Let p(q) = q**3 + 26*q**2 + 47*q - 22. Let o be p(-24). Determine n, given that -3 + 2*n - 1/3*n**o = 0.
3
Let c(t) = -t**2 - 5*t - 2. Let l be c(-4). Determine i so that i**2 - 3*i**2 + 2*i**3 + l*i**2 + 2*i**2 = 0.
-1, 0
Let t = -78/19 + 9493/2280. Let g(m) be the second derivative of t*m**6 + 1/4*m**2 + 0 + 3*m + 9/16*m**4 + 23/80*m**5 + 13/24*m**3. Factor g(v).
(v + 1)**3*(7*v + 2)/4
Factor 3/7*t**2 + 1/7*t**3 + 0 - 3/7*t**4 - 2/7*t + 1/7*t**5.
t*(t - 2)*(t - 1)**2*(t + 1)/7
Let t(u) = u + 8. Let i be t(-6). Let g(h) be the second derivative of 0*h**4 - i*h - 2*h**2 + 1/10*h**5 + 0 - h**3. Determine w so that g(w) = 0.
-1, 2
Let b be (0 + -1)/(9 + -11). Determine q so that q + 0 + b*q**2 = 0.
-2, 0
Let y(j) = 22*j - 307. Let f be y(14). Determine n so that -1/3*n**2 - f + 4/3*n = 0.
1, 3
Let n be 1*2 + ((-110)/(-40) - 4). Determine q, given that -n*q**2 - 1/2*q + 5/4*q**3 + 0 = 0.
-2/5, 0, 1
Suppose -18*u + 38 = -16. Let l(c) be the third derivative of -4*c**2 + 0 - 3/40*c**4 + 1/100*c**5 + 0*c + 1/5*c**u. Find y such that l(y) = 0.
1, 2
Let q(a) be the first derivative of a**4/2 - 4*a**3/3 + a**2 + 24. Solve q(u) = 0.
0, 1
Let l(o) = -o**3 - 6*o**2 - 9*o - 54. Let g be l(-6). Find d such that 0 + 0*d**2 + g*d + 0*d**3 + 0*d**4 - 1/4*d**5 = 0.
0
Solve 0*n + 0 + 1/2*n**3 + 5*n**2 = 0 for n.
-10, 0
Let l(c) = -1. Let i(j) = j**3 + 5*j**2 + 8*j + 5. Let z be (-2)/12 - (-20)/(-24). Let w(s) = z*l(s) - i(s). Factor w(m).
-(m + 1)*(m + 2)**2
What is h in -2 - 5*h**4 + 4*h + 10*h**4 - 3*h**3 - 3*h**4 - h**3 = 0?
-1, 1
Let y be 2/(-2)*-3*1. Factor -2*g**5 + 4*g**y - 2*g**3 - 2*g**4 + 3*g**2 - g**2 + 0*g**5.
-2*g**2*(g - 1)*(g + 1)**2
Let t = -78 - -83. Let 0*w - 1/6*w**3 + 0*w**2 + 1/3*w**4 + 0 - 1/6*w**t = 0. What is w?
0, 1
Let g = -33833/5 - -6832. What is r in -147/5*r**4 - g*r**2 - 378/5*r**3 - 108/5*r - 12/5 = 0?
-1, -2/7
Solve 0*a**2 + 0*a + 0 + 1/10*a**3 + 1/10*a**4 = 0 for a.
-1, 0
Let l be ((-3)/6)/(10/(-80)). Solve 3/2 - 3/2*t**2 - 3*t**3 + 3/4*t**5 + 9/4*t + 0*t**l = 0 for t.
-1, 1, 2
Let a(m) be the third derivative of -121*m**5/180 - 11*m**4/18 - 2*m**3/9 + 22*m**2. Solve a(f) = 0.
-2/11
Let r(z) be the first derivative of z**7/420 + z**6/36 + z**5/20 - 3*z**4/4 + 2*z**3 - 6. Let t(j) be the third derivative of r(j). Factor t(n).
2*(n - 1)*(n + 3)**2
Solve 2/13*u**3 - 16/13*u**2 + 40/13*u - 32/13 = 0.
2, 4
Let j(h) = -4*h**4 - 3*h**3 - 7. Let b(t) = t**4 + t**3 + 2. Suppose -3*v = 3*y + 18, -4*v + 0 = -4. Let d(k) = y*b(k) - 2*j(k). Factor d(f).
f**3*(f - 1)
Let d be (0 + 1)/(5/35). Let j = -5 + d. Factor 1/4*r + 9/4*r**j + 11/4*r**3 + r**4 - 1/4.
(r + 1)**3*(4*r - 1)/4
Let i = -644 - -3197/5. Let j = -21/5 - i. Solve 2/5*d**2 - j*d + 0 = 0.
