Determine f, given that o(f) = 0.
-2/3, 1, 2
Suppose -208 = -3*d - 202. Factor -1/4*o**d + 1/2*o + 1/4 - 1/2*o**3.
-(o - 1)*(o + 1)*(2*o + 1)/4
Let k = 6 + -4. Let -323*p + 2*p**3 + 316*p + 5*p**3 - 2*p**2 + k = 0. What is p?
-1, 2/7, 1
Let w(m) = m**4 + m**3 + m**2. Let i be 40/50 + (-2)/(-10). Let o(x) = 18*x**4 + 18*x**3 + 9*x**2. Let a(n) = i*o(n) - 15*w(n). Find k such that a(k) = 0.
-2, 0, 1
Factor -165/2*k + 35/2*k**2 - 25.
5*(k - 5)*(7*k + 2)/2
Suppose 0 = 5*c + 31 + 9. Let j = -4 - c. Factor t**j + 0*t**4 - 4*t**4.
-3*t**4
Suppose -5*x - 7 = -17. Let o(n) = n**2 - n + 2. Let s be o(x). Factor -3*j**2 + 2*j**4 + 3*j**4 - 4*j**s - 2*j.
j*(j - 2)*(j + 1)**2
Let s = 14 + -12. Factor -5 + 5 + 0*h**5 - s*h**5 + 2*h**3.
-2*h**3*(h - 1)*(h + 1)
Let z(q) = q**4 + q**3 - q**2 + q - 1. Let f(a) = 10*a**5 - 25*a**4 - 50*a**3 + 20*a**2 - 20*a + 35. Let p(h) = -f(h) - 30*z(h). Determine i so that p(i) = 0.
-1, -1/2, 1
Let m(x) be the first derivative of -2/9*x**2 + 3 + 0*x + 2/27*x**3. Find y such that m(y) = 0.
0, 2
Let w(p) be the third derivative of -1/336*p**8 + 0 + 1/6*p**4 + 0*p**3 + 0*p - 2/105*p**7 + 1/15*p**5 + 2*p**2 - 1/40*p**6. Solve w(d) = 0.
-2, -1, 0, 1
Let g(d) = 4*d + 16. Let a be g(-8). Let o be (9/(-24))/(4/a). Determine y so that -1 + o*y - 1/2*y**2 = 0.
1, 2
Factor -u**2 + 29*u + 16*u + 6*u**2.
5*u*(u + 9)
Let i(m) be the second derivative of 0 + 0*m**3 + m + 0*m**4 + m**2 - 1/30*m**5. Let a(h) be the first derivative of i(h). Factor a(b).
-2*b**2
Let x = 9 - 10. Let u = x - -3. Determine s so that 2/7*s**u + 0 + 2/7*s = 0.
-1, 0
Let x(k) = k**3 + 7*k**2 - 21*k - 25. Let j be x(-9). Find f such that 8/11*f**3 + 0 - 2/11*f**j - 6/11*f**4 + 0*f = 0.
0, 1/3, 1
Factor -r**5 + 4*r**3 - 66*r**4 + 2*r**5 + 70*r**4.
r**3*(r + 2)**2
Let s = -90 - -1621/18. Let w = s + 5/18. Suppose -z**2 + z**3 + 1/3*z - w*z**4 + 0 = 0. What is z?
0, 1
Let l(p) be the first derivative of -p**3 - 15*p**2/2 + 18*p - 7. Solve l(g) = 0 for g.
-6, 1
Let m(b) be the second derivative of b**7/21 - 8*b**6/75 + b**5/50 + b**4/15 - 13*b. Factor m(o).
2*o**2*(o - 1)**2*(5*o + 2)/5
Factor 0 - 2/5*w + 2/5*w**3 - 1/5*w**4 + 1/5*w**2.
-w*(w - 2)*(w - 1)*(w + 1)/5
Factor -2/17*q**2 + 4/17*q + 0.
-2*q*(q - 2)/17
Let i = 232 - -473. Solve -120*g - i*g**3 - 12 + 108*g**2 - 4*g**5 - 543*g**2 - 55*g**5 - 525*g**4 - 88*g**5 = 0 for g.
-1, -2/7
Let b(m) be the third derivative of m**6/300 - 2*m**5/75 + m**4/15 + m**2. Factor b(y).
2*y*(y - 2)**2/5
Suppose 0 = 7*h - 9 - 12. Suppose -1/3*y**h - 5/3*y + 4/3*y**2 + 2/3 = 0. Calculate y.
1, 2
Let t(q) = q**2 + 1. Let c(p) = 6*p**2 - 2*p + 5. Let o = 2 - -18. Suppose 4*h = 2*h + o. Let j(u) = h*t(u) - 2*c(u). Factor j(l).
