Let r(g) be the first derivative of 0*g - 1 - 2/21*g**3 - 1/7*g**2. Factor r(f).
-2*f*(f + 1)/7
Let l = 37 + -110/3. Let m be (-4)/2 - 84/(-36). Suppose -2/3 + m*a**2 - l*a = 0. Calculate a.
-1, 2
Let c(x) = -x**2 + 16*x - 15. Let f be c(15). Let z(w) be the second derivative of -1/36*w**4 + w + f + 0*w**2 + 0*w**3. Factor z(g).
-g**2/3
Find a, given that 0 - 6/13*a**3 + 2/13*a**2 + 6/13*a - 2/13*a**4 = 0.
-3, -1, 0, 1
Let s(l) = -3*l**3 - 4*l**2 - 5*l. Let b(g) be the second derivative of -g**5/10 - g**4/4 - 2*g**3/3 - 2*g. Let j(m) = 4*b(m) - 3*s(m). Factor j(t).
t*(t - 1)*(t + 1)
Suppose 0 + 3/4*p**5 + 0*p**2 + 0*p - 1/2*p**3 + 1/4*p**4 = 0. What is p?
-1, 0, 2/3
Let i(h) be the third derivative of -1/6*h**3 + 5*h**2 - 1/24*h**4 + 0 + 0*h - 1/240*h**5. Factor i(r).
-(r + 2)**2/4
Let 2*b + 2*b**3 - 20*b**2 + 9*b + 3*b**3 + 4*b = 0. What is b?
0, 1, 3
Let u(v) = 2*v - 5. Let b be u(4). Factor -r**5 + 3*r**5 - 6*r**b + 4*r**3.
2*r**3*(r - 1)*(r + 1)
Suppose 3*z + 5 = t, 2*z = 3*z - 2*t + 5. Let p be 1 + z + 32/18. Factor -8/3*r + p + 4/3*r**2 - 2/9*r**3.
-2*(r - 2)**3/9
Let v(x) = -x**3 - 7*x**2 - x - 2. Let d be v(-7). Let n(g) be the second derivative of 3*g**2 - 5/2*g**3 + g**4 - 3/20*g**d + 0 - g. What is i in n(i) = 0?
1, 2
Suppose j + 5 - 1 = 0. Let i be (-20)/(-32)*j/(-10). Let 0*v - i*v**3 + 0 + 1/4*v**2 = 0. What is v?
0, 1
Let j(w) be the second derivative of w**7/105 - 4*w**6/75 + 3*w**5/25 - 2*w**4/15 + w**3/15 - 4*w. Factor j(a).
2*a*(a - 1)**4/5
Let q(m) be the first derivative of m**3/4 - 3*m**2/2 + 9*m/4 - 2. Find g, given that q(g) = 0.
1, 3
Let 8/11*m**5 + 30/11*m**4 + 0 - 6/11*m**2 + 0*m + 16/11*m**3 = 0. What is m?
-3, -1, 0, 1/4
Factor 2/3*b**3 - 2/9*b**4 + 0 + 4/9*b - 2/9*b**5 + 10/9*b**2.
-2*b*(b - 2)*(b + 1)**3/9
Let n = 3 - -13. Suppose -5*g + n = -g. What is c in -2/5*c**5 + 0*c**2 + 0 + 0*c + 4/5*c**g - 2/5*c**3 = 0?
0, 1
Factor -1 + 1/4*q**2 - q + 1/4*q**3.
(q - 2)*(q + 1)*(q + 2)/4
Let y(i) be the second derivative of -i**7/840 + i**5/40 - 5*i**4/12 + 7*i. Let d(n) be the third derivative of y(n). Factor d(b).
-3*(b - 1)*(b + 1)
Let i(q) be the third derivative of 2*q**2 - 1/90*q**5 - 16/9*q**3 + 0*q + 2/9*q**4 + 0. Determine c, given that i(c) = 0.
4
Let l(t) be the second derivative of t**6/15 + 2*t**5/5 + t**4/2 - 2*t. Let l(i) = 0. What is i?
-3, -1, 0
Let q be (-3)/(((-3)/14)/1). Suppose 2*x + 6 = q. Factor 0*a**5 + 5*a**4 - a**5 + 3*a**2 + a**3 - 4*a**4 - x*a**2.
-a**2*(a - 1)**2*(a + 1)
Let z(i) be the first derivative of -3*i**5/5 - 27*i**4/4 - 24*i**3 - 24*i**2 - 21. Determine b so that z(b) = 0.
-4, -1, 0
Let s(l) = l - 2. Let j be s(6). Factor -2*n**2 + 0*n**4 + 1 + 6*n**4 - 5*n**j.
(n - 1)**2*(n + 1)**2
What is n in -5*n**4 + 0*n**4 + 176*n**3 - 191*n**3 - 10*n**2 = 0?
