 1)**2*(n + 1)/13
Let w be 4 + 0/4 + -2. Determine z so that 2/9 + 2/9*z**w + 4/9*z = 0.
-1
Suppose 7*o + 78 = -27. Let i be (-7)/(70/o) + 0. Let 7/4*w**3 + i*w**2 - 1/4*w + 1/2*w**4 - 1/2 = 0. What is w?
-2, -1, 1/2
Let g(z) = -z**3 + z**2 + z + 4. Suppose 3 = -5*n - 5*m - 2, n + 3*m + 3 = 0. Let w be g(n). Factor -2*d - d + 6*d**3 - 3*d + 3*d**w - 3*d**2.
3*d*(d - 1)*(d + 1)*(d + 2)
Suppose 5 = 5*r, h + 2*r = 4*h - 10. Factor -4 - 1/4*v**5 - h*v**3 + 7/4*v**4 + 4*v + 2*v**2.
-(v - 2)**4*(v + 1)/4
Let t(f) be the first derivative of f**8/840 + 2*f**7/525 - f**5/75 - f**4/60 + 3*f**2 + 1. Let d(a) be the second derivative of t(a). Factor d(x).
2*x*(x - 1)*(x + 1)**3/5
Let s(y) be the first derivative of 0*y**4 + 1/3*y**3 + 1 + 0*y**2 - 1/10*y**5 - 1/2*y. Solve s(j) = 0 for j.
-1, 1
Let s(x) = -x + 12. Let o be s(9). Let d(j) = j**2 + 5*j - 4. Let v be d(-6). Solve 2*r**3 + 0*r**v - 5*r**o + r**3 + 2*r**2 = 0 for r.
0, 1
Let g(q) be the third derivative of -q**9/30240 + q**7/2520 + q**5/60 - 3*q**2. Let x(a) be the third derivative of g(a). Suppose x(n) = 0. What is n?
-1, 0, 1
Let o(q) be the third derivative of -q**7/945 - q**6/270 + q**5/90 + 48*q**2. Factor o(z).
-2*z**2*(z - 1)*(z + 3)/9
Suppose 0 = -5*j + 2*o - 11 + 3, -5*j - 5*o + 20 = 0. Find d, given that 32/3*d**4 + 14/3*d**5 + j*d + 4/3*d**2 + 0 + 22/3*d**3 = 0.
-1, -2/7, 0
Suppose f - 31 + 28 = 0. Let o(h) be the second derivative of 1/3*h**4 + 2/15*h**6 + 0 - 2*h + 0*h**2 - 1/42*h**7 - 3/10*h**5 - 1/6*h**f. Factor o(t).
-t*(t - 1)**4
Let c(l) be the first derivative of -2*l**3/33 + l**2/11 + 4*l/11 - 16. Let c(p) = 0. What is p?
-1, 2
Solve 3*y + 3*y - 6*y**3 - 2*y**4 - y + 3*y = 0.
-2, 0, 1
Let a be (6/9)/((-10)/69). Let f = 211/35 + a. Find u such that -8/7*u**2 - 2/7*u**3 - f*u - 4/7 = 0.
-2, -1
Let t(i) be the third derivative of i**5/120 + 5*i**4/24 + 25*i**3/12 - 5*i**2. Determine a so that t(a) = 0.
-5
Let g = 1 + 1. Factor -g*j**3 + 4*j**3 - 3*j**3 + j.
-j*(j - 1)*(j + 1)
Suppose -32*j**3 - 5*j + 18*j**3 + 19*j**3 = 0. What is j?
-1, 0, 1
Let z be 106/(-5)*(-2)/4. Let w = -51/5 + z. Suppose 2/5*s**3 - 2/5 + w*s**2 - 2/5*s = 0. What is s?
-1, 1
Let s(v) be the first derivative of -2/5*v**2 + 2/15*v**3 - 3 + 0*v. Factor s(f).
2*f*(f - 2)/5
Let w be ((2/(-27))/(-1))/((-11)/(-33)). Suppose 8/9*i + 0 + w*i**3 + 8/9*i**2 = 0. Calculate i.
-2, 0
Let f(j) be the first derivative of j**6/6 - 6*j**5/5 + 13*j**4/4 - 4*j**3 + 2*j**2 + 6. Solve f(k) = 0.
0, 1, 2
Find s such that 0 + 2*s**2 + 0*s + 1/4*s**3 = 0.
-8, 0
Let h be -12*2*3/(-24). Factor a**2 + 5*a**2 - 2*a**3 - 7*a**h + 3*a**4.
