- 10. Suppose z(b) = 0. Calculate b.
-3, -1/3
Find m, given that -m**4 + 3*m**3 - 2000 + 2000 - 4*m = 0.
-1, 0, 2
Let n(f) be the second derivative of f**5/160 + f**4/24 + 5*f**3/48 + f**2/8 + 7*f. What is a in n(a) = 0?
-2, -1
Let t(b) = -26*b**4 + 74*b**3 - 4*b**2 - 96*b + 24. Let k(w) = -w**3 + w**2 + w + 1. Let c(f) = -8*k(f) + t(f). Find y such that c(y) = 0.
-1, 2/13, 2
Let w = 28 + -25. Let y(z) be the second derivative of 1/3*z**w + 0*z**2 + 0 + 1/6*z**4 + 3*z. Solve y(t) = 0.
-1, 0
Let k = -3935 - -15867/4. Let r = k - 31. Factor -1/2 + 3/4*o**2 + 7/4*o**3 - 3/4*o + r*o**4.
(o + 1)**3*(3*o - 2)/4
Let x be -2*(-5)/((-20)/(-8)). Factor 6*r**4 - 16*r**4 + 2*r**5 - 14*r**2 + 18*r**3 + 0*r**3 + x*r.
2*r*(r - 2)*(r - 1)**3
Let s = -469 - -16885/36. Let o(r) be the third derivative of 0 + 1/90*r**5 + 0*r + 2*r**2 + s*r**4 - 1/9*r**3 - 1/180*r**6. Determine w, given that o(w) = 0.
-1, 1
Let a = 11 + -21/2. Find f, given that a*f - 1/2*f**3 + 1/2 - 1/2*f**2 = 0.
-1, 1
Solve -2/7*m**2 + 0 - 1/7*m = 0.
-1/2, 0
Let a(o) = -9*o - 9. Let u(f) = -f**2 + 8*f + 8. Let g(l) = -4*a(l) - 3*u(l). Factor g(j).
3*(j + 2)**2
Let s = 7 - 5. Suppose 0*k - 4*k + 2*k**2 + 8 - s*k - 2*k = 0. Calculate k.
2
Let c(s) be the first derivative of s**5/30 - s**4/9 + s**3/9 - 3*s + 3. Let m(v) be the first derivative of c(v). Factor m(h).
2*h*(h - 1)**2/3
Let w(j) be the first derivative of j**7/735 + j**6/420 + 5*j**2/2 - 1. Let r(d) be the second derivative of w(d). What is t in r(t) = 0?
-1, 0
Factor 2/7 + 6/7*r**3 + 10/7*r + 2*r**2.
2*(r + 1)**2*(3*r + 1)/7
Solve -3/2*q**4 + 3*q + 3/2*q**2 - 3*q**3 + 0 = 0.
-2, -1, 0, 1
Suppose 2*t = -0*t + 12. Suppose -4*c + h + 12 = c, -4*h - t = c. Solve 3*x**3 + 3*x**5 + 3*x + 6*x**4 - 4*x**c - 9*x**3 - 3*x**4 - x**4 + 2 = 0.
-1, -2/3, 1
Let k be (3/14)/((-150)/(-35)). Let g(c) be the third derivative of -k*c**5 - 1/24*c**4 + 0 - 1/60*c**6 + 0*c**3 + 0*c - 2*c**2. Solve g(w) = 0.
-1, -1/2, 0
Let i(q) = -2*q**5 - 2*q**4 + 6*q**3 + 2*q**2 - 4*q. Let n(u) = -3*u**5 - u**4 + 6*u**3 + 3*u**2 - 5*u. Let a(h) = -5*i(h) + 4*n(h). Factor a(c).
-2*c**2*(c - 1)**3
Let g(k) be the second derivative of k**4/114 - 4*k**3/19 + 36*k**2/19 + 17*k. Factor g(t).
2*(t - 6)**2/19
Let z(p) = p**2 + p**3 + 9*p**2 - 8*p + 2 - 3*p**2. Let a be z(-8). Solve -4*v**4 + a*v + 2*v**4 + 6*v**3 - v**2 - 5*v**2 = 0.
0, 1
Let z(l) = -5*l**2 - 10*l + 2. Let k(y) = -16*y**2 - 29*y + 7. Let b(i) = 2*k(i) - 7*z(i). Solve b(x) = 0 for x.
-4, 0
Let s(o) be the second derivative of -o**5/35 - o**4/21 + 2*o**3/21 + 2*o**2/7 - 6*o. Factor s(g).
-4*(g - 1)*(g + 1)**2/7
Let r be -3*(-2 - 6/(-9)). Suppose 9*g = r*g + 15. Suppose 0*f**2 + 0 - 2/9*f**g + 2/9*f = 0. Calculate f.
