*v**2 + 0*v**3 - 15*v**3 + t*v**5 + v**3 + 4*v**4 = 0 for v.
-1, -2/7, 0, 1
Let v = -3/14 + 37/42. Let x(c) be the third derivative of 0 + 0*c - c**2 - 1/6*c**4 - 1/60*c**5 - v*c**3. What is o in x(o) = 0?
-2
Determine g, given that 14*g + 28 + 15*g - 5*g - 4*g**2 = 0.
-1, 7
Let o(z) be the third derivative of -z**8/560 + 3*z**7/280 - z**6/40 + z**5/40 + 7*z**3/6 + 3*z**2. Let t(u) be the first derivative of o(u). Factor t(q).
-3*q*(q - 1)**3
Let w(d) be the first derivative of 3*d**5 - 33*d**4/2 + 23*d**3 - 9*d**2 - 8. Find r such that w(r) = 0.
0, 2/5, 1, 3
Let i(f) be the second derivative of -f**6/15 - f**5/35 + f**4/6 + 2*f**3/21 + 7*f. Solve i(q) = 0.
-1, -2/7, 0, 1
Let j(x) = x**3 - x**2 - 1. Let h(r) = 8*r**3 - 9*r**2 + r - 7. Suppose 0 = 2*n + 2*c + 22, -n - 2*c - 64 = 4*n. Let q(w) = n*j(w) + 2*h(w). Factor q(t).
2*t*(t - 1)**2
Let f(u) be the third derivative of u**5/150 + u**4/20 + 2*u**3/15 + u**2. Factor f(o).
2*(o + 1)*(o + 2)/5
Let y(x) be the second derivative of 0*x**2 + 7*x - 2/189*x**7 + 1/27*x**3 - 1/54*x**4 + 0 + 1/27*x**6 - 1/30*x**5. Factor y(k).
-2*k*(k - 1)**3*(2*k + 1)/9
Suppose 5*p - 4*v + 4 = -0*v, -3*p + 2*v = 2. Let l be (-2 + 5/2)*p. Factor l + 2/3*h - 2/3*h**3 + 0*h**2.
-2*h*(h - 1)*(h + 1)/3
Let b(h) be the third derivative of 3*h**7/70 + h**6/4 + 7*h**5/20 - h**4/2 - 2*h**3 - 6*h**2. Determine i so that b(i) = 0.
-2, -1, 2/3
Let z(x) be the third derivative of -x**8/3360 + x**6/720 - x**3/3 - 3*x**2. Let y(l) be the first derivative of z(l). Determine o so that y(o) = 0.
-1, 0, 1
Let w(v) = v - 16. Let y be w(16). Factor y*g + 2/9*g**3 + 8/9 - 2/3*g**2.
2*(g - 2)**2*(g + 1)/9
Let f(p) be the third derivative of p**7/5040 + p**4/24 + 4*p**2. Let j(b) be the second derivative of f(b). Let j(v) = 0. Calculate v.
0
Let p = -8 + 6. Let c be (1/p)/(12/(-8)). Solve c*j**2 - 1/3 + 0*j = 0.
-1, 1
Let u = 30 - 28. Let p(r) be the first derivative of -2/5*r**5 - u - 1/3*r**6 - r**2 - 2*r + 4/3*r**3 + r**4. Factor p(t).
-2*(t - 1)**2*(t + 1)**3
Let a = 43 + -40. Let j(i) be the third derivative of 0 + 0*i + a*i**2 - 1/12*i**4 - 1/3*i**3 - 1/120*i**5. Factor j(n).
-(n + 2)**2/2
Let n be (1 - 0 - -2) + 15. Let k be 32/n - 2/(-9). Solve 5 - 2 - 4*a - 3 + 2*a**k = 0.
0, 2
Let c = 13 + -10. Let d(b) = -b. Let r be d(-1). What is h in 0 - h**c + 3*h - 2*h**2 - 6*h - r - h**2 = 0?
-1
Let o = 16 - 13. Suppose o = 6*n - 9. Factor -1/3 - 3*u**2 - n*u.
-(3*u + 1)**2/3
Factor 2/7*j**5 + 0 + 4/7*j**2 - 4/7*j**4 - 2/7*j + 0*j**3.
2*j*(j - 1)**3*(j + 1)/7
Let q(u) be the third derivative of u**7/630 + u**6/90 + u**5/30 + u**4/18 + u**3/18 - 4*u**2. Suppose q(m) = 0. What is m?
-1
Let b(r) = 2*r**3 - r**2 - 8*r - 5. Let k(p) = 22*p - 13*p + 5 - 3*p**3 + 1. Let j(v) = -6*b(v) - 5*k(v). Find u such that j(u) = 0.
