13. Let c(q) be the first derivative of -3/4*q**4 - o*q**2 + 3*q**3 - 2 + 0*q. Find z such that c(z) = 0.
0, 1, 2
Let t(d) = -2*d**3 - 8*d**2 + 2*d - 4. Let u(h) = -2*h**3 - 7*h**2 + 2*h - 3. Let o = -8 - -14. Let b(g) = o*u(g) - 5*t(g). Factor b(p).
-2*(p - 1)*(p + 1)**2
Factor 8/3*c**2 - 13/3*c - 1/3*c**3 + 2.
-(c - 6)*(c - 1)**2/3
Let i(p) be the third derivative of -p**6/1440 - p**5/240 - p**4/96 + p**3/3 - 3*p**2. Let r(k) be the first derivative of i(k). Determine g so that r(g) = 0.
-1
Let u(z) be the second derivative of 0 - 2*z - 1/3*z**2 - 11/18*z**3 - 13/36*z**4 - 1/15*z**5. Determine g so that u(g) = 0.
-2, -1, -1/4
What is i in -2/5 - 2/5*i**4 + 2/5*i**5 - 4/5*i**3 + 4/5*i**2 + 2/5*i = 0?
-1, 1
Let w(s) be the first derivative of s**4/22 + 2*s**3/33 - s**2/11 - 2*s/11 + 59. Let w(y) = 0. Calculate y.
-1, 1
Let g be (10/6)/(-3 - (-115)/30). Factor 0*f + 1/4*f**g + 0.
f**2/4
Let w(x) be the third derivative of x**6/480 + x**5/240 - 8*x**2. Find f, given that w(f) = 0.
-1, 0
Let g(d) = 3*d**2 + 57*d - 343. Let p(t) = 10*t**2 + 172*t - 1030. Let c(q) = 16*g(q) - 5*p(q). Find z, given that c(z) = 0.
13
What is m in 0 + 1/3*m**4 + 1/3*m - 1/3*m**2 - 1/3*m**3 = 0?
-1, 0, 1
Suppose 3*k = 2 - 11. Let s be (k/12)/(54/(-192)). Factor 2/9*z**2 - s*z + 8/9.
2*(z - 2)**2/9
Suppose 11*u + 40 = 6*u. Let d = u + 11. Factor 0 + 2/3*s**d + 0*s**2 - 2/3*s.
2*s*(s - 1)*(s + 1)/3
Factor 9 + 4*w**3 + w**3 - 15*w**2 + 11.
5*(w - 2)**2*(w + 1)
Let o(l) = -3*l**4 + 3*l**3 + 3*l**2 - 3*l. Let a(t) = t**4 - t**3 - t**2 + t. Let j(i) = -10*a(i) - 5*o(i). Determine k so that j(k) = 0.
-1, 0, 1
Let v(q) be the first derivative of q**3/27 - q**2/9 - q/3 + 20. Suppose v(j) = 0. What is j?
-1, 3
Let 0 + 0*t**3 + 2/3*t + t**2 - 1/3*t**4 = 0. Calculate t.
-1, 0, 2
Let j(u) be the second derivative of u**4/12 + 3*u**3/2 + 3*u**2/2 - u. Let z be j(-9). Factor -1/3 + 1/3*t**z + 1/3*t**2 - 1/3*t.
(t - 1)*(t + 1)**2/3
Solve -5/6*k + 1/6*k**2 + 1/6*k**3 + 1/2 = 0 for k.
-3, 1
Let t(h) be the third derivative of -h**8/168 - 2*h**7/105 + h**5/15 + h**4/12 + 27*h**2. Factor t(r).
-2*r*(r - 1)*(r + 1)**3
Suppose -4*k - 30 = 14. Let u = k + 17. Let 9/2*m**3 + 0 - u*m**2 + 3*m**4 - 6*m - 3/2*m**5 = 0. What is m?
-1, 0, 2
Let r(m) be the second derivative of 11/4*m**4 + 3/14*m**7 + 0*m**2 + 13/10*m**6 + m**3 + 0 + 57/20*m**5 + 8*m. Determine n so that r(n) = 0.
-2, -1, -1/3, 0
Let a be 2/(-2) + (1 - -4). Find b, given that -4*b**4 + a*b**2 - 3*b**4 + 2*b + 16*b**3 - 15*b**2 = 0.
0, 2/7, 1
Let f(z) be the third derivative of z**10/10080 - z**9/2520 + z**7/420 - z**6/240 + z**4/24 - 4*z**2. Let x(y) be the second derivative of f(y). Factor x(p).
3*p*(p - 1)**3*(p + 1)
Suppose 2*y = -3*o + 7, 3*y + 3*o - 1 = 8. Let n(g) be the second derivative of 4/5*g**5 - g**4 + g**y + 0*g**3 + g - 1/5*g**6 + 0. Factor n(r).
