erivative of g**7/420 - g**6/45 + g**5/12 - g**4/6 + g**3/2 + g**2. Let k(f) be the first derivative of q(f). Solve k(b) = 0.
1, 2
Let c be ((0 + -5)/(-10))/((-6)/(-4)). Let 0 - 1/3*w + 0*w**2 - c*w**5 + 2/3*w**3 + 0*w**4 = 0. What is w?
-1, 0, 1
Let c(m) be the second derivative of m**8/6720 - m**7/1260 + m**6/720 + m**4/6 + 2*m. Let s(t) be the third derivative of c(t). Factor s(a).
a*(a - 1)**2
Let u(i) be the third derivative of 0*i + 13/80*i**6 + 0*i**4 + 0*i**3 - 1/7*i**7 - 2*i**2 + 0 - 1/20*i**5. Determine r, given that u(r) = 0.
0, 1/4, 2/5
Let b be 2 + 3*(-30)/(-27). Factor 14*p**3 + 0 - 8/3*p - b*p**2.
2*p*(3*p - 2)*(7*p + 2)/3
Factor -8*i**3 - 8*i**2 + 4*i**4 + 4 - 165*i + 4*i**5 + 169*i + 0*i**3.
4*(i - 1)**2*(i + 1)**3
Let t(c) = -7*c**3 + 5*c**2 + c + 1. Let y(i) = 6*i**3 - 4*i**2 - 2*i. Suppose 4*p = 8*p - 16. Let a(s) = p*t(s) + 5*y(s). Solve a(q) = 0 for q.
-2, 1
Let b = -109/30 - -13/3. Let i(q) be the second derivative of 0 + 1/2*q**4 + 1/5*q**6 - b*q**5 - 2*q**2 - q + q**3. Find z such that i(z) = 0.
-2/3, 1
Factor 16 + 12*q**3 - 16 + 2*q**4 + 10*q**2.
2*q**2*(q + 1)*(q + 5)
Factor -33*o + 11*o + 82*o - 30*o**2 - 40 + 5*o**3.
5*(o - 2)**3
Determine i so that -2/13*i**4 + 4/13*i**2 - 12/13*i**5 - 12/13*i + 24/13*i**3 - 2/13 = 0.
-1, -1/6, 1
Let n = 12 - 7. Let q be (-1)/n + 38/40. Factor -1/4*k**3 - q*k + 3/4*k**2 + 1/4.
-(k - 1)**3/4
Let n(r) be the first derivative of -9*r**3/7 + 24*r**2/7 + 12*r/7 - 10. What is q in n(q) = 0?
-2/9, 2
Suppose 6*v - 12 = -0. Factor 1/3*j + 0 - 1/3*j**v.
-j*(j - 1)/3
Let x(s) be the first derivative of -3/4*s**4 + 3*s**2 + 9/5*s**5 + 3 + 0*s - 1/2*s**6 - 3*s**3. Solve x(n) = 0.
-1, 0, 1, 2
Suppose -2027 = 5*k - 2*f, -k + f - 406 = -0*f. Let j = 2847/7 + k. Factor 2/7*n**4 + 8/7*n**3 + 2/7 + j*n**2 + 8/7*n.
2*(n + 1)**4/7
Let q(h) be the third derivative of -h**7/42 + h**6/8 - 13*h**2. Factor q(k).
-5*k**3*(k - 3)
Factor -6*y + 9 + 2*y**2 + 2*y**2 - 8*y - 3.
2*(y - 3)*(2*y - 1)
Let n(c) be the first derivative of c**4/4 - 2*c**3/3 - 3*c**2/2 - 17. Let n(v) = 0. Calculate v.
-1, 0, 3
Factor -16/9*p - 2/3*p**2 - 8/9.
-2*(p + 2)*(3*p + 2)/9
Let f(v) be the third derivative of 0*v + 1/360*v**6 + 1/90*v**5 + 0*v**3 + 1/72*v**4 - 3*v**2 + 0. Factor f(m).
m*(m + 1)**2/3
Suppose f = -2*i - f + 10, 0 = 2*i + 5*f - 25. Let -3/2*n**3 + i*n + 3/4*n**2 - 9/4*n**4 + 0 = 0. What is n?
-1, 0, 1/3
Suppose -u + 10 = -0*u. Let o be ((-2)/u)/(1/(-6)). Factor 0 - o*g**3 + 0*g + 4/5*g**2 + 2/5*g**4.
2*g**2*(g - 2)*(g - 1)/5
Let l be (2/(-3))/(8/48). Let y(w) = -2*w - 4. Let u be y(l). Suppose 3*o**3 + 6*o**3 - 3*o**u - 9*o**2 - o + 4*o = 0. What is o?
