Factor b*f**2 - 5/4*f**4 - 1/2*f + 0 + 1/2*f**3.
-f*(f - 1)*(f + 1)*(5*f - 2)/4
Suppose 6*w - 5*w - 4 = 0. Determine i, given that -2*i**3 + 3*i**4 - 6*i**w - 4*i**4 = 0.
-2/7, 0
Factor 2/3*q + 0 + 2*q**3 + 2/3*q**4 + 2*q**2.
2*q*(q + 1)**3/3
Let s(i) be the first derivative of 9*i**5/70 - i**4/6 - 2*i**3/21 + 4*i + 4. Let k(d) be the first derivative of s(d). Determine x, given that k(x) = 0.
-2/9, 0, 1
Let y(z) = 22*z**2 - 18*z - 4. Let q(h) = -7*h**2 + 6*h + 1. Let g(v) = -16*q(v) - 5*y(v). Find f, given that g(f) = 0.
1, 2
Let o(k) be the second derivative of k**4/12 + k**3/3 + 16*k. Find s such that o(s) = 0.
-2, 0
Let z = 119/2 - 829/14. Factor -2/7*v**3 + 0 - z*v**4 + 2/7*v + 2/7*v**2.
-2*v*(v - 1)*(v + 1)**2/7
Factor 6*a**3 + 10*a**3 - 2*a**4 - 4*a**2 - 22*a**3.
-2*a**2*(a + 1)*(a + 2)
Let c = 74 + -443/6. Let y(x) be the first derivative of 0*x - 1/6*x**6 - 3 + c*x**2 - 4/15*x**5 + 1/6*x**4 + 4/9*x**3. Solve y(l) = 0 for l.
-1, -1/3, 0, 1
Let 16/5*n**2 - 8/5 - 2/5*n - 2/5*n**5 + 4/5*n**3 - 8/5*n**4 = 0. What is n?
-4, -1, 1
Let v(c) be the second derivative of 25/14*c**7 + 0 - 3*c**6 - 2*c**4 - 4*c + 0*c**2 - 27/5*c**5 + 0*c**3. Factor v(g).
3*g**2*(g - 2)*(5*g + 2)**2
Suppose 0 = -4*n + 3*l + 9 + 10, 5*n - 18 = -2*l. Find a, given that 46/9*a**2 + 160/9*a**n - 8/9 + 3200/9*a**5 + 56/9*a - 808/9*a**3 = 0.
-2/5, 1/4
Let o(r) be the second derivative of 0*r**2 + 0*r**3 - r + 0 - 1/30*r**5 - 4/27*r**6 + 1/27*r**4. Determine g so that o(g) = 0.
-2/5, 0, 1/4
Let a be (-12)/16 + (-22)/(-8). Let t(x) be the first derivative of 1/2*x + 0*x**a - 2 - 1/6*x**3. Factor t(i).
-(i - 1)*(i + 1)/2
Let l(t) be the third derivative of 1/35*t**5 + 0*t + 2*t**2 + 1/735*t**7 + 1/21*t**3 + 0 + 1/105*t**6 + 1/21*t**4. Factor l(r).
2*(r + 1)**4/7
Let u(c) be the first derivative of -2*c**3 - 2/5*c**5 - 3/2*c**4 + 3 - c**2 + 0*c. Factor u(y).
-2*y*(y + 1)**3
Let m(c) be the first derivative of c**4/114 - 4*c**3/57 + 4*c**2/19 + 7*c + 2. Let y(d) be the first derivative of m(d). Suppose y(p) = 0. What is p?
2
Let 1/4*a**3 + 1/4*a**2 - 1/4*a - 1/4 = 0. Calculate a.
-1, 1
Let j(i) be the third derivative of 7*i**2 + 0*i - 7/11*i**5 + 0 + 49/165*i**7 + 49/660*i**6 - 8/33*i**3 + 19/33*i**4. Factor j(f).
2*(f + 1)*(7*f - 2)**3/11
Let v(d) be the third derivative of d**4/24 + 4*d**3/3 - 2*d**2. Let h be v(-8). Suppose -2*b**4 + 2*b**2 + h*b**2 + b**5 + b - 2*b = 0. What is b?
-1, 0, 1
Let k(a) be the first derivative of 1/30*a**4 + 3 - 1/5*a**2 + 0*a**3 - 4*a. Let b(p) be the first derivative of k(p). Suppose b(y) = 0. What is y?
-1, 1
Suppose -2/11*f**3 + 0 + 0*f**2 + 0*f + 2/11*f**4 = 0. What is f?
0, 1
Let j(f) be the third derivative of -f**8/112 + 2*f**7/105 + f**6/60 - f**5/15 + f**4/24 + 42*f**2. Suppose j(o) = 0. Calculate o.