-2*l*(l - 2)
Let b(p) be the third derivative of -1/28*p**4 + 0*p**3 + 0 + 0*p - 1/140*p**5 - 5*p**2. Solve b(m) = 0.
-2, 0
Let m = -13 - -19. Let o be (-2 + 1 - -1) + m. Let f(n) = -n**3 + n - 1. Let y(c) = -2*c**5 - 4*c**4 - 8*c**3 + 6*c - 6. Let w(t) = o*f(t) - y(t). Factor w(q).
2*q**3*(q + 1)**2
Let v(j) = -j**3 + 7*j**2 - j + 10. Let n be v(7). Let q be ((-1)/3*(21 + -20))/(-1). Factor 0*d + 0 - 1/3*d**2 - q*d**n.
-d**2*(d + 1)/3
Factor 38/3*r**4 + 2/3*r**2 - 4/3*r + 14/3*r**5 + 0 + 10*r**3.
2*r*(r + 1)**3*(7*r - 2)/3
Let h(t) = -27*t**4 - 189*t**3 - 252*t**2 + 384*t + 96. Let k(q) = -q**3 - q**2. Let z(d) = -h(d) - 6*k(d). Factor z(i).
3*(i - 1)*(i + 4)**2*(9*i + 2)
Let u(j) = -6*j + 1. Let w be u(-3). Let k = w - 13. Determine x so that 1/2 + 4*x**3 - 15/4*x + k*x**2 = 0.
-2, 1/4
Let w(k) be the second derivative of -k**7/504 - 7*k**6/720 - k**5/60 + k**4/12 - k. Let q(v) be the third derivative of w(v). Find i, given that q(i) = 0.
-1, -2/5
Let n = 14 + -12. Suppose n*r - 14 = -6. Suppose 2/5*p**3 + 0*p**2 - 2/5*p**r + 0 + 0*p = 0. What is p?
0, 1
Let k(g) be the third derivative of g**8/2240 - g**7/360 + g**6/360 + g**4/12 + 3*g**2. Let b(y) be the second derivative of k(y). Determine o so that b(o) = 0.
0, 1/3, 2
Let k(a) = 2*a**4 + 2*a**3 - 2*a**2 + a - 3. Let q(l) = -l**4 - l**3 + l**2 - l + 2. Let s(v) = -2*k(v) - 3*q(v). Solve s(i) = 0 for i.
-1, 0, 1
Let b be (-15)/24 - -1 - 0. Let n(k) be the first derivative of -1/16*k**4 + b*k**2 + 1/2*k + 0*k**3 + 1. Factor n(f).
-(f - 2)*(f + 1)**2/4
Let w = 155/3 - 51. Let h(v) = -v**3 + 2*v**2 + 2*v - 4. Let u be h(2). Factor -4/3*r**2 + 0 + u*r**3 + w*r**5 + 4/3*r**4 - 2/3*r.
2*r*(r - 1)*(r + 1)**3/3
Let s(u) be the second derivative of -u**6/60 - u**5/20 - 6*u. Suppose s(g) = 0. What is g?
-2, 0
Let v(c) be the second derivative of c**7/13860 - c**5/660 + c**4/3 + 2*c. Let f(r) be the third derivative of v(r). Find p, given that f(p) = 0.
-1, 1
Let r(v) be the first derivative of -v**5/15 + 2*v**3/9 - v/3 + 2. Factor r(x).
-(x - 1)**2*(x + 1)**2/3
Let t(n) be the second derivative of n + 0*n**3 + 0 + 1/100*n**5 + 0*n**4 + 0*n**2. Suppose t(u) = 0. Calculate u.
0
Let r be (1*(1 - 4))/(1*-1). Let y(z) be the first derivative of 1/12*z**4 - 2 + 0*z - 1/3*z**r + 1/3*z**2. Find s such that y(s) = 0.
0, 1, 2
Let v = 6 + -6. Let q be 2*(-3 + 2)/(-4). Factor -3/4*c**3 + v + 0*c - q*c**2 - 1/4*c**4.
-c**2*(c + 1)*(c + 2)/4
Let z(b) be the second derivative of 9/40*b**5 + 0*b**4 - 1/20*b**6 + 0 + 0*b**2 + 4*b - b**3. Factor z(n).
-3*n*(n - 2)**2*(n + 1)/2
Let y(x) be the second derivative of -x**5/15 + x**4/8 + x**3/6 + 2*x**2 + x. Let w(t) be the first derivative of y(t). Factor w(n).
-(n - 1)*(4*n + 1)
Let w = -1145 - -1147. Solve 0*t + 3/2*t**w + 0 + 3/2*t**3 = 0.
-1, 0
Let g = 202 - 807/4. What is b in g*b**5 - 5/4*b**2 - 3/4*b**3 - 1/2*b + 1/4*b**4 + 0 = 0?