-1, 0, 1
Let y be 10/15*2/8. Let d(k) be the second derivative of 0 - 1/10*k**5 + 1/30*k**6 + 1/42*k**7 - 1/6*k**4 - 2*k + y*k**3 + 1/2*k**2. Solve d(f) = 0.
-1, 1
Factor -3/5*d**3 + 3/5*d**2 + 3/5*d - 3/5.
-3*(d - 1)**2*(d + 1)/5
Let s(n) be the first derivative of -4 - n**6 + 1/2*n**4 - 4/3*n**3 + 0*n**2 + 0*n + 8/5*n**5. Find r such that s(r) = 0.
-2/3, 0, 1
Suppose 1/2*o**2 - o + 1/2 = 0. Calculate o.
1
Let z be 6/(-4)*(-36)/27 + 3. Let o(v) be the third derivative of 3*v**2 - 1/240*v**z + 0*v + 0 - 1/24*v**4 - 1/6*v**3. Factor o(k).
-(k + 2)**2/4
Let l(u) be the first derivative of -u**3/3 - u**2/2 - 6. Find o such that l(o) = 0.
-1, 0
Let n be 0 + 3/6*6. Determine q, given that -q + 2*q**n - 3*q**4 + q**2 + q**4 + q**2 - q = 0.
-1, 0, 1
Let j be ((-8)/10)/(-5*(-8)/(-100)). Factor -1/3 + l + 1/3*l**3 - l**j.
(l - 1)**3/3
Let v be 3/(1 + 15/(-18)). Suppose -7*y = -4*y - v. Factor y*h + 4 - 17*h**2 - h**2 - 26*h**3 - 10*h**4 - 4*h.
-2*(h + 1)**3*(5*h - 2)
Let z(b) be the first derivative of 1/2*b**2 - 1/2*b - 2 - 1/6*b**3. Solve z(p) = 0.
1
Let b be (-6)/21 - 4/(-7). Factor b - 4/7*q + 2/7*q**2.
2*(q - 1)**2/7
Let k be ((-5)/(-10))/(-1 + 3). Let v = -2 + 5. What is i in -1/4*i**v - k*i**2 + 0 + 0*i = 0?
-1, 0
Suppose -5*c = -2 - 3. Suppose 3*v - 5 = -2. Factor c + 0*i**2 - 2*i**2 + v.
-2*(i - 1)*(i + 1)
Let a(d) be the third derivative of 0*d**3 - 2*d**2 + 0*d**5 + 0 + 0*d**4 + 1/60*d**6 + 1/105*d**7 + 0*d. Suppose a(t) = 0. Calculate t.
-1, 0
Suppose 3*d - 14 = 4*c + 15, -4*d + 7 = c. Suppose 2*u**3 + 2*u**2 - 4*u**3 + 2*u**5 - u**d - 3*u**4 = 0. Calculate u.
-1, 0, 1/2, 2
Let j = 2/629 + 45911/1887. Let k = j + -24. Factor 0 + 0*y - k*y**2.
-y**2/3
Let t = -261 + 3397/13. Factor -2/13*y**4 + 0 - t*y**3 - 2/13*y**2 + 0*y.
-2*y**2*(y + 1)**2/13
Let v(k) be the first derivative of k**5/10 - k**4/4 + k**3/6 + 13. Factor v(s).
s**2*(s - 1)**2/2
Suppose 4*h = -5*g - 10, 3*h + 12 + 7 = 2*g. Let k(c) be the third derivative of 1/6*c**3 + 1/120*c**6 + 1/20*c**5 + c**g + 0*c + 0 + 1/8*c**4. Factor k(i).
(i + 1)**3
Solve 4/11 + 8/11*h**2 + 10/11*h + 2/11*h**3 = 0 for h.
-2, -1
Let n(h) be the first derivative of h**4/6 - 2*h**3/9 - 2*h**2/3 - 11. Factor n(x).
2*x*(x - 2)*(x + 1)/3
Suppose 3*v + 18 - 49 = n, 0 = -n - 1. Factor 0*p**3 - 6*p**3 - 8 - 20*p + 4*p**4 - 12*p**2 + v*p**3.
4*(p - 2)*(p + 1)**3
Let a(x) = -x**2 + x + 1. Let q(k) = -16*k - 3 + 3*k**3 + k**3 - 4*k**2 + 18*k - k**4. Let v(z) = -6*a(z) - 3*q(z). Let v(w) = 0. Calculate w.
1
Let x be 8/60*(-1)/(-2). Let m(r) be the second derivative of 0 - 2*r - 5/6*r**3 - 7/20*r**5 + 3/4*r**4 + x*r**6 + 1/2*r**2. Solve m(y) = 0 for y.
1/2, 1
Let q(y) be the third derivative of -y**8/336 + y**7/42 - 3*y**6/40 + 7*y**5/60 - y**4/12 + 29*y**2. Determine b, given that q(b) = 0.