-2*(r - 1)**3*(3*r + 1)
Suppose -3*u + 3*k + 15 = 0, -3*u - k + 5*k + 14 = 0. Let z be 1/(-2) - (-15)/u. Factor f**4 - 2*f**5 + z*f**5 - f**5.
-f**4*(f - 1)
Suppose 8/9*p + 0 - 2/9*p**3 - 8/9*p**2 + 2/9*p**4 = 0. Calculate p.
-2, 0, 1, 2
Suppose -14*l + 15*l - 2 = 0. Factor -2/5*b**l + 4/5*b + 0.
-2*b*(b - 2)/5
Let p be (1/4)/((-252)/96 + 3). Solve 1/3*s**2 + p*s + 0 = 0.
-2, 0
Let l = 22 - 22. Factor 2/5*c**5 + 0*c + 2/5*c**3 + l + 0*c**2 + 4/5*c**4.
2*c**3*(c + 1)**2/5
Find g such that 5/4*g**5 + 13/4*g**4 + 9/4*g**3 + 0 - 1/2*g - 1/4*g**2 = 0.
-1, 0, 2/5
Let g(y) be the third derivative of 0*y + 6*y**2 - 1/3*y**4 + 7/180*y**6 - 1/10*y**5 + 4/9*y**3 + 0. Let g(p) = 0. Calculate p.
-1, 2/7, 2
Let n(m) = -4*m**3 + 4*m + 2. Let b be -1 - 3/(3/4). Let p(r) = -2 + 6*r**3 + 9*r - 15*r**3 + 7. Let o(l) = b*n(l) + 2*p(l). Find q such that o(q) = 0.
-1, 0, 1
Let f(l) be the second derivative of l**7/147 + l**6/35 + 3*l**5/70 + l**4/42 - l. Factor f(u).
2*u**2*(u + 1)**3/7
Solve -3/2 + 45/4*r**4 + 117/4*r**2 + 27/4*r + 129/4*r**3 = 0 for r.
-1, 2/15
Factor 2*y**2 - 6 + 0*y**3 + 20*y + 2*y**3 - 12*y**2 - 6*y.
2*(y - 3)*(y - 1)**2
Suppose -3*u = u. Suppose 25 = -2*o + 5*v, -20 = 3*o - 8*o - 4*v. Solve u*s**3 + 2/3*s**4 - 4/3*s**2 + 2/3 + o*s = 0.
-1, 1
Suppose -5*s - 2*f + 33 = 0, -5*s + 2*f + 9 + 8 = 0. Let c(l) be the second derivative of 0*l**4 + 2*l + 0 + 0*l**3 - 1/20*l**s + 0*l**2. Factor c(u).
-u**3
Let w(t) be the third derivative of 1/6*t**3 - 9*t**2 + 0 - 1/420*t**7 - 1/240*t**6 + 0*t + 5/48*t**4 + 1/40*t**5. Factor w(d).
-(d - 2)*(d + 1)**3/2
Let g(o) be the third derivative of o**8/504 + o**7/45 + 19*o**6/180 + 5*o**5/18 + 4*o**4/9 + 4*o**3/9 - 13*o**2. Factor g(k).
2*(k + 1)**3*(k + 2)**2/3
Let n(y) be the first derivative of 14*y**6 + 116*y**5/5 - 3*y**4 - 12*y**3 + 4*y**2 - 17. Solve n(h) = 0.
-1, 0, 2/7, 1/3
Determine u so that 4*u**4 - 2*u**4 + 6*u**2 + 4*u**2 + 42*u**3 + 6*u**4 = 0.
-5, -1/4, 0
Factor -1/3*x**3 - 1/3*x**2 + 1/3*x + 1/3.
-(x - 1)*(x + 1)**2/3
Let o be (-35)/(-21)*54/30. Let n = 1/18 + 4/9. Determine w so that -1/2*w + n + 1/2*w**o - 1/2*w**2 = 0.
-1, 1
Let y = 19/7 + -55/28. What is b in 0*b + 1/4*b**3 - y*b**4 + 0 + 1/2*b**2 = 0?
-2/3, 0, 1
Let t(f) be the second derivative of -f**5/330 - f**4/132 + 3*f**2/2 - 2*f. Let p(w) be the first derivative of t(w). Let p(d) = 0. Calculate d.
-1, 0
Let u(m) be the third derivative of -11*m**7/630 - m**6/180 + 52*m**2. Suppose u(s) = 0. What is s?
-2/11, 0
Let x(t) = -t**2 + 2*t. Let k(h) = h**2 - h. Let z(c) = -6*k(c) - 3*x(c). Factor z(d).