0, 1
Let w be (-1 - -3 - 6)/(-60 - -59). Let 3/4*x**5 + 3/4*x - 3/2*x**3 - 3/4*x**w - 3/4 + 3/2*x**2 = 0. What is x?
-1, 1
Factor -6*n**2 + 0 + 2*n + 5/2*n**3.
n*(n - 2)*(5*n - 2)/2
Let g(t) = -3*t**4 + 4*t**3 - 5*t**2 + 4*t. Let c(f) = 4*f**4 - 5*f**3 + 6*f**2 - 5*f. Let l(p) = -4*c(p) - 5*g(p). Factor l(z).
-z**2*(z - 1)*(z + 1)
Let h(q) = -3*q**2 - 19*q + 11. Let x(u) = u**2 + 5*u - 3. Let j(b) = 6*h(b) + 22*x(b). Suppose j(n) = 0. What is n?
0, 1
What is o in 0 - 8/19*o**2 - 2/19*o = 0?
-1/4, 0
Determine y, given that 1/5*y + 0 - 2/5*y**2 - 4/5*y**4 - 7/5*y**3 = 0.
-1, 0, 1/4
Let n be 1*(22/11 + 0/1). Determine v so that 7/4*v**3 + 9/2*v**n + 1/4*v**4 + 5*v + 2 = 0.
-2, -1
Let f(k) be the third derivative of -k**5/60 - k**4/3 - 4*k**3/3 + k**2. Let p be f(-6). Factor p*g**3 + 8 + 6*g**2 + 12*g - g**3 - 2*g**3.
(g + 2)**3
Let t(h) = -4*h**2 - 31*h + 11. Let z be t(-8). Suppose -2/3*c + 4/3*c**2 + 2/3*c**5 - 4/3*c**4 + 0*c**z + 0 = 0. What is c?
-1, 0, 1
Let b(j) be the third derivative of -j**7/735 - j**6/210 + j**5/70 + j**4/21 - 4*j**3/21 - 2*j**2. Determine w so that b(w) = 0.
-2, 1
Suppose 5*o = c, -2*o - 3*c + 19 = 2*o. Factor 1/4*j**2 - j + o.
(j - 2)**2/4
Let q be (-20 + 19)/(14/(-9)). Let x(d) be the first derivative of 4 + 1/7*d**2 + q*d**4 - 4/7*d**3 + 0*d. Factor x(o).
2*o*(3*o - 1)**2/7
Let t(g) be the third derivative of g**7/210 + g**6/10 + 11*g**5/30 - 7*g**4/2 + 49*g**3/6 + g**2 + 38. Factor t(w).
(w - 1)**2*(w + 7)**2
Let g(b) be the first derivative of -64*b**3/3 - 16*b**2 - 4*b + 4. Factor g(q).
-4*(4*q + 1)**2
Let v(o) be the first derivative of -o**6/1800 - 2*o**3/3 + 3. Let z(w) be the third derivative of v(w). Factor z(x).
-x**2/5
Let z(n) = -8*n - 5. Let h be z(-1). Factor 2*b**h + 2/3*b**5 - 2/3*b**2 - 2*b**4 + 0 + 0*b.
2*b**2*(b - 1)**3/3
Let f be ((-2)/(-3))/(56/42). Determine u, given that f*u**2 - 1/2*u + 0 = 0.
0, 1
Let p(x) be the second derivative of -x**5/20 + 7*x**4/12 - 11*x**3/6 + 5*x**2/2 + 34*x. Solve p(t) = 0.
1, 5
Let n(r) be the second derivative of 0 - r + 0*r**3 - 1/60*r**4 + 1/10*r**2. Suppose n(w) = 0. Calculate w.
-1, 1
Suppose 3*d - 48 = -d. Factor -6 - 12*y - d + y**2 - 3*y**2.
-2*(y + 3)**2
Let k = -14 - 1. Let h be ((-4)/(-14))/(k/(-21)). Factor 8/5 + h*v**2 + 8/5*v.
2*(v + 2)**2/5
Let g be (6/(-8))/((-6)/4). Let t be 5/2*24/30. Solve j - g*j**t - 1/2 = 0.
1
Let f(q) be the first derivative of -3*q**4/5 + 9*q**3/5 - 9*q**2/5 + 3*q/5 + 2. Factor f(n).
-3*(n - 1)**2*(4*n - 1)/5
Let t(z) be the third derivative of z**5/100 - z**4/20 - 3*z**3/10 - 11*z**2. Factor t(u).
3*(u - 3)*(u + 1)/5
Let j(w) = -6*w**3 - 51*w**2 - 6*w - 21. Let a(i) = 2*i + i - 2*i + i**3 + 4 + 10*i**2. Let y(q) = -21*a(q) - 4*j(q). Factor y(t).
