 Factor 1/2*m**2 + 1/4 - 3/4*m**4 - c*m + 1/4*m**5 + 1/2*m**3.
(m - 1)**4*(m + 1)/4
Let n(z) be the first derivative of -z**3/3 + z**2/2 + 12. Factor n(y).
-y*(y - 1)
Suppose 23 = 4*y - 1. Factor -15*z**2 + z + y*z**2 - 3 - 13*z.
-3*(z + 1)*(3*z + 1)
Suppose 4 = -3*n + 4*m, 3*n - m + 2*m = 1. Let x(v) be the second derivative of 0*v**2 + 0*v**3 + 0*v**4 + 2*v + n + 1/30*v**6 - 1/20*v**5. Factor x(w).
w**3*(w - 1)
Suppose -3*r - 17 + 8 = -p, -5*r - 4 = 2*p. Determine f so that 32/9 + 224/9*f + 11830/9*f**4 - 96*f**2 - 4472/9*f**p = 0.
-2/13, 2/7, 2/5
Let c(d) be the first derivative of d**5 + 5*d**4 + 25*d**3/3 + 5*d**2 - 28. Factor c(t).
5*t*(t + 1)**2*(t + 2)
Suppose 5*z = 43 + 92. Let l = z - 27. What is o in l*o + 1/2*o**3 + 0 + 1/2*o**2 = 0?
-1, 0
Let t(x) = x**2 - 19*x + 13. Let p(i) = 3*i**2 - 37*i + 27. Let r(w) = -3*p(w) + 5*t(w). Find z such that r(z) = 0.
2
Let n = -12 + 5. Let s = -2 - n. Suppose -4*h**2 - 3*h**5 + 2*h**3 - h**5 + 2*h**s + 4*h**4 = 0. What is h?
-1, 0, 1, 2
Determine b, given that 3/2*b + 1 + 1/2*b**2 = 0.
-2, -1
Let g = 80 - 78. Let 2/5*t**4 + 0*t**g + 0 + 0*t + 2/5*t**3 = 0. Calculate t.
-1, 0
Let p be (-23)/(-46) - (-3)/2. Factor -1/4*w**3 + 1/2*w**4 + 0 + 0*w + 0*w**p - 1/4*w**5.
-w**3*(w - 1)**2/4
Let z(f) = f - 4. Let y be z(6). Suppose 0*a**2 - 4 + y*a**2 + 2 - 2*a**3 + 2*a = 0. What is a?
-1, 1
Let x(j) be the third derivative of -7*j**5/240 + 5*j**4/32 - j**3/12 - 4*j**2. Factor x(g).
-(g - 2)*(7*g - 1)/4
Let u = 9 - 8. Let f(t) = 4*t**3 + t**2 - 2*t + 1. Let k be f(u). Find d, given that -2*d - 2*d**4 + 2*d**5 + 0*d**5 - d**2 - 3*d**2 + 6*d**k = 0.
-1, 0, 1
Determine l so that -2/5*l**3 + 2/5*l**4 + 0 + 0*l**2 + 0*l = 0.
0, 1
Let n be (6 + (-6 - 0))*-1. Solve -4/5*x**4 + 0*x + 0*x**2 + n - 2/5*x**3 - 2/5*x**5 = 0 for x.
-1, 0
Let z be (-1437)/36 + 5/20. Let c = 40 + z. Factor -1/3*m**2 + 1/3*m - 1/3*m**3 + c.
-(m - 1)*(m + 1)**2/3
Let t(v) = -2*v**2 + 6. Let z(a) = -a**3 - a**2 + a - 1. Let h(u) = -t(u) - 2*z(u). Factor h(j).
2*(j - 1)*(j + 1)*(j + 2)
Let r be -1 - (0 + -3 - 0). Solve c**r - 7*c**4 + 10*c**4 - 6*c**3 + 2*c**2 = 0.
0, 1
Let l(u) be the third derivative of -u**5/60 - u**3/6 + 3*u**2. Let x(z) = -7*z**2 + 2*z - 6. Let j(g) = 6*l(g) - x(g). Let j(r) = 0. Calculate r.
0, 2
Let v(f) be the first derivative of -1 + 1/60*f**4 + 1/10*f**2 + f + 1/15*f**3. Let b(u) be the first derivative of v(u). Determine k so that b(k) = 0.
-1
Let u be (0 - -12) + -4 + 3. Factor 0*m + 2*m - u*m**2 + 13*m**2.
2*m*(m + 1)
Let i(k) be the first derivative of -2*k**3/39 - 3*k**2/13 - 4*k/13 + 6. Factor i(q).
-2*(q + 1)*(q + 2)/13
Suppose -2*r + 5*r - 3*r**4 + 9*r**5 - 2*r - 15*r**3 + 5*r + 3*r**2 = 0. What is r?