0, 1
Let p(v) = -56*v**3 + 35*v**2 - 11*v - 7. Let l(u) = -55*u**3 + 34*u**2 - 10*u - 6. Let w(o) = -7*l(o) + 6*p(o). Factor w(b).
b*(7*b - 2)**2
Let f be (-488)/(-240) + -1 + -1. Let y(t) be the third derivative of 0 + 0*t**3 + 1/30*t**5 - 2*t**2 - f*t**6 + 0*t**4 + 1/105*t**7 + 0*t. Factor y(g).
2*g**2*(g - 1)**2
Let k(c) = -14*c - 560. Let n be k(-40). Determine w so that -8/11*w**2 + 0 + 6/11*w**4 + n*w**3 - 2/11*w**5 + 0*w = 0.
-1, 0, 2
Suppose -8 = -4*a, 0 = -3*m + 5*m + a - 12. Factor 4*t - 4*t - 3*t**4 + 2*t**m + 4*t**4.
t**4*(2*t + 1)
Let s(q) be the second derivative of q**4/6 + 2*q**3/21 + 5*q. What is w in s(w) = 0?
-2/7, 0
Let v(d) be the first derivative of d**6/2 - 12*d**5/5 + 9*d**4/2 - 4*d**3 + 3*d**2/2 - 16. Let v(q) = 0. What is q?
0, 1
Let r be -1 + (-10)/(-2)*2. Let g be 3/r + 10/6. Solve -4*j**4 - 2*j - j**g + 5*j**3 - j + 3*j = 0.
0, 1/4, 1
Let 3/4*t - 1/4*t**3 + 0*t**2 - 1/2 = 0. Calculate t.
-2, 1
Let l(q) be the second derivative of -q**7/42 + q**6/10 - 3*q**5/20 + q**4/12 + 40*q. Let l(f) = 0. Calculate f.
0, 1
Let k(z) = 6*z**5 - z**4 - 25*z**3 - 6*z**2 + 19*z - 7. Let a(j) = -3*j**5 + 12*j**3 + 3*j**2 - 9*j + 3. Let p(b) = -7*a(b) - 3*k(b). Let p(g) = 0. What is g?
-2, -1, 0, 1
Let n(f) = f**3 + 4*f**2 + f + 4. Let y be n(-4). Let g = 10 - 10. Factor 2/3*w**2 + g + y*w + 2/3*w**4 - 4/3*w**3.
2*w**2*(w - 1)**2/3
Find g, given that 3*g**2 + 0*g**2 - 5 - 10*g**2 + 20*g - 8*g**2 = 0.
1/3, 1
Let z be (-8)/(-14)*(-21)/(-6). Suppose 3*m + 2 = 4*m. Factor 1 + z*q**m + 0 - q**2 - 2*q.
(q - 1)**2
Let t(s) be the third derivative of s**5/20 + s**4/4 + s**3/2 - 27*s**2. Factor t(v).
3*(v + 1)**2
Let z = -7 - -10. Determine k, given that k**2 - 2/3*k + 0 - 1/3*k**z = 0.
0, 1, 2
Let a = -44/5 - -172/15. Factor 6*m - a*m**2 - 4/3.
-2*(m - 2)*(4*m - 1)/3
Let o be (16/6)/(8/12). What is r in -4*r + 6*r**3 + 2*r**2 + 4*r + 2*r**5 + 6*r**o = 0?
-1, 0
Suppose 3 = 5*x - 12. Let h be (-1)/2 - (x + -5). Suppose 1/2*b**3 + 0*b - b**2 + h*b**4 + 0 = 0. Calculate b.
-1, 0, 2/3
Let v(n) be the second derivative of 0 + 1/2*n**2 + n - 1/12*n**3 - 1/8*n**4. Determine x, given that v(x) = 0.
-1, 2/3
Factor 14*v**4 - 32*v**3 - 21 - 11 + 122*v**2 + 112*v**3 + 64*v + 22*v**2.
2*(v + 2)**3*(7*v - 2)
Let r(i) be the first derivative of 0*i**3 - 4/25*i**5 + 3 + 1/10*i**4 + 0*i**2 + 1/15*i**6 + 0*i. Find n such that r(n) = 0.
0, 1
Let s(g) be the first derivative of g**7/56 - g**6/20 + g**4/8 - g**3/8 - 2*g - 1. Let b(r) be the first derivative of s(r). Factor b(x).
3*x*(x - 1)**3*(x + 1)/4
Let l(k) = k**2 - 6*k + 3. Let y(t) = t. Let s(q) = -3*l(q) - 6*y(q). Find x such that s(x) = 0.
1, 3
Let h = -22 - -200. Suppose -155*s**2 - 8 - 21*s**2 + h*s**3 + 165*s**3 - 118*s**2 + 84*s = 0. Calculate s.
2/7
Let d(x) be the first derivative of 7*x**3/8 + 57*x**2/16 - 9*x/4 + 3. Factor d(t).