3*t*(t - 1)**2
Let b(n) = n**3 - 8*n**2 + 7. Let a be b(8). Let g = a + -7. Factor 2/5*x**2 - 2/5*x + g.
2*x*(x - 1)/5
Let i(p) be the third derivative of -2*p**7/105 + p**6/15 + p**5/5 - 4*p**4/3 + 8*p**3/3 - 2*p**2 - 43*p. Factor i(a).
-4*(a - 2)*(a - 1)**2*(a + 2)
Let w(y) = y**3 + 2*y**2 + 2*y. Let a(n) = -3*n**2 - 2*n. Let j(r) = 6*a(r) + 7*w(r). Let v(k) = 3*k**3 - 2*k**2 + k. Let b(t) = -2*j(t) + 5*v(t). Factor b(q).
q*(q - 1)**2
Solve 3*w**3 - w**2 + 8*w**2 + w**2 + 6*w + w**2 = 0.
-2, -1, 0
Factor 0*a + 1/5*a**3 + 0*a**2 + 0.
a**3/5
Let w(d) be the first derivative of -d**8/420 + d**7/210 + d**6/90 - d**5/30 + 8*d**3/3 + 6. Let x(f) be the third derivative of w(f). Factor x(i).
-4*i*(i - 1)**2*(i + 1)
Let m(r) be the second derivative of 3/10*r**5 + 0 - 1/3*r**4 + 2/15*r**6 - 1/7*r**7 + 0*r**2 + 0*r**3 + 3*r. Suppose m(p) = 0. What is p?
-1, 0, 2/3, 1
Let j(s) be the second derivative of s**8/36960 - s**6/3960 + s**4/12 + 2*s. Let h(a) be the third derivative of j(a). Solve h(g) = 0 for g.
-1, 0, 1
Let f(r) be the third derivative of 0*r + 0 + 4*r**2 + 0*r**3 - 1/42*r**5 + 1/42*r**4. Factor f(w).
-2*w*(5*w - 2)/7
Let r(s) = -3*s**5 - 9*s**4 - 6*s**3 - 6*s**2 + 3. Let j(a) = -a**3 + a**2 - 1. Let y(t) = -3*j(t) - r(t). Factor y(d).
3*d**2*(d + 1)**3
Let n(x) be the second derivative of x**7/273 + 3*x**6/65 + 16*x**5/65 + 28*x**4/39 + 16*x**3/13 + 16*x**2/13 - 6*x. Factor n(i).
2*(i + 1)*(i + 2)**4/13
Let w(y) be the third derivative of 3*y**2 + 0*y**3 + 0*y**5 + 0 + 0*y + 0*y**4 - 1/240*y**6 + 1/840*y**7. Factor w(r).
r**3*(r - 2)/4
Let t(v) be the third derivative of -9*v**8/112 + v**7/35 + 9*v**6/20 - v**5/5 - 9*v**4/8 + v**3 - 5*v**2. Solve t(c) = 0 for c.
-1, 2/9, 1
Factor -11*m**2 + 6*m**3 - 9*m**3 + 5*m**2.
-3*m**2*(m + 2)
Let a(k) = 7*k**5 - 3*k**4 - 10*k**3 + 8*k**2 + 7*k - 7. Let w(g) = g**5 + g**4 - g**2 + g - 1. Let h(d) = a(d) - 2*w(d). Let h(m) = 0. Calculate m.
-1, 1
Let i = 11 + -8. Let n = i + 1. Factor 0*s**3 - 1/2*s**2 + 0*s + 0 + 1/2*s**n.
s**2*(s - 1)*(s + 1)/2
Let w(f) = f**4 + f**3 + f**2 - f - 1. Let z(g) = -4*g**4 + 4*g**2 - 2. Let i(r) = -4*w(r) - 2*z(r). Solve i(u) = 0 for u.
-1, 1, 2
Let j(n) be the third derivative of n**8/22680 - n**7/22680 - n**5/20 + 3*n**2. Let u(t) be the third derivative of j(t). Factor u(c).
2*c*(4*c - 1)/9
Let z be 8/12 - (-17)/6. Let 0 + 5/2*l**2 + 3/2*l**4 + 1/2*l + z*l**3 = 0. What is l?
-1, -1/3, 0
Let m(f) be the first derivative of 0*f**2 - 1/4*f**6 + 1/10*f**5 + 0*f + 2 - 1/6*f**3 + 3/8*f**4. What is s in m(s) = 0?
-1, 0, 1/3, 1
Let j(k) be the first derivative of -3/28*k**4 + 2/7*k**3 - 7 - 6/7*k + 3/14*k**2. Solve j(n) = 0.
-1, 1, 2
Let f(v) be the third derivative of -v**8/168 - 2*v**7/21 - 11*v**6/30 + 16*v**5/15 + 95*v**4/12 + 50*v**3/3 + v**2. Let f(l) = 0. 