-1, 0
Determine c, given that -c**3 + 72*c**2 - 74*c**2 - 2*c**3 - c**4 = 0.
-2, -1, 0
Suppose o + 3*o - 12 = 0. Let 3*y - y**o + 4 - y**3 - 13*y + 8*y**2 = 0. What is y?
1, 2
Let z(a) = 10*a**2 - 2*a. Let w(o) = o**3 + 49*o**2 - 11*o. Let i(d) = -4*w(d) + 22*z(d). Factor i(j).
-4*j**2*(j - 6)
Let p(n) = 6*n**3 - 5*n**2 - n + 5. Let u(i) = 3*i**3 + i + 6 + 3*i**2 - 3*i + 3*i**3 - 7*i**2. Let m(x) = 6*p(x) - 5*u(x). What is d in m(d) = 0?
0, 2/3, 1
Let v(k) = k**2 - k - 2. Let o be v(-2). Let b(w) = 4 - o + 5 - 4. Let j(l) = -l**2 + 4*l + 1. Let c(s) = -5*b(s) + j(s). Factor c(n).
-(n - 2)**2
Factor a**3 + a**2 - 6*a + a + 3*a.
a*(a - 1)*(a + 2)
Suppose -6*j + 5 - 4*j - 13*j**4 + 9*j**3 + j**3 + 8*j**4 = 0. Calculate j.
-1, 1
Solve 2*m**5 - 3*m**3 + 0*m**4 + 8*m**2 + 10*m**3 + 5*m**3 + 2*m + 8*m**4 = 0 for m.
-1, 0
Let y(h) = 5*h**2 + 9 - 1 + 3*h**2 - 33*h. Let p(k) = -k**2 + 4*k + 0 - 2 + 0 + 1. Let o(b) = 51*p(b) + 6*y(b). Let o(u) = 0. Calculate u.
1
Let h(v) = -v**3 - 4*v**2 - 5*v - 4. Let y be h(-3). Suppose 3*d = y*s + 12, -d = -2*s - s - 11. Factor 0 - 3/4*a**d + 3/2*a.
-3*a*(a - 2)/4
Let n be 3/6 - 478/(-12). Let r = n - 40. What is o in -r*o**5 - 1/3*o**4 + 0 + 0*o**2 + 0*o**3 + 0*o = 0?
-1, 0
Let x(w) be the first derivative of -w**8/2520 + w**6/270 - w**4/36 + 5*w**3/3 - 8. Let m(o) be the third derivative of x(o). Solve m(u) = 0.
-1, 1
Let p(l) = -l**5 - 16*l**4 + 15*l**3 - 3*l**2 - 5. Let g(j) = -8*j**4 + 8*j**3 - 2*j**2 - 2. Let x(h) = -5*g(h) + 2*p(h). Factor x(d).
-2*d**2*(d - 2)*(d - 1)**2
Let x = 5/2 - 2. Suppose -2*i + c = -7, -2*i + 3*i - c = 6. Factor i - x*b**2 + 1/2*b.
-(b - 2)*(b + 1)/2
Let f(z) be the third derivative of z**8/33600 + z**7/4200 - z**6/400 - 7*z**5/60 - 2*z**2. Let t(o) be the third derivative of f(o). Factor t(i).
3*(i - 1)*(i + 3)/5
Suppose 0 = -6*v + 2*v - 4*l + 92, -2*l - 4 = 0. Suppose -25 = -c + a + 3*a, -4*c + a = -v. Factor -2*d**2 - 5*d**4 - d**c + 4*d**4 + d + 3*d**4.
-d*(d - 1)**3*(d + 1)
Let p = -36 + 10. Let g be (1*-1)/(65/p). Determine w, given that -2/5*w**2 + 0 + 2/5*w**4 + 0*w - g*w**3 + 2/5*w**5 = 0.
-1, 0, 1
Solve -6/5*p + 0*p**2 + 6/5*p**3 - 3/5 + 3/5*p**4 = 0 for p.
-1, 1
Let v(o) be the third derivative of 2*o**2 + 3/8*o**4 - 1/20*o**6 + 0 - 1/2*o**3 + 0*o - 1/112*o**8 - 1/10*o**5 + 3/70*o**7. Factor v(k).
-3*(k - 1)**4*(k + 1)
Let d**3 + 0 + 4/3*d + 8/3*d**2 = 0. Calculate d.
-2, -2/3, 0
Determine n, given that -2/5*n**3 + 2/5*n - 4/5 + 2*n**2 - 6/5*n**4 = 0.
-1, 2/3, 1
Let p(m) be the third derivative of -1/40*m**6 - 1/2*m**4 + 0 + 0*m**3 + 1/5*m**5 + 3*m**2 + 0*m. Factor p(q).