0, 1, 2
Let q(s) = -s**3 - 7*s**2 - 6*s + 7. Let d be q(-6). Let y = d - 3. Suppose -3/4*g**y + 5/4*g**2 + 1/4*g - 1/2 - 1/4*g**3 = 0. What is g?
-1, 2/3, 1
Let l be -5*1/((-5)/3). Factor -l - 3/4*y**2 + 3*y.
-3*(y - 2)**2/4
Let u = -14 + 4. Let g = -7 - u. Factor 0*p + 2/9*p**g + 0*p**2 + 0.
2*p**3/9
Let d(b) = -4*b + 23. Let i be d(11). Let c be (-7)/28 - i/20. Let -c*k**3 + 2/5*k**4 + 0*k**2 - 2/5 + 4/5*k = 0. Calculate k.
-1, 1
Let m be 15/12*((-44)/10 - -5). Factor -3/2*s**2 + m*s + 0.
-3*s*(2*s - 1)/4
Suppose -11 + 1 = -5*g. Let o be 1*-1*(0 + 0). Factor 1/3*h + o*h**g - 1/3*h**3 + 0.
-h*(h - 1)*(h + 1)/3
Find a, given that -a**2 - 24*a**3 + 4*a**5 + 3*a - a + 28*a**4 - 14*a**5 + 5*a**2 = 0.
-1/5, 0, 1
Let s(x) be the second derivative of -1/10*x**5 + 0*x**4 + 0 - 9*x + 1/3*x**3 + 1/2*x**2 - 1/30*x**6. Factor s(w).
-(w - 1)*(w + 1)**3
Let g(l) be the second derivative of 0*l**2 + 4*l + 0 + 1/120*l**5 + 0*l**3 + 1/72*l**4. Factor g(z).
z**2*(z + 1)/6
Suppose 0 = 7*r - 2*r. Suppose r = -x + 6*x - 10. Factor -1/3*j + 1/3*j**3 + 0 + 0*j**x.
j*(j - 1)*(j + 1)/3
Solve 0 + 0*d**3 + 3/2*d**5 - 3/2*d - 3*d**2 + 3*d**4 = 0.
-1, 0, 1
Let w(b) be the second derivative of b**4/16 + b**3/4 - 6*b. Factor w(g).
3*g*(g + 2)/4
Let t be ((-2)/(-8)*-2*0)/2. Determine d so that 0*d**3 + 2/9*d**4 + 0*d - 2/9*d**2 + t = 0.
-1, 0, 1
Let r(b) be the first derivative of 0*b - 1/13*b**2 - 8 + 2/39*b**3. Factor r(x).
2*x*(x - 1)/13
Let o(m) = -m - 2. Let h be o(0). Let w be h/(-6) + 10/(-75). Let 0 - w*v + 0*v**2 + 1/5*v**3 = 0. What is v?
-1, 0, 1
Let b(w) be the first derivative of 4/9*w**3 + 2 + 2/3*w - 2/5*w**5 - 4/3*w**2 + 2/3*w**4. Determine u, given that b(u) = 0.
-1, 1/3, 1
Factor -1/3*p + 0 - 1/6*p**2.
-p*(p + 2)/6
Let p(s) be the second derivative of 3*s**5/20 + s**4/4 + 19*s. Solve p(j) = 0 for j.
-1, 0
Let o(b) be the third derivative of b**5/240 - b**4/24 + 43*b**2. Factor o(y).
y*(y - 4)/4
Determine a, given that 0*a + 0*a**3 - 8/13*a**2 + 0 - 2/13*a**5 + 6/13*a**4 = 0.
-1, 0, 2
Suppose -k + 3 = w - 0, -3*k + 3*w = 9. Determine c so that -4/3*c**2 + 0*c + k - 10/3*c**3 = 0.
-2/5, 0
Let j(u) be the second derivative of -u**7/840 + u**6/60 - u**5/10 - u**4/3 + 2*u. Let d(r) be the third derivative of j(r). What is i in d(i) = 0?
2
Let x = 33 - 27. Find s such that 15/2*s + 3/2*s**3 + x*s**2 + 3 = 0.
-2, -1
Let p = -428 - -1286/3. Determine s so that -2/3*s**2 - p*s + 0 = 0.
-1, 0
Let b(z) = -15*z**3 - 10*z**2 - 5*z - 5. Let k(y) = -22*y**3 - 15*y**2 - 7*y - 7. Let q(v) = -7*b(v) + 5*k(v). Let q(i) = 0. Calculate i.
-1, 0
Let b = -4 + 7. Suppose 0 = 5*z - 2*q - 2*q - 28, -5*z = q - 18. Solve -4*u**b - 8*u**2 + 6 + u**5 - 2 + u**5 + z*u**4 + 2*u = 0 for u.
-2, -1, 1
Let x be (-5 - -4) + 20/8.