e the first derivative of u(m). Solve h(c) = 0 for c.
1
Factor 2/11*s - 2/11*s**3 + 0 - 2/11*s**4 + 2/11*s**2.
-2*s*(s - 1)*(s + 1)**2/11
Let g = -2 + 3. Let a(u) = u**2 + u. Let y(s) = 2*s**3 - s**2 - s. Let o(l) = g*a(l) + y(l). Find c such that o(c) = 0.
0
Let y(n) be the second derivative of 21*n**5/20 + 5*n**4/4 - 8*n**3 + 6*n**2 + 11*n. Factor y(b).
3*(b - 1)*(b + 2)*(7*b - 2)
Let j = 38 - 35. Suppose 0*o**j + 0*o + 0*o**2 - 2/3*o**4 + 2/3*o**5 + 0 = 0. What is o?
0, 1
Let t = 28 + -25. Let r(m) be the first derivative of -4/9*m**2 - 8/9*m + 2 - 2/27*m**t. Find v, given that r(v) = 0.
-2
Let t(k) be the second derivative of -2*k**7/105 - 8*k**6/15 - 32*k**5/5 - 128*k**4/3 - 512*k**3/3 - 2048*k**2/5 + 2*k. Solve t(d) = 0.
-4
Let k = 41 + -21. Let n be (-5)/k - 9/(-4). Factor 2*m**4 + 3*m**4 + n*m**5 + 2*m**3 - 4*m**4 - 5*m**4.
2*m**3*(m - 1)**2
Let h(p) be the third derivative of 0*p - p**2 + 1/150*p**5 + 1/60*p**4 + 0 - 2/15*p**3. Let h(w) = 0. Calculate w.
-2, 1
Let y(a) = -2*a**2 + 5*a - 10. Let t be y(8). Let n be 8/6*(-21)/t. Find l, given that 0 + 8/7*l**4 + 2/7*l**3 - 8/7*l**2 - n*l = 0.
-1, -1/4, 0, 1
Let i(k) = -k**2 - 5*k + 4. Let s be i(-5). Let t(o) = o - 1. Let m be t(s). Factor 0*v**2 + 3*v**m - 2*v**3 - 2*v**2 + v.
v*(v - 1)**2
Factor 3/7*j**3 - 3/7*j**2 + 0 - 3/7*j**5 + 3/7*j**4 + 0*j.
-3*j**2*(j - 1)**2*(j + 1)/7
Suppose 40*d - 2 = 39*d. Let z(g) be the first derivative of -1/3*g**3 - 4 + 2*g - 1/2*g**d. Factor z(u).
-(u - 1)*(u + 2)
Determine u so that 3*u**4 - 3*u**3 - 3 + 3/2*u**5 - 12*u**2 - 21/2*u = 0.
-1, 2
Determine m so that -4*m**5 + 27*m - 2*m**5 + 9*m**4 + 0*m**5 + 15*m**3 - 6 - 39*m**2 + 0*m**5 = 0.
-2, 1/2, 1
Suppose d - 7*d = 0. Suppose d + 1/3*l - 1/3*l**2 = 0. Calculate l.
0, 1
Suppose 2*a - 2 = 4. Let q(x) be the second derivative of -1/42*x**4 + 0*x**2 + 1/21*x**a + 0 + 2*x. Factor q(f).
-2*f*(f - 1)/7
Suppose 19*z = 51 + 6. Let -2/3*h**4 + 4/3*h**z + 8/3*h**2 - 16/3*h + 0 = 0. What is h?
-2, 0, 2
Let f(w) be the second derivative of -w**6/15 - w**5/4 - 8*w. Let p(v) = -v**4 - 2*v**3. Let q(z) = -4*f(z) + 10*p(z). Let q(a) = 0. Calculate a.
0
Let t(l) be the third derivative of -l**5/90 + l**4/9 - 4*l**3/9 - 5*l**2. Factor t(u).
-2*(u - 2)**2/3
What is s in 52*s**4 - 15*s**3 - 10*s - 25*s**2 - 27*s**4 + 5*s**5 - 20*s**4 = 0?
-1, 0, 2
Let a(j) be the second derivative of 1/10*j**6 + 0 + 0*j**3 + 3/20*j**5 + 0*j**2 + 0*j**4 + 3*j. Factor a(b).
3*b**3*(b + 1)
Let v(u) be the first derivative of -5 + 2/15*u**3 + 0*u - 1/5*u**2. Factor v(k).
2*k*(k - 1)/5
Let s(w) be the third derivative of w**7/5040 + w**6/720 + w**5/240 - w**4/8 - 3*w**2. Let u(z) be the second derivative of s(z). Let u(c) = 0. What is c?
-1
Let m(x) be the second derivative of 2*x**6/15 - 3*x**5/5 + x**4 - 2*x**3/3 + 9*x. Factor m(k).