-3*q*(q - 2)**2
Let c(h) be the third derivative of h**8/1512 + h**7/315 + h**6/270 - h**5/135 - h**4/36 - h**3/27 - 6*h**2. Let c(p) = 0. What is p?
-1, 1
Factor -3/4*f**3 - 3/2*f**2 + 0 + 3/4*f**4 + 0*f.
3*f**2*(f - 2)*(f + 1)/4
Let h(t) be the third derivative of t**7/945 - t**6/270 + t**4/54 - t**3/27 - 7*t**2. Factor h(v).
2*(v - 1)**3*(v + 1)/9
Suppose -z = -2*z + 6. Let k be 8/(-6)*z/(-4). What is t in -2*t**k + 4*t - 2*t + 2*t - 2 = 0?
1
Let h(i) be the third derivative of 0 - 1/24*i**4 - 1/12*i**5 + 0*i + 0*i**3 - 2*i**2 - 1/30*i**6. Factor h(a).
-a*(a + 1)*(4*a + 1)
Let z(h) = -h**5 - 11*h**3 - 8*h**2 + 7*h + 3. Let k(f) = 6*f**3 + 4*f**2 - 4*f - 2. Let m(i) = 5*k(i) + 2*z(i). Factor m(s).
-2*(s - 2)*(s - 1)*(s + 1)**3
Let k(r) be the first derivative of r**7/945 + r**6/540 - r**5/270 - r**4/108 + 2*r**2 + 5. Let u(f) be the second derivative of k(f). Factor u(x).
2*x*(x - 1)*(x + 1)**2/9
Let x(z) be the second derivative of z**5/30 - z**3/3 - 2*z**2/3 + 8*z. Factor x(w).
2*(w - 2)*(w + 1)**2/3
Let f(l) = -3*l**3 + 11*l. Let i(y) = -2*y**3 + 7*y. Let b(w) = -5*f(w) + 8*i(w). Let g be b(1). Factor m - m**2 - 2 - 2*m**2 + g + 4*m**2.
(m - 1)*(m + 2)
Let w(v) = 2*v + 23. Let y be w(-10). Let s(f) be the first derivative of 1 + 1/12*f**y + 0*f + 1/8*f**2. Factor s(a).
a*(a + 1)/4
Let m(a) be the first derivative of 0*a + 0*a**3 + a**2 + 1/3*a**6 + 0*a**5 - a**4 - 2. Factor m(s).
2*s*(s - 1)**2*(s + 1)**2
Let z(j) be the second derivative of 4/9*j**3 + 0 - j + 1/18*j**4 + 4/3*j**2. Factor z(r).
2*(r + 2)**2/3
Let z = 10 + -6. Let a(x) = x**3 + x**2 - x + 1. Let d(c) = -2*c**4 - 6*c**3 - 4*c**2 + 4*c - 4. Let q(t) = z*a(t) + d(t). Find p such that q(p) = 0.
-1, 0
Let p(v) be the third derivative of -v**7/210 - v**6/75 - v**5/300 + v**4/60 - 12*v**2. What is z in p(z) = 0?
-1, 0, 2/5
Let v(b) be the first derivative of b**6/3 - 2*b**5/5 - b**4 + 16. Factor v(k).
2*k**3*(k - 2)*(k + 1)
Let p(h) be the third derivative of -h**5/360 + h**4/16 + 5*h**3/18 + 7*h**2 - 3. Factor p(a).
-(a - 10)*(a + 1)/6
Let y(i) = 3*i**2 - 8*i. Let m(u) = -u**2 + u - 1. Let j = -5 - -1. Let c(l) = j*m(l) - y(l). Determine w, given that c(w) = 0.
-2
Let g(t) be the second derivative of -9*t**5/50 - t**4/15 + 3*t**3/5 + 2*t**2/5 - t. Factor g(i).
-2*(i - 1)*(i + 1)*(9*i + 2)/5
Let f = -478/11 + 44. Solve 4/11*u + 2/11*u**3 + 0 + f*u**2 = 0 for u.
-2, -1, 0
Let z be 3/18 + 3/18 + 0. Let -1/3*x**2 + 0 - z*x = 0. Calculate x.
-1, 0
Suppose -5*a = -12 - 3. Let -a - 2*r**2 + 3 = 0. Calculate r.
0
Let a be 64/(4 + 4)*2/8. Let n(m) be the first derivative of -1 + 0*m - 1/4*m**3 - 3/4*m**a. Determine v so that n(v) = 0.
-2, 0
Determine c so that 0*c + 1 - 1/4*c**3 - 3/4*c**2 = 0.
-2, 1
Let a(h) = h + 9. Let c be a(-7). Solve 21*v**4 + 12 + 24*v**2 - 57*v**3 + 77*v**c - 26*v**2 - 3*v**5 - 48*v = 0.
1, 2
Let b be (-72)/