-1, 0, 2
Determine b so that -12*b**5 + 99*b**2 + 69*b**3 + 13*b - 538 + 38*b + 547 = 0.
-1, -1/2, 3
Let v = 3/14 + -5/56. Let d(t) be the second derivative of 0 - t + 0*t**4 - 1/120*t**6 + v*t**2 + 1/40*t**5 - 1/12*t**3. What is j in d(j) = 0?
-1, 1
Factor 9/5*f**4 - 16/5*f**3 + 0 - 4/5*f**2 + 0*f.
f**2*(f - 2)*(9*f + 2)/5
Let o(h) = -h**3 - 3*h**2 - 3*h - 3. Let j be o(-3). Suppose g + 10 = j*g. Factor 5*t**3 - 4*t**3 - g + 6*t + t**3 - 6*t**2.
2*(t - 1)**3
Suppose 7*w - 8 = 3*w. Let g(d) = -d**3 - 6*d**2 + 7*d + 2. Let v be g(-7). Factor 3*j**4 + j**w - 2*j**3 - 1 - v*j**5 + j**5 + 3*j - 3*j**2.
-(j - 1)**4*(j + 1)
Let j = -40 - 0. Let f be j/(-18) - 8/36. Solve -2*z**4 + z - 2*z**3 + 0*z**4 + 2*z**3 + 5*z**3 - 4*z**f = 0 for z.
0, 1/2, 1
Let l(b) be the third derivative of -b**5/150 - b**4/15 - 4*b**3/15 + 17*b**2. Solve l(j) = 0.
-2
Let f(s) be the third derivative of 2*s**7/105 + s**6/10 + s**5/5 + s**4/6 - 2*s**2. Find l such that f(l) = 0.
-1, 0
Let u(g) be the second derivative of g**7/210 + g**6/60 - g**4/12 - g**3/6 - g**2 + g. Let o(z) be the first derivative of u(z). Let o(n) = 0. Calculate n.
-1, 1
Suppose 3*x = x - 10. Let d be (-6)/(-9)*x/(-10). Factor 0 + 0*k - d*k**2.
-k**2/3
Let t(l) = 9*l + 1. Let y be t(3). Suppose 2*z**5 - 25*z**4 + z**2 - 3*z**2 - 3*z**3 + y*z**4 = 0. What is z?
-2, -1/2, 0, 1
Let u(i) be the third derivative of -1/30*i**5 + 0 - 1/30*i**6 + 0*i + 1/12*i**4 + 0*i**3 - 2*i**2. Factor u(a).
-2*a*(a + 1)*(2*a - 1)
Let b = 4 - 2. Suppose -3*k**3 + 0 + 0*k**3 + b - k**2 + 5*k**4 - 6*k**4 + 3*k = 0. What is k?
-2, -1, 1
Factor 0*s**2 + 0 + 4/13*s**4 - 2/13*s**3 - 2/13*s**5 + 0*s.
-2*s**3*(s - 1)**2/13
Factor -27/5*d - 12/5 - 18/5*d**2 - 3/5*d**3.
-3*(d + 1)**2*(d + 4)/5
Suppose -26 + 6 = 5*x - 4*w, -4*w = -20. Factor x*i**3 + 0 + 3/5*i**4 + 0*i + 0*i**2.
3*i**4/5
Suppose -2*w = f - 3, -2*w + 4*f + 2 = 14. Let v(r) be the first derivative of 0*r**2 + 1 + 0*r + w*r**3 - 1/2*r**4. Solve v(o) = 0 for o.
0
Factor 4*y**2 - 3*y**4 + 4*y**3 - y**4 - 2*y - 2*y.
-4*y*(y - 1)**2*(y + 1)
Suppose -4 = 2*h, -h + 6 + 2 = 5*l. Determine o so that -o - 3*o**4 - l*o**3 + 3*o**2 - o + 5*o**3 - o = 0.
-1, 0, 1
Let l(c) be the third derivative of -c**6/840 + c**5/35 - 15*c**4/56 + 25*c**3/21 - 4*c**2. Find k, given that l(k) = 0.
2, 5
Let d(v) be the first derivative of 2*v**3/3 + 8*v**2 + 32*v + 7. Find h such that d(h) = 0.
-4
Factor -30*d**2 - 15*d + 16*d**2 + 17*d**2 + 18.
3*(d - 3)*(d - 2)
Let z = -182 + 185. Determine d, given that -2/3*d + 4/3*d**2 - 2/3 - 2/3*d**5 + 4/3*d**z - 2/3*d**4 = 0.
-1, 1
Let s(l) be the third derivative of -3*l**8/896 - 13*l**7/560 - l**6/24 + l**5/20 + l**4