-3*d**2
Let j be 12/90*5 + 33/(-50). Let u(z) be the third derivative of 0*z + 0*z**4 - j*z**5 - 3*z**2 + 1/15*z**3 + 0. What is p in u(p) = 0?
-1, 1
Let c(k) be the first derivative of k**6/180 - k**5/60 - k**4/6 - k**3 + 6. Let b(g) be the third derivative of c(g). Suppose b(i) = 0. What is i?
-1, 2
Let a = -167 - -2673/16. Let n(f) be the second derivative of -1/40*f**6 + 0*f**2 + 1/16*f**4 + 1/42*f**7 - a*f**5 + 0 - 2*f + 1/24*f**3. Solve n(t) = 0.
-1, -1/4, 0, 1
Let f(c) be the second derivative of 0 + 0*c**2 + c + 0*c**5 + 1/18*c**4 - 1/18*c**3 + 1/126*c**7 - 1/45*c**6. Factor f(x).
x*(x - 1)**3*(x + 1)/3
Let 12 + 5*w**2 + 5*w - 12 - 20*w = 0. Calculate w.
0, 3
Let q(b) be the second derivative of b**7/126 - 2*b**6/45 + b**5/20 + b**4/9 - 2*b**3/9 + b. Let q(c) = 0. Calculate c.
-1, 0, 1, 2
Let x(j) = 7*j**3 + 77*j**2 + 37*j - 13. Let n(h) be the first derivative of h**4/2 + 26*h**3/3 + 6*h**2 - 4*h - 5. Let i(t) = 11*n(t) - 4*x(t). Factor i(o).
-2*(o + 2)**2*(3*o - 1)
Suppose 152 = -11*y + 196. Find g such that -2/7*g**2 + 0*g + 4/7*g**3 - 2/7*g**y + 0 = 0.
0, 1
Let c(m) = m**3. Let v(u) = -3*u - 2. Let y(l) = 2*c(l) + 2*v(l). Determine g, given that y(g) = 0.
-1, 2
Let h be (-8 + (-1724)/(-216))/((-10)/6). Let d(s) be the second derivative of -1/36*s**4 + h*s**6 + 0*s**5 + 0*s**3 + 0 + 0*s**2 - 3*s. Solve d(c) = 0.
-1, 0, 1
Let f(w) = w - 1. Let y(n) = 2*n - 3. Let q(k) = -3*f(k) + y(k). Let c be q(-2). Suppose 0*d - 2/7*d**c + 0 - 2/7*d**3 = 0. What is d?
-1, 0
Let d(h) be the first derivative of -1/7*h**3 + 2/7*h**2 + 1/42*h**4 + 3*h - 3. Let n(r) be the first derivative of d(r). Let n(l) = 0. Calculate l.
1, 2
Let x = -34117322/45 + 758108. Let f = x + 278/5. Factor 10/9*u**3 - 8/3*u + 2/3*u**2 + f.
2*(u - 1)*(u + 2)*(5*u - 2)/9
Let d(a) be the first derivative of -a**4/14 + 2*a**3/21 + 2*a**2/7 - 24. Factor d(m).
-2*m*(m - 2)*(m + 1)/7
Factor -6*g**2 + 2*g**2 + 2*g**2 + 180*g + 7*g**2 + 1620.
5*(g + 18)**2
Let o(r) be the second derivative of -r**6/360 - r**5/30 - r**4/6 - r**3/3 + 3*r. Let t(h) be the second derivative of o(h). Factor t(n).
-(n + 2)**2
Factor 5/4*u**2 - 1/4*u**3 - 3/4*u + 0 - 1/4*u**4.
-u*(u - 1)**2*(u + 3)/4
Suppose -u + 3 = 5*r + 16, -2*u = r - 1. Suppose 0 = 3*n + 3 - 15. Let 3*o + 5*o - 9*o**n - 32*o**u + 16*o**3 + 18*o**3 - o**4 = 0. Calculate o.
0, 2/5, 1, 2
Suppose 0 = -11*v - 2 + 24. Factor 4/5*h**v - 2/5*h**3 + 0 + 0*h.
-2*h**2*(h - 2)/5
Factor 0*l + 2/13*l**2 - 2/13.
2*(l - 1)*(l + 1)/13
Let m(h) be the second derivative of -h**5/30 - h**4/6 - h**3/3 + 3*h**2/2 + 2*h. Let r(x) be the first derivative of m(x). Factor r(p).
-2*(p + 1)**2
Let m(y) be the first derivative of -y**6/720 - 2*y**3/3 - 4. Let h(z) be the third derivative of m(z). What is n in h(n) = 0?
0
Let z = -18 - -10. Let h be (-9)/(-15)*z/(-12). Factor -4/5*k**4 + 0