3*(t + 3)*(7*t - 2)/8
Let k be (1/2)/((-2)/(-12)). Let r(h) be the third derivative of h**2 + 0*h**k - 1/105*h**7 + 0*h - 1/10*h**5 + 1/12*h**4 + 0 + 1/20*h**6. Factor r(s).
-2*s*(s - 1)**3
Suppose 5 = 4*v + v. Let s(a) be the first derivative of v - a**2 - 1/6*a**3 - 2*a. Factor s(y).
-(y + 2)**2/2
Let s = 56/51 - -4/17. Let u = -611/3 + 204. Solve -u - s*x**2 + 5/3*x = 0 for x.
1/4, 1
Let a = -47 + 380. Let w = 1009/3 - a. Factor 2/3*k + 4/3*k**4 + 0 + 8/3*k**2 + w*k**3.
2*k*(k + 1)**2*(2*k + 1)/3
Let c = 99 + -95. Factor 0 + 1/4*j**c - 1/4*j**2 + 0*j + 0*j**3.
j**2*(j - 1)*(j + 1)/4
Let f = -80/3 - -27. Let n be -5 - ((-112)/12 - -4). Solve f*g**2 + 0*g - n = 0.
-1, 1
Let b(v) be the third derivative of v**5/30 - 5*v**4/6 + 25*v**3/3 - 35*v**2. Find n, given that b(n) = 0.
5
Suppose -4*n = 3*m - 9, 2*n - 3*m = 5*n - 6. Factor 0*w**3 - w + w**n - 2*w + 2*w.
w*(w - 1)*(w + 1)
Suppose -p = -j + 4, j = -2*j + 4*p + 11. Suppose q - 4*y = 1 + 9, -18 = -4*q + j*y. Find w, given that 0 + 8/3*w**q + 2/3*w**3 + 8/3*w = 0.
-2, 0
Suppose 1/3*q**3 + 4/3*q + 0 + 4/3*q**2 = 0. What is q?
-2, 0
Let w(s) be the first derivative of 3*s**4/20 - s**3/5 - 3*s**2/10 + 3*s/5 + 5. Factor w(y).
3*(y - 1)**2*(y + 1)/5
Let s = 36 + -36. Factor -2/9*p**3 + 0 + s*p - 2/9*p**2.
-2*p**2*(p + 1)/9
Let o be ((-175)/140)/(30/(-32)). Factor 20/3*a - o*a**3 - 4*a**2 - 8/3 + 4/3*a**4.
4*(a - 1)**3*(a + 2)/3
Let o be (-3)/6 + (-1)/(-2). Let c(k) = o - 2*k + 6*k**2 - 3 - 2*k**2. Let n(s) = 11*s**2 - 5*s - 8. Let m(z) = 8*c(z) - 3*n(z). Solve m(x) = 0 for x.
-1, 0
Let t = -8 + 10. Suppose -12 + 18*f**2 + 9*f**3 - 15*f**3 - 57*f**t - 12*f**3 - 3*f**4 - 36*f = 0. What is f?
-2, -1
Let k(m) = -m + 4. Let z be k(3). Let f(s) be the first derivative of z + 2/3*s**3 - s**2 - 1/6*s**4 + 2/3*s. Factor f(i).
-2*(i - 1)**3/3
Let q(m) be the first derivative of m**3/12 + m**2/4 - 6. What is g in q(g) = 0?
-2, 0
Let z(s) = -s**3 + 5*s**2 - 3*s - 2. Let t be z(4). Let h = -2 + t. Solve 0*p**2 + h + 1/5*p**3 + 0*p**4 + 0*p - 1/5*p**5 = 0.
-1, 0, 1
Let w(j) be the third derivative of j**5/60 - j**4/24 - j**3/3 + 7*j**2. Factor w(n).
(n - 2)*(n + 1)
Let v(g) be the third derivative of g**8/336 + g**7/105 - g**5/30 - g**4/24 + 6*g**2. What is i in v(i) = 0?
-1, 0, 1
Let x be 1*6*8/12. Let h(n) be the first derivative of -2*n**3 + 1/2*n**x - 1/2*n**6 + n**5 - 2 + n + 1/2*n**2. Factor h(r).
-(r - 1)**3*(r + 1)*(3*r + 1)
Let b(j) = -2*j**2 - 14*j - 10. Let r be b(-6). Let l(f) be the second derivative of -3/40*f**5 - 7/24*f**4 + 0*f**r + 0 + 4*f - 1/6*f**3. Factor l(n).
-n*(n + 2)*(3*n + 1)/2
Let v(w) be the first derivative of 3*w**5/5 + w**4 - w**3/3 - w**2 - 1. Factor v(u).
u*(u + 1)**2*(3*u - 2)
Let m(a) be the third derivative of -a**8/1008 + 