-1, 0, 1/3, 1
Let l(y) = y**2 + 5*y. Let f be l(-5). Factor 8*d - 6*d**3 + 2*d**5 + 0*d**2 + f*d**2 - 8*d**2 + 4*d**4.
2*d*(d - 1)**2*(d + 2)**2
Let k = 28 + -26. Suppose 0 = k*z - 4*r, -4*z - z + 4*r = 0. Factor z + 25/4*o**5 + 0*o + 0*o**2 + 5*o**4 + o**3.
o**3*(5*o + 2)**2/4
Let h(m) be the first derivative of m**4/2 - m**3 - m**2/2 + 2*m - 1. Let p be h(2). Solve 2/5*k**p - 4/5*k**2 + 2/5*k**5 + 2/5 + 2/5*k - 4/5*k**3 = 0.
-1, 1
Suppose 0*f + f = 4. Let o(w) be the first derivative of -1/12*w**f + 0*w**3 + 2 + 2/3*w + 1/2*w**2. Factor o(z).
-(z - 2)*(z + 1)**2/3
What is l in 0*l - l**3 + 0 + 1/2*l**5 - 1/2*l**4 + 0*l**2 = 0?
-1, 0, 2
Let j(w) be the first derivative of w**6/36 + w**5/30 - w**4/12 - w**3/9 + w**2/12 + w/6 - 2. Factor j(a).
(a - 1)**2*(a + 1)**3/6
Let o(h) = -h. Let x(c) = -3*c**2 - 7*c - 3. Let l(q) = -o(q) + x(q). Factor l(y).
-3*(y + 1)**2
Let y be 80/75 - 3/(30/4). Let p(w) be the first derivative of -1 + 2*w + y*w**3 - 2*w**2. Let p(i) = 0. What is i?
1
Let z = 32/147 - -10/147. Factor 0 - z*f**2 + 2/7*f.
-2*f*(f - 1)/7
Let h be 1*-2 + 25/210*17. Let c(q) be the second derivative of 0*q**2 + 0 - 1/21*q**3 + h*q**4 + q. Factor c(v).
2*v*(v - 1)/7
Let u be (-78)/4*(-3)/(-6). Let q = u + 10. Let 0 - 1/4*l**4 + q*l - 1/4*l**3 + 1/4*l**2 = 0. Calculate l.
-1, 0, 1
Factor 14 + 2/7*n**2 + 4*n.
2*(n + 7)**2/7
Let o(m) = -3*m - 23. Let q be o(-9). Factor 0*v - 2/7 + 0*v**3 - 2/7*v**q + 4/7*v**2.
-2*(v - 1)**2*(v + 1)**2/7
Suppose v - h + 9 = 3*v, v = h - 3. Let g(w) be the first derivative of 1 - 1/4*w**v + 1/4*w + 1/12*w**3. Determine x so that g(x) = 0.
1
Suppose -10 = 3*b - 8*b. Suppose 2*s = 2*r - 6, 2*s + 4*r + b - 14 = 0. Factor s + m + 1/2*m**2.
m*(m + 2)/2
Suppose -10*z + 21 - 1 = 0. Factor 2/7*w**z + 8/7 + 8/7*w.
2*(w + 2)**2/7
Let u(t) be the first derivative of -2*t**5/35 + 3*t**4/14 - 4*t**3/21 - 13. Factor u(m).
-2*m**2*(m - 2)*(m - 1)/7
Factor -1/4*z**5 + 0*z + 0 - 1/4*z**4 + 1/4*z**2 + 1/4*z**3.
-z**2*(z - 1)*(z + 1)**2/4
Let g(w) = -3*w**3 - 1. Let b be g(-1). Suppose -2*c - 2*x + 12 = 0, 5*x = -b*c + 4*x + 10. Factor -1/4*v**c + 1/2 - 1/4*v**2 - 3/4*v**3 + 3/4*v.
-(v - 1)*(v + 1)**2*(v + 2)/4
Let i = 73/96 + -3/32. Factor -i*s**4 + 1/3*s**3 + 1/3*s**5 + 0*s**2 + 0*s + 0.
s**3*(s - 1)**2/3
Let f(j) be the second derivative of -j**9/68040 + j**8/30240 + j**7/11340 - j**6/3240 - 5*j**4/12 - j. Let v(l) be the third derivative of f(l). Factor v(z).
-2*z*(z - 1)**2*(z + 1)/9
Let c(r) = -r**3 + 4*r**2 - 4*r - 1. Let z be c(3). Let q be (-64)/(-22)*z/(-8). Factor q*u - 8/11 + 10/11*u**2.
2*(u + 2)*(5*u - 2)/11
What is x in -51/11*x**2 + 1/11*x**3 + 867/11*x - 4913/11 = 0?
17
Let u(d) be the third derivative of d**5/120 - d**4/12 - d**3 - d**2 - 26*d. Factor u(f).