3*a**2*(a - 2)*(a - 1)
Factor 54 - f**4 - 29 - 25.
-f**4
Let n(d) be the second derivative of -d**4/96 + d**3/8 - 5*d**2/16 - 17*d. Suppose n(t) = 0. What is t?
1, 5
Suppose 0 = 5*x - 3*u + u - 10, 3*u = x - 2. Factor 1/3 + 1/3*j**x - 2/3*j.
(j - 1)**2/3
Suppose 2*d - 120 = -2*d. Suppose -3*t**3 - 5*t**5 + d*t**4 + 2*t**5 - 36*t**4 = 0. Calculate t.
-1, 0
Let p(l) = -l**3 + l**2 + 1. Let c(d) = -120*d**5 + 298*d**4 - 112*d**3 - 14*d**2 + 8*d + 2. Let k(u) = c(u) - 2*p(u). Find v such that k(v) = 0.
-1/4, 0, 1/3, 2/5, 2
Solve -4*w**2 - 9 - 5*w + 17*w + 0*w + 1 = 0 for w.
1, 2
Let u be (1 + 1 - 6) + 36/7. Factor 6/7*k + u*k**2 - 2/7.
2*(k + 1)*(4*k - 1)/7
Factor 2557 - 2557 - 18*a**2 + 3*a.
-3*a*(6*a - 1)
Let 320 + 4*t**2 + 27*t + 53*t + t**2 = 0. What is t?
-8
Let d = -1/25810 + -929041/3071390. Let b = d + 10/17. Determine p, given that 0 - b*p**2 + 2/7*p**4 - 2/7*p + 2/7*p**3 = 0.
-1, 0, 1
Let t be 12/24*(10/4 + -2). Suppose -t*q**4 + 1/2*q**2 + 1/2*q**3 - 1/4*q**5 - 1/4*q - 1/4 = 0. What is q?
-1, 1
Suppose -r - 15 = -6*r. Suppose 5*p = 25 - 5. Suppose -2*v**r + 2*v + p - 2*v**4 + v**4 - 3 = 0. What is v?
-1, 1
Suppose 5*d - 13 = 2. Let q(j) = 7*j**5 - 4*j**4 + 7*j**3 + 5*j**2. Let s(u) = 4*u**5 - 2*u**4 + 4*u**3 + 3*u**2. Let b(c) = d*q(c) - 5*s(c). Factor b(n).
n**3*(n - 1)**2
Let z = 70/3 + -137/6. Factor -1/4*a - 1/4*a**3 + 0 - z*a**2.
-a*(a + 1)**2/4
Let c(w) be the third derivative of w**6/360 + w**5/30 + w**4/6 + w**3/2 + 4*w**2. Let l(g) be the first derivative of c(g). Factor l(a).
(a + 2)**2
Let g = -18 - -19. Let w be (g/3 - -1)/2. Factor w*p**3 - 2*p + 0*p**2 - 4/3.
2*(p - 2)*(p + 1)**2/3
Let u be 212/24 + 2/(-6). Let q = u + -8. Solve q*a**2 + 2*a + 2 = 0.
-2
Let j(o) be the second derivative of -o**5/5 - 4*o**4/3 + 2*o**3/3 + 8*o**2 + 21*o. Suppose j(m) = 0. Calculate m.
-4, -1, 1
Let o(q) = 5*q**4 + 7*q**3 + 6*q. Let z be (-1)/5 - 72/15. Let t(h) = -4*h**4 - 6*h**3 - 5*h. Let g(c) = z*o(c) - 6*t(c). Factor g(u).
-u**3*(u - 1)
Let a = 58 - 404/7. Factor -12/7*d**3 - 8/7*d**4 - 2/7*d**5 - a*d - 8/7*d**2 + 0.
-2*d*(d + 1)**4/7
Factor -1/7*k**2 - 8/7 + 6/7*k.
-(k - 4)*(k - 2)/7
Let q(y) = -7*y**3 + y. Let v be q(-1). Let h be (4/8)/(2/v). Factor h*p**4 + 0 + 1/2*p**5 + 0*p + 1/2*p**2 + 3/2*p**3.
p**2*(p + 1)**3/2
Factor -1/4*t**3 + 1/4*t**2 + 0*t + 0.
-t**2*(t - 1)/4
Solve 0*g**4 - 19*g**2 - 18*g**5 - 6*g - 1 - 25*g**3 - 16*g**4 - g + 14*g**5 = 0.
-1, -1/2
Let n(v) be the first derivative of -8*v**4/5 - 16*v**3/3 - 17*v**2/5 - 4*v/5 - 28. Factor n(r).