-2, -1, 0
What is k in 4*k**2 + k**5 + 2*k**3 + 2*k**5 - 2 - k - 4*k**5 - 2*k**4 = 0?
-2, -1, 1
Let j(d) be the third derivative of 3/40*d**6 + 1/10*d**5 - 3/16*d**4 + 0*d - d**2 - 1/70*d**7 - 1/2*d**3 + 0 - 3/224*d**8. Let j(a) = 0. Calculate a.
-1, -2/3, 1
Let o be (-2)/4*(1 - 1). Let z be 80/36 - (-14)/(-63). Let -2/3*n**3 + 2/3*n + o + 0*n**z = 0. Calculate n.
-1, 0, 1
Let g(i) be the third derivative of -2*i**7/315 - i**6/180 + i**5/45 + i**4/36 + 25*i**2. Solve g(z) = 0.
-1, -1/2, 0, 1
Let o be ((-4)/(-6))/(4/30). Suppose -j + 1 = -2*t - 3, -3*j + 10 = -o*t. Determine i so that 3/4*i**3 + 0 - 1/2*i**2 + j*i + 5/4*i**4 = 0.
-1, 0, 2/5
Let g(q) be the first derivative of -32*q**5/5 + 10*q**4 - 4*q**3/3 - 2*q**2 + 17. Suppose g(a) = 0. What is a?
-1/4, 0, 1/2, 1
Suppose 2/5*l**2 - 4/5*l + 2/5 = 0. Calculate l.
1
Let k be 8056/26 - (-8 - -8). Let y = 310 - k. Factor 0*q**2 - 4/13 - 6/13*q + y*q**3.
2*(q - 2)*(q + 1)**2/13
Let p = 6 - 2. Suppose 0 = -f + 3 + 3. Suppose -f*r**3 + 4*r**4 - r**2 - 3*r**2 + 0*r**p = 0. Calculate r.
-1/2, 0, 2
Factor 0*q + 3/4*q**5 + 0*q**3 - 1/2*q**4 + 0 + 0*q**2.
q**4*(3*q - 2)/4
Let t(r) = -4*r**3 - 5*r**3 + 9*r**2 + 0*r - r - 4*r**4. Let o(v) = 2*v**4 + 5*v**3 - 5*v**2 + v. Let d(c) = 5*o(c) + 3*t(c). Find p, given that d(p) = 0.
-1, 0, 1
Let o(w) be the first derivative of 0*w**2 + 0*w - 9/5*w**5 + 1/2*w**6 + 3/2*w**4 - 10 + 0*w**3. Factor o(y).
3*y**3*(y - 2)*(y - 1)
Suppose 2*j = -y, 0 = 8*j - 12*j + 2*y + 16. Let n = -1816/9 + 202. Find b such that 4/9*b - n*b**j + 0 = 0.
0, 2
Let w = 7 + -3. Let y(m) be the second derivative of -m + 0 + m**2 + 1/3*m**w - m**3. Factor y(f).
2*(f - 1)*(2*f - 1)
Let j = -8 - 13. Let c = j + 23. Find a, given that 2/7 + 6/7*a - 8/7*a**c = 0.
-1/4, 1
Let g(q) be the first derivative of 2*q**3/21 - 3*q**2/7 + 4*q/7 - 5. Suppose g(k) = 0. What is k?
1, 2
Factor -1/8*c**2 + 9/4*c - 81/8.
-(c - 9)**2/8
Let s(c) = -c - 4*c + 1 - 4 - c - 3*c**2. Let n(a) = -6*a**2 - 13*a - 5. Let p(y) = 3*n(y) - 5*s(y). Find k, given that p(k) = 0.
-3, 0
Let f(n) be the third derivative of n**7/1680 + n**6/360 - n**5/240 - n**4/24 + n**3/6 + 2*n**2. Let g(q) be the first derivative of f(q). Factor g(t).
(t - 1)*(t + 1)*(t + 2)/2
Let l(o) be the first derivative of 3*o**4 - 8*o**3/3 + 5. Solve l(r) = 0.
0, 2/3
Let o be 0/(105/35*(-1)/3). Find l, given that 0 + o*l - 2/5*l**3 + 0*l**2 - 2/5*l**4 = 0.
-1, 0
Factor 27 + 52*q**2 - 2*q**4 - 199*q + 6*q**4 + 117 - 41*q + 40*q**3.
4*(q - 1)**2*(q + 6)**2
Let h(n) = -n**2 + 9*n + 12. Let g be h(9). Factor j**2 + j**2 - 8*j**2 + 15*j - g*j + 3*j**3.
3*j*(j - 1)**2
Let j be -2 - -1*(-2 + 1). Let w = j + 7. Let 9*y + y**3 + y**w - 9*y = 0. What is y?
