + 24*x**4 - 15*x**4 + 3*x**5.
3*x**2*(x + 1)**3
Factor -1 + 0 + 4*b + 0*b + b**3 + b**2 - 5*b.
(b - 1)*(b + 1)**2
Suppose 0 = -10*k + 8*k + 18. Factor 5*j**2 + k + 2 - 3 + j**2 + 16*j.
2*(j + 2)*(3*j + 2)
Let i(o) = -216*o**2 - 141*o. Let b(j) = -43*j**2 - 28*j. Let c(w) = 21*b(w) - 4*i(w). Let s(m) = 11*m**2 + 7*m. Let f(h) = 5*c(h) + 18*s(h). Factor f(z).
3*z*(z + 2)
Let t(d) = -d**2 - 9*d + 2. Let k be t(-9). Suppose 3*w + 4 = 4*r, 0 = w + 3*r - k*r - 8. Let 2*x - 34*x**3 - 25*x**4 + x**w + 8*x**3 = 0. Calculate x.
-1, -1/3, 0, 1/4
Let b(f) = 5*f + 15. Let k be b(-3). Factor k - 4/3*r - 14/3*r**2.
-2*r*(7*r + 2)/3
Let -6 + 0*p**2 - 8*p + 2*p**3 + 14 + 8 - 4*p**2 = 0. What is p?
-2, 2
Let a(t) be the first derivative of -t**5/20 + t**4/8 + t**3/4 - t**2/2 - t + 33. Factor a(l).
-(l - 2)**2*(l + 1)**2/4
Let n = -7 + 14. Factor -14*t**4 - 54*t**2 - 22*t - 4 - n*t**3 - 4*t - 39*t**3.
-2*(t + 1)**3*(7*t + 2)
Let d(p) = 4*p**2 + 2*p. Let z be d(-1). Suppose -4/5 - 6/5*q - 2/5*q**z = 0. What is q?
-2, -1
Let f(d) = d**3 - 11*d**2 + 10*d + 2. Let b be f(10). Solve 9*i**2 + 0 + 9*i**b - 22*i + 4 = 0 for i.
2/9, 1
Factor -8*y - 31*y**2 + 12 + 12*y**2 + 15*y**2.
-4*(y - 1)*(y + 3)
Let w be 0 - (-1 + -1 + -3). Suppose 0 = q + 5, -5*s + w*q = -0*s - 35. Factor -2*g + 2*g**3 - 4/3*g**s + 4/3.
2*(g - 1)*(g + 1)*(3*g - 2)/3
Find t such that 2/5*t**2 + 0*t + 2/5*t**3 + 0 = 0.
-1, 0
Let j be (6/(-1568)*2)/(-3). Let h = 1763/392 + j. Find o such that -h*o**5 - 4*o - 3/2*o**4 - 2 + 17/2*o**3 + 7/2*o**2 = 0.
-1, -2/3, 1
Suppose -4*o + 6 = -6. Factor 6*p**2 + p**o + 3*p**3 - p**3 + 0*p**3.
3*p**2*(p + 2)
Solve -1/2*b**3 - 1/4 + 1/2*b + 1/4*b**4 + 0*b**2 = 0 for b.
-1, 1
Suppose -4*m + 9 = 1. Let p be ((-1)/m)/((-10)/40). Let -8*x**p + 0*x**2 - 117*x**3 + 44*x**2 - 372*x**5 + 57*x**5 - 456*x**4 + 12*x = 0. What is x?
-1, -2/5, -1/3, 0, 2/7
Let g = 6 + -4. Let f(l) be the second derivative of -l**3/6 + l**2/2 + 2*l. Let s(y) = -2*y**2 + 2*y. Let u(c) = g*f(c) + s(c). Factor u(w).
-2*(w - 1)*(w + 1)
Let t(l) = -6*l**3 - 36*l**2 - 21*l + 21. Let p be (1/2)/(3/24). Let q(w) = 7*w**2 + 8*w - w - p + w**3 - 3*w. Let j(i) = -21*q(i) - 4*t(i). Factor j(m).
3*m**2*(m - 1)
Let p(n) = -n**3. Let z(c) = 19*c**3 + 21*c**2 + 6*c. Let v(t) = -4*p(t) - z(t). Factor v(g).
-3*g*(g + 1)*(5*g + 2)
Let -2/15*h**3 + 0*h**2 + 0*h + 0 - 2/15*h**5 + 4/15*h**4 = 0. What is h?
0, 1
Factor -2 + 3 - 7*t**2 + 27*t - 25 + 4*t**2.
-3*(t - 8)*(t - 1)
Let k(h) be the first derivative of -10*h**5/7 + 40*h**4/7 + 2*h**3/21 - 44*h**2/7 - 24*h/7 + 4. Suppose k(s) = 0. What is s?
-2/5, 1, 3
Suppose 0 + 2/15*p**4 - 2/15*p**3 + 2/15*p - 2/15*p**2 = 0. Calculate p.
-1, 0, 1
Let g(m) = -m + 1. Let o be g(-2). Let d(s) be the first derivative of -2/21*s**o + 1/14*s**4 - 1 + 0*s + 0*s**2. Determine z, given that d(z) = 0.
0, 1
Let d(u) be the second derivative of 0*u**3 - 1/135*u**6 - u + 2/189*u**7 + 0*u**5 + 0 + 0*u**2 + 0*u**4. Factor d(f).
2*f**4*(2*f - 1)/9
Factor 0*l**2 + 5*l**2 + 16 - 4*l**2 - 5*l**2.
-4*(l - 2)*(l + 2)
Let z(q) be the first derivative of q**6/240 - q**5/120 - q**4/24 - 2*q**2 + 2. Let g(y) be the second derivative of z(y). Let g(r) = 0. What is r?
-1, 0, 2
Let w(z) be the second derivative of z**5/140 + z**4/24 - z**3/7 + z**2/2 - 2*z. Let s(c) be the first derivative of w(c). Factor s(h).
(h + 3)*(3*h - 2)/7
Solve 3*t + t**3 - 5*t**2 + 2*t**3 - t**2 = 0 for t.
0, 1
Let l be 1/((2/1)/30). Let r be (2 + l/(-6))/(-1). Factor -1/2*z + 0 - r*z**2.
-z*(z + 1)/2
Find v, given that -v - 9*v + 3*v**3 + 7*v = 0.
-1, 0, 1
Let j = -107 - -110. Let p(q) be the third derivative of 7/40*q**6 + 9/20*q**5 + 0 + 0*q + 4*q**2 + 0*q**j + 1/4*q**4. Solve p(d) = 0 for d.
-1, -2/7, 0
Let p(q) be the second derivative of 3*q**5/100 - q**4/20 + 12*q. Determine m so that p(m) = 0.
0, 1
Let m = 0 + 1. Suppose -2 + f**4 + 5 - f**3 - 3*f**2 + f - m = 0. What is f?
-1, 1, 2
Let c = 29 + -85/3. Let t(o) be the first derivativ