-1, -2/3, 0, 1
Let k(o) = 20*o**2 + 28*o - 184. Let u(p) = 8*p**2 + 11*p - 74. Let x(w) = -5*k(w) + 12*u(w). Solve x(l) = 0.
-4, 2
Let r be ((-6)/(-4))/(4/8). Determine b so that 2*b + 4*b**3 - 3*b**r + 2 - 2*b**2 - 3*b**3 = 0.
-1, 1
Let p be 0 + -1 + 8/2. Determine d so that -2*d**3 - p*d**3 + 4*d**3 + 3*d + 2 = 0.
-1, 2
What is u in 6*u - 8*u**2 + 79*u**3 - 4 + 4*u - 77*u**3 = 0?
1, 2
Let a(b) be the second derivative of -b**4/4 - b**3 - 3*b**2/2 + 3*b. Factor a(w).
-3*(w + 1)**2
Let g(l) be the first derivative of 1/7*l**3 + 4 + 0*l**2 - 3/7*l. Factor g(x).
3*(x - 1)*(x + 1)/7
Let n(i) be the second derivative of 0*i**2 + 4*i + 0*i**4 + 0 + 0*i**3 - 3/20*i**5. Factor n(a).
-3*a**3
Let q = -1 - -4. Find y, given that -3 - q*y - 7*y + y - 3 - 3*y**2 = 0.
-2, -1
Solve 0*s + 75*s + 32 + 29*s - 28*s**2 = 0.
-2/7, 4
Suppose 4*c + 68 = 20. Let h = -12 - c. Solve -2/5*l**3 + 6/5*l**4 + h - 6/5*l**2 + 2/5*l = 0.
-1, 0, 1/3, 1
Suppose 5*g + 3 = 8. Let s = 4 + g. Factor 6*v**3 - 2*v - 4*v**5 - 4*v**3 + 2*v**s + 2*v**3.
-2*v*(v - 1)**2*(v + 1)**2
Let t = -101 + 105. Solve 1/4*g**t + 0*g + 1/4*g**3 + 0*g**2 + 0 = 0 for g.
-1, 0
Let r = 34 + -29. Factor 2/9*v**r + 0*v**2 + 0*v**4 + 0 + 0*v**3 + 0*v.
2*v**5/9
Let v(i) = 120*i**3 + 540*i**2 - 300*i. Let x(k) = -10*k**3 - 45*k**2 + 25*k. Let c(a) = 2*v(a) + 25*x(a). Factor c(y).
-5*y*(y + 5)*(2*y - 1)
Let o(j) be the second derivative of j**8/36960 + j**7/2310 + j**6/440 - j**4/12 - 4*j. Let w(k) be the third derivative of o(k). Find n such that w(n) = 0.
-3, 0
Let i be 0/(0 + -3 + 2). Let p = i + 4. Suppose -y**3 + 2*y + 3*y**3 + 0*y**3 - p*y**2 = 0. What is y?
0, 1
Let f(l) be the second derivative of -l**6/6 - 3*l**5/2 - 65*l**4/12 - 10*l**3 - 10*l**2 + 21*l. Factor f(x).
-5*(x + 1)**2*(x + 2)**2
Let m(p) be the first derivative of p**6/420 - p**5/105 + p**4/84 - 2*p**2 + 2. Let v(u) be the second derivative of m(u). Factor v(z).
2*z*(z - 1)**2/7
Factor 16*x**2 + 14*x**5 + 14*x**5 + 10*x**5 - 36*x**5 - 6*x**3 - 4*x**4 - 8*x.
2*x*(x - 2)*(x - 1)**2*(x + 2)
Let v be ((-62)/(-5))/((-14)/(-7)). Let m = -28/5 + v. Factor m*x**3 + 0 + 0*x + 6/5*x**2.
3*x**2*(x + 2)/5
Let z be 2/(3/6 - 0). Let p(s) be the first derivative of 2 - 1/7*s**2 + 1/14*s**z + 0*s + 0*s**3. Find g, given that p(g) = 0.
-1, 0, 1
Suppose -45*v = -40*v + 3*u - 27, 5*v = 5*u - 5. Factor 0 + t**2 + t**v + 1/4*t**4 + 0*t.
t**2*(t + 2)**2/4
Factor 3*m**3 + 3*m**3 - 3*m**2 - 2170*m**4 + 6*m**2 + 2173*m**4.
3*m**2*(m + 1)**2
Let a(i) be the first derivative of 0*i**2 + 1 + 2/9*i - 2/27*i**3. Determine m so that a(m) = 0.
-1, 1
Let f(l) be the third derivative of l**7/252 - l**6/60 + l**5/60 - l**4/12 - 2*l**2. Let p(o) be the second derivative of f(o). Factor p(k).
2*(k - 1)*(5*k - 1)
Solve 50/3 + 2/3*c**2 - 20/3*c = 0.