(f - 6)*(f + 2)/2
Let f(l) be the second derivative of 0*l**3 - 1/42*l**4 + 3*l + 0*l**2 + 0*l**5 + 1/105*l**6 + 0. Factor f(x).
2*x**2*(x - 1)*(x + 1)/7
Factor 8/7*f**5 + 0 + 20/7*f**4 - 4/7*f**2 - 4/7*f + 12/7*f**3.
4*f*(f + 1)**3*(2*f - 1)/7
Suppose -1/4*j + 1/2*j**2 - 1/4*j**3 + 0 = 0. What is j?
0, 1
Let k = 760/2611 - 2/373. Suppose 0 = 4*s + 6*s - 20. Let -k*x**s - 2/7 - 4/7*x = 0. What is x?
-1
Find m such that -1/4*m**5 + 0*m - 3/4*m**3 - 3/4*m**4 - 1/4*m**2 + 0 = 0.
-1, 0
Suppose 9*u - 11*u + 52 = 0. Factor 2*c - 2 + 24*c**2 - u*c**2 - 6*c.
-2*(c + 1)**2
Let p(b) = b**2 + 3. Let v be p(3). Let n(y) = y**3 - 6*y**2 - 7*y + 3. Let g be n(7). Solve -g*k**2 - 5*k**2 - 2*k**5 - v*k**3 + 0*k - 2*k - 8*k**4 = 0.
-1, 0
Solve 8*t**4 - 14*t**3 + 33*t**2 - 37*t**2 + 2 - 2 = 0 for t.
-1/4, 0, 2
Let z(h) be the first derivative of 2*h**5/45 - h**4/3 + 2*h**3/3 + 57. Let z(i) = 0. Calculate i.
0, 3
Solve 0*q + 0 - 3/2*q**3 - 1/6*q**2 = 0.
-1/9, 0
Factor 1/3*l**5 - 1/3*l**3 - 1/3*l**2 + 0*l + 1/3*l**4 + 0.
l**2*(l - 1)*(l + 1)**2/3
Let n(p) be the third derivative of p**6/30 + 2*p**5/3 + 17*p**4/6 + 16*p**3/3 - 33*p**2. Determine i, given that n(i) = 0.
-8, -1
Let g = -165/2 - -84. Suppose -2*l + 2 = -l. Find s such that 1/2 - s + 2*s**4 - g*s**2 + l*s**3 = 0.
-1, 1/2
Let d(p) be the second derivative of p**5/5 + p**4/3 - p**3/3 + p**2 - 3*p. Let a(g) = -g**3 - g**2 + g - 1. Let c(h) = 2*a(h) + d(h). Factor c(k).
2*k**2*(k + 1)
Let h(k) = -2*k**3 - 3*k**2 + 2*k. Let i(p) = p**3 + 2*p**2 - p. Let x(n) = -2*h(n) - 3*i(n). Factor x(f).
f*(f - 1)*(f + 1)
Suppose -2*q + 0 + 6 = 0, 2*k = 4*q - 10. Suppose 9*m**4 + 12*m**3 + k + 7*m**2 - 4*m**2 - 1 = 0. What is m?
-1, -1/3, 0
Suppose y - 4*y + 0*y - 3*y**2 = 0. What is y?
-1, 0
Factor 31*j**2 + 22*j**3 - 10*j**2 + 6*j - 4*j**3.
3*j*(2*j + 1)*(3*j + 2)
Let g(m) be the third derivative of -m**5/300 - m**4/120 + m**3/15 + 8*m**2. Suppose g(j) = 0. Calculate j.
-2, 1
Factor -r - 1 + 24*r**2 + 2 - 25*r**2 + r**3.
(r - 1)**2*(r + 1)
Determine f, given that 0 - 9/8*f**3 + 3/4*f + 15/8*f**2 = 0.
-1/3, 0, 2
Let j = -1835/12 + 153. Let n(r) be the first derivative of -2 - j*r**4 + 2/9*r**3 + 0*r - 1/6*r**2. Let n(v) = 0. Calculate v.
0, 1
Let n be (-18)/(-4) + 1/2. Suppose n*y = y. Factor y - 2/9*k + 0*k**2 + 2/9*k**3.
2*k*(k - 1)*(k + 1)/9
Let z(c) = 4*c + 2*c - 4 + 4*c**3 - 5*c**2 - 7*c. Let i(f) = 3*f**3 - 5*f**2 - f - 3. Let r(l) = 6*i(l) - 5*z(l). Suppose r(w) = 0. Calculate w.
-2, -1, 1/2
Let h = -21 + 26. Let y(u) be the third derivative of 2*u**2 + 0*u + 0 + 0*u**3 + 0*u**4 + 1/15*u**h + 1/21*u**7 - 7/60*u**6. Suppose y(z) = 0. Calculate z.
0, 2/5, 1
Suppose -8*v - 12 = -10*v. Suppose c + v = 4*c. Factor -1/2 + 