4*k*(k - 1)**3
Let i = 540212/12213 - 14/1357. Let j = i - 44. Factor 2/9*o**4 - 10/9*o + j*o**3 - 4/9 - 2/3*o**2.
2*(o - 2)*(o + 1)**3/9
Let t(w) be the first derivative of 1/2*w**6 - 3/2*w**4 + 4 + 2*w**3 - 3*w + 3/2*w**2 - 3/5*w**5. Let t(s) = 0. What is s?
-1, 1
Let v = 14 - 7. Suppose -3*i = -v*i. Find u such that -2/9*u**2 + i - 4/9*u = 0.
-2, 0
Let g(k) be the second derivative of k**4/4 + 2*k**3 + 6*k**2 + 8*k. Factor g(r).
3*(r + 2)**2
Let c(d) be the second derivative of 0 - 1/6*d**4 + 1/15*d**6 + 0*d**5 + 1/42*d**7 - 3*d - 1/6*d**3 + 0*d**2. Factor c(q).
q*(q - 1)*(q + 1)**3
Let y(z) = 5*z**2 + 9*z + 6. Let c(o) = -21*o**2 - 36*o - 24. Let n(m) = 2*c(m) + 9*y(m). Find j such that n(j) = 0.
-2, -1
Let n(y) be the first derivative of 2*y**5/85 - y**4/34 - 2*y**3/51 + y**2/17 - 10. Determine a so that n(a) = 0.
-1, 0, 1
Factor -2/3*g**4 + 2/9*g - 10/9*g**3 + 0 - 2/9*g**2.
-2*g*(g + 1)**2*(3*g - 1)/9
Let i = 386/483 - -4/69. Let y be 2 + (32/14 - 2). Factor -y*a**2 + i*a**3 + 2*a - 4/7.
2*(a - 1)**2*(3*a - 2)/7
Suppose 0 = -3*c + 5*k, -3*c = -k + 4*k. Determine m so that c*m - 1/7 + 1/7*m**2 = 0.
-1, 1
Let c = 14848/15 - 3959/4. Let q = c + 431/420. Solve -q*h**2 - 4/7*h**4 - 10/7*h**3 + 0 - 2/7*h = 0 for h.
-1, -1/2, 0
Let h(r) be the second derivative of 3*r + 9/5*r**5 + 0 + 0*r**2 + 7/3*r**4 + 2/3*r**6 + 2/21*r**7 + 4/3*r**3. Factor h(w).
4*w*(w + 1)**3*(w + 2)
Suppose 0 + 2/9*a + 0*a**2 - 2/9*a**3 = 0. What is a?
-1, 0, 1
Let k(o) be the first derivative of o**6/2 - 3*o**5/5 - 15*o**4/4 - 3*o**3 + 3. Factor k(x).
3*x**2*(x - 3)*(x + 1)**2
Let r(n) = n + 10. Let h be r(-7). Suppose -196 + 3*j**3 + 196 + h*j**2 = 0. What is j?
-1, 0
Let d(q) be the second derivative of 0 - 1/30*q**5 + 1/3*q**2 + 1/9*q**3 - 1/18*q**4 - 3*q. Factor d(t).
-2*(t - 1)*(t + 1)**2/3
Let v(g) be the second derivative of -g**7/84 - g**6/20 - g**5/20 - 9*g. Factor v(o).
-o**3*(o + 1)*(o + 2)/2
Let y be -3*(1 + (-2)/1). Suppose 2*b - 4*t - 4 - 2 = 0, 2*b - 15 = -5*t. Solve -15*n**4 + 19*n**2 + n**3 + 5*n**y - 7*n**2 - 4*n - b*n**3 = 0.
-1, 0, 2/5, 2/3
Let s(q) be the third derivative of q**9/151200 + q**8/25200 + q**7/12600 - q**5/30 - 6*q**2. Let k(z) be the third derivative of s(z). Factor k(p).
2*p*(p + 1)**2/5
Let w = -2122/9 + 236. Let b(n) be the second derivative of -w*n**4 - 1/9*n**3 + 0*n**2 - 1/63*n**7 - 4/45*n**6 + 0 + n - 1/5*n**5. What is a in b(a) = 0?
-1, 0
Let a(o) be the third derivative of 1/240*o**5 - 1/840*o**7 + 0*o**6 - 2*o**2 + 0*o**3 + 0*o + 0 + 0*o**4. Factor a(t).
-t**2*(t - 1)*(t + 1)/4
Let o be (3 + (-30)/9)*-1. Let v(m) be the first derivative of 3 + 1/2*m**2 + 0*m + o*m**3. Find j such that v(j) = 0.
-1, 0
Suppose -3*k - 5*j + 0 = 19, -2*k + 5*j = -29. Factor 3*v**k - 2 + 6*v + 3*v + 8.