-1, 0
Let z(k) be the third derivative of -k**5/12 + 5*k**4/2 - 30*k**3 + 14*k**2. Factor z(b).
-5*(b - 6)**2
Let k(b) be the second derivative of -b**4/48 + b**3/8 - b**2/4 - 2*b. Factor k(j).
-(j - 2)*(j - 1)/4
Let f(k) be the second derivative of 1/480*k**6 + 1/32*k**4 + 1/2*k**2 + 1/24*k**3 + 0 - 2*k + 1/80*k**5. Let g(q) be the first derivative of f(q). Factor g(h).
(h + 1)**3/4
Let j(u) be the second derivative of -u**5/20 + u**4/4 - u**3/2 + u**2/2 - 2*u. Determine w so that j(w) = 0.
1
Let l(p) be the first derivative of -p**6/21 + 12*p**5/35 - 13*p**4/14 + 8*p**3/7 - 4*p**2/7 - 8. Suppose l(v) = 0. Calculate v.
0, 1, 2
Let a be (7/(-21))/((-2)/18). Let z(x) be the second derivative of 2/9*x**2 + 1/54*x**4 - 1/9*x**a + 0 - x. Factor z(j).
2*(j - 2)*(j - 1)/9
Let u = 3 + -2. Factor -2 + 5*l**4 - l + 21*l**2 + u + 12*l + 17*l**3 + 3.
(l + 1)**3*(5*l + 2)
Let b(o) be the first derivative of 0*o**3 - 3 + 0*o**2 - 1/16*o**4 - 1/24*o**6 - 1/10*o**5 + 0*o. Solve b(z) = 0.
-1, 0
Let z(p) = 3*p**2 - 11*p - 2. Let k(r) = -7 + 0*r**2 + 8 - r**2 + 6*r. Let b(t) = -5*k(t) - 3*z(t). Solve b(f) = 0.
-1/4, 1
Suppose 27 = -2*g - 3*d - 2*d, -4*d = 20. Let n be 1 + -1*(g + 0). Solve -1/6*o**3 + 0*o + 0 + 1/6*o**n = 0 for o.
0, 1
Let g(o) be the second derivative of o**7/21 - o**6/15 - 7*o**5/5 - 13*o**4/3 - 19*o**3/3 - 5*o**2 - 9*o. Solve g(c) = 0 for c.
-1, 5
Factor -6*t**4 - 3*t**4 + 0*t**4 + 30*t**3 + 6*t - 27*t**2.
-3*t*(t - 2)*(t - 1)*(3*t - 1)
Let m be ((-2)/12)/((-1)/2). Factor 0*a + 0 - m*a**2.
-a**2/3
Let b(z) be the third derivative of z**7/1575 - 7*z**6/900 + 11*z**5/450 - z**4/36 - 23*z**2. Determine c, given that b(c) = 0.
0, 1, 5
Let n(a) = a**3 + 6*a**2 - 3*a - 4. Let s be (-7)/(-49) + 72/(-14). Let k(o) = 2*o**3 + 6*o**2 - 3*o - 5. Let c(z) = s*n(z) + 4*k(z). Let c(r) = 0. Calculate r.
0, 1
Suppose 0 = 2*f + 2*x - 3 - 9, -x = 5*f - 46. Factor 3*j**4 - 2*j**2 + f*j**3 - 6*j**4 - j**3 - 4*j**2.
-3*j**2*(j - 2)*(j - 1)
Factor -2/7*x**4 - 72/7*x**2 - 64/7 - 16*x - 20/7*x**3.
-2*(x + 2)**3*(x + 4)/7
Let r(t) = t**2 - t - 11. Let s be r(0). Let n = 13 - s. Determine q so that n*q**2 - 6 - 9*q - 24*q**2 + 3*q**3 = 0.
-1, 2
Let t be (2 - 2) + 4/12. Let p = -69 - -209/3. Suppose -p*i + 0 - t*i**2 = 0. What is i?
-2, 0
Let q(h) = -h**4 - h**2 + h + 1. Let i(d) = -8*d**4 + 3*d**3 - 2*d**2 + 2*d + 5. Let f(g) = -i(g) + 5*q(g). Solve f(u) = 0 for u.
-1, 0, 1
Let f be 5/12 - (-5)/20. Factor -4/3*g**2 - f*g**3 + 0 - 2/3*g.
-2*g*(g + 1)**2/3
Factor 2/11 + 4/11*i + 2/11*i**2.
2*(i + 1)**2/11
Let l = -209 + 3136/15. Let k(a) be the second derivative of -2*a - l*a**3 + 0*a**2 + 0 + 1/30*a**4. Factor k(h).
2*h*(h - 1)/5
Factor -1/2*s**2 + 2 - 2*s + 1/2*s**3.
(s - 2)*(s - 1)*(s + 2)/2
Let y(s) be the first derivative of 