5
Suppose -3*l + 2*l = -3. Factor -14*k**l + 24*k - 14*k**2 + 4 - 17*k**2 + 4 + 13*k**2.
-2*(k - 1)*(k + 2)*(7*k + 2)
Let f(x) be the first derivative of x**9/3024 - x**8/420 + x**7/168 - x**6/180 - 2*x**3/3 - 2. Let n(d) be the third derivative of f(d). Factor n(v).
v**2*(v - 2)*(v - 1)**2
Suppose 14*f**2 + 58*f**2 - 75 - 30*f**3 + 30*f - f**4 + 4*f**4 = 0. What is f?
-1, 1, 5
Let s(h) be the first derivative of -h**4/4 - h**3/3 + h**2/2 + h - 6. Let z(j) = 4*j**3 + 8*j**2 + 2*j - 2. Let u(c) = -4*s(c) - 2*z(c). Factor u(d).
-4*d*(d + 1)*(d + 2)
Find j such that 0*j + 61*j**5 + 0*j - 56*j**5 = 0.
0
Let w(v) = 9*v**2 + 6*v - 11. Let i(u) = 55*u**2 + 35*u - 65. Let d(k) = 4*i(k) - 25*w(k). Suppose d(r) = 0. Calculate r.
-3, 1
Let t(z) be the third derivative of z**9/241920 + z**8/80640 - z**7/10080 - z**5/20 - 2*z**2. Let p(i) be the third derivative of t(i). Solve p(w) = 0.
-2, 0, 1
Solve -2/3*s + 0 - 1/3*s**3 + s**2 = 0 for s.
0, 1, 2
Factor -3*h**4 + 5 - 4 + 15*h**3 + 1 + 22 - 18*h**2 - 12*h.
-3*(h - 2)**3*(h + 1)
Let k = 21 - 14. Let r(i) be the second derivative of 0*i**3 + 1/50*i**5 + i - 2/75*i**6 + 0*i**2 + 0*i**4 + 0 + 1/105*i**k. Determine g so that r(g) = 0.
0, 1
Solve -224/9*p**4 - 46/9*p**2 + 0 - 4/9*p - 176/9*p**3 = 0 for p.
-2/7, -1/4, 0
Let x(i) be the second derivative of i**6/60 + 10*i. What is c in x(c) = 0?
0
Let v(c) = -c**3 + 3*c**2 - c - 2. Let o be v(2). Let w(z) = z + 2. Let r be w(o). Factor k + k + 0*k - 4 + r*k**2.
2*(k - 1)*(k + 2)
Let b(i) be the first derivative of -4*i**5/15 + 11*i**4/3 - 140*i**3/9 + 50*i**2/3 + 34. Factor b(a).
-4*a*(a - 5)**2*(a - 1)/3
Determine v, given that 0 + 4/3*v - 2/3*v**3 - 2/3*v**2 = 0.
-2, 0, 1
Suppose r = 5*r. Let b = 207/2 - 103. Determine q, given that r*q + 1/2*q**2 - b = 0.
-1, 1
Let p = 127/3 + -83/2. Let j(d) be the second derivative of 0 - p*d**4 + 4/3*d**3 + 1/5*d**5 - d - d**2. Factor j(l).
2*(l - 1)**2*(2*l - 1)
Let n(v) be the second derivative of 1/24*v**3 - 1/48*v**4 + 0*v**2 - 2*v + 0. Suppose n(o) = 0. What is o?
0, 1
Let m(k) = -5*k**3 - 45*k**2 - 55*k - 15. Let d(s) = s + 1. Let q(j) = -15*d(j) - m(j). Factor q(p).
5*p*(p + 1)*(p + 8)
Factor 7*r - 3*r**2 - r - 3*r.
-3*r*(r - 1)
Let d(f) be the second derivative of 0*f**4 + 0*f**3 - 1/42*f**7 + 1/90*f**6 + 1/30*f**5 + 0 + 0*f**2 - 3*f. Suppose d(g) = 0. Calculate g.
-2/3, 0, 1
Let r(q) = 10*q**2 + 14*q. Let x(l) = l**2 + l - 1. Let g(n) = r(n) - 12*x(n). Determine t so that g(t) = 0.
-2, 3
Suppose -d = -2 - 2. Factor -4*l - 2*l - 2 + 0*l**d + 4*l**4 + 6*l**3 - 2*l**2.
2*(l - 1)*(l + 1)**2*(2*l + 1)
Let p(k) = 51*k**4 - 30*k**3 - 51*k**2 + 30*k. Let s(c) = -5*c**4 + 3*c**3 + 5*c**2 - 3*c. Let l(b) = -2*p(b) - 21*s(b). Factor l(u).
3*u*(u - 1)**2*(u + 1)
Factor -4*c