3*(v + 1)*(v + 2)
Let b(f) be the first derivative of 3*f**5/40 + 3*f**4/4 + 11*f**3/4 + 9*f**2/2 + 27*f/8 + 7. Factor b(s).
3*(s + 1)**2*(s + 3)**2/8
Let h(k) be the first derivative of 3*k**4/4 - 3*k**2/2 + 5. Find x such that h(x) = 0.
-1, 0, 1
Let a(y) be the first derivative of -y**5/40 + 3*y**4/16 - y**3/2 + 5*y**2/8 - 3*y/8 - 27. Factor a(r).
-(r - 3)*(r - 1)**3/8
Factor 80/7*g + 50/7*g**2 + 32/7.
2*(5*g + 4)**2/7
Let v(z) be the third derivative of 1/6*z**3 + 0*z + 1/30*z**5 - 1/336*z**8 + 1/8*z**4 + 0 - 1/70*z**7 + 5*z**2 - 1/60*z**6. Factor v(r).
-(r - 1)*(r + 1)**4
Let m(x) be the first derivative of -x**5/5 + 3*x**4/8 + 3*x**2/2 - 3. Let o(v) be the second derivative of m(v). Factor o(i).
-3*i*(4*i - 3)
Suppose -4*z + o = -10 - 3, 0 = -o - 5. Suppose -z*v + 8 = 2*v. Suppose -2*u**3 - 2*u**3 - u**4 + 7*u**2 - 3*u**2 + v*u**4 = 0. What is u?
0, 2
Let d(h) = -10*h**4 + 8*h**3 + 18*h**2 + 4*h - 8. Let o(n) = -n**4 + n**2 + n. Let l(b) = -d(b) + 12*o(b). Find g, given that l(g) = 0.
-2, -1, 1
Suppose -2 = -s - 0. Find b such that 8*b - 3*b**s - 6 + b + b - b = 0.
1, 2
Let k = 538 - 2688/5. Find u, given that -6/5*u**2 + 4/5*u**3 - 8/5*u + 8/5 + k*u**4 = 0.
-2, 1
What is t in -162/7*t - 30/7*t**3 - 3/7*t**4 - 108/7*t**2 - 81/7 = 0?
-3, -1
Suppose -t + 2 + 4 = 0. Suppose -t*h + 18 + 0 = 0. Factor -3/2*f**h - 6*f**4 - 7/2*f**5 + 0*f + f**2 + 0.
-f**2*(f + 1)**2*(7*f - 2)/2
Solve l**2 - 21*l**3 - 15*l**3 - 9*l**2 = 0.
-2/9, 0
Let m(t) = -t**3 + 8*t**2 - 3*t + 7. Let f be m(8). Let x = -17 - f. Factor x*u**2 + 0*u - 2/5*u**3 - 1/5*u**4 + 0.
-u**3*(u + 2)/5
Factor -2/9*x**3 + 0 + 2/9*x**2 + 2/9*x - 2/9*x**4.
-2*x*(x - 1)*(x + 1)**2/9
Let w(x) be the second derivative of -5/33*x**4 + 5/33*x**3 + 1/11*x**5 - 1/33*x**6 - 1/11*x**2 + 1/231*x**7 + 0 - 3*x. Factor w(j).
2*(j - 1)**5/11
Suppose -7*z - 3 = -3. Let c(v) be the second derivative of 1/80*v**5 - v - 1/24*v**3 + z*v**4 + 0 + 0*v**2. Suppose c(r) = 0. What is r?
-1, 0, 1
Let f(t) be the third derivative of t**5/15 + t**4/3 + 8*t**2. What is h in f(h) = 0?
-2, 0
Suppose 0*h + 3*h + 43 = -5*i, -2*h - 4*i = 32. Let s(u) = u**2 - u. Let t(q) = q**3 - 3*q**2 + 9*q + 1. Let y(c) = h*s(c) - t(c). Factor y(l).
-(l + 1)**3
Let h(o) = 5*o**3 - 24*o**2 + 196*o - 508. Let j(d) = d**3 + d + 1. Let a(y) = h(y) - 4*j(y). Let a(c) = 0. Calculate c.
8
Let f = 370/3 + -121. Let o(x) = -x**3 - 3*x**2 - 3*x - 2. Let w be o(-2). Determine c, given that -f*c**3 + 4/3*c**4 + 2/3*c**2 + 1/3*c + w = 0.
-1/4, 0, 1
Let j be (165/90 + -2)*16/(-3). Suppose -2/9*r**5 + 0*r - 8/9*r**3 + 0 + 0*r**2 - j*r**4 = 0. What is r?
-2, 0
Let b be 1 - (-44)/(-16) - -2. Let c(q) be the second deriva