-2*(r + 2)*(4*r + 1)**2/5
Let z(u) = -u**2 - 11*u - 8. Let o(m) = -2*m**2 - 2*m + 2. Let j be o(2). Let c be z(j). Solve -2/7*r**3 - 2/7*r**c + 2/7*r + 2/7 = 0 for r.
-1, 1
Factor 4/9*u - 2/9 - 2/9*u**2.
-2*(u - 1)**2/9
Find k, given that 0 + 9/2*k**3 + 3*k**4 + 6*k - 12*k**2 - 3/2*k**5 = 0.
-2, 0, 1, 2
Let x(m) = 15*m**3 + 12*m**2 + 11*m - 10. Let f(t) = -t**3 - t + 1. Let v(n) = 24*f(n) + 3*x(n). Factor v(b).
3*(b + 1)**2*(7*b - 2)
Factor 1/2*d**2 + 0 - 3/4*d + 1/4*d**3.
d*(d - 1)*(d + 3)/4
Factor -4*y**2 - y + 1 - 2*y - 5*y - 5.
-4*(y + 1)**2
Let p be (-24)/36*(-3)/12. Let -p*i**2 - 1/6*i + 1/6*i**3 + 1/6*i**4 + 0 = 0. Calculate i.
-1, 0, 1
Let b(y) be the first derivative of 7*y**6/2 - 3*y**5 - 69*y**4/4 + 29*y**3 - 6*y**2 - 12*y - 24. Factor b(z).
3*(z - 1)**3*(z + 2)*(7*z + 2)
Suppose 0 = -z - 5, x - 20 = 7*z - 3*z. Suppose 5*k = 3*b - 12, -2*b = 4*k - 3 - 5. Factor x*l**5 + 2*l - 4*l**4 + 4*l**2 - 2*l**5 + k*l.
-2*l*(l - 1)*(l + 1)**3
Let z be (12/8 + -2)*-4. Let w(b) be the first derivative of -2 - 1/6*b**6 + 1/5*b**5 + 0*b**3 + 0*b**z + 0*b**4 + 0*b. Factor w(f).
-f**4*(f - 1)
What is v in 2/19*v**2 + 32/19 - 16/19*v = 0?
4
Let m(l) be the second derivative of -l**6/150 + l**5/25 - l**4/15 - 12*l. Suppose m(v) = 0. What is v?
0, 2
Let x(p) be the second derivative of p**8/16800 - p**7/6300 - p**6/900 - p**4/2 + 9*p. Let z(v) be the third derivative of x(v). Let z(j) = 0. Calculate j.
-1, 0, 2
Let i(g) be the second derivative of -g**8/336 - g**7/105 + g**5/30 + g**4/24 + 3*g**2/2 - 3*g. Let p(o) be the first derivative of i(o). What is v in p(v) = 0?
-1, 0, 1
Let g be (3 - 8/3)*-9. Let y = g + 3. Factor 14 - k - 8 + 4*k + y*k - 3*k**2.
-3*(k - 2)*(k + 1)
Let i(p) be the second derivative of -p**6/195 + p**5/130 + p**4/39 + 6*p - 3. Solve i(y) = 0.
-1, 0, 2
Let u(y) be the first derivative of y**6/7 - 26*y**5/35 + 8*y**4/7 - 8*y**3/21 - 13. Factor u(j).
2*j**2*(j - 2)**2*(3*j - 1)/7
Factor 6*x + 2/5*x**3 + 14/5 + 18/5*x**2.
2*(x + 1)**2*(x + 7)/5
Factor -65*z**5 - 2*z**4 + 3*z**4 + 66*z**5.
z**4*(z + 1)
Let l(o) be the second derivative of -o**5/40 + o**3/12 + 7*o. Factor l(m).
-m*(m - 1)*(m + 1)/2
Let l(g) be the third derivative of 0*g - g**2 + 1/24*g**3 - 1/240*g**5 + 0 + 0*g**4. Let l(k) = 0. What is k?
-1, 1
Let s(l) be the third derivative of -l**6/96 + l**5/8 - 15*l**4/32 - 3*l**2. Factor s(m).
-5*m*(m - 3)**2/4
Suppose 0 = 153*f - 158*f. Factor 6/7*n**4 - 4/7*n**3 + 0*n**2 + 0*n + f - 2/7*n**5.
-2*n**3*(n - 2)*(n - 1)/7
Factor z**3 + 42 - 26 + 3*z**3 - 12*z**2.
4*(z - 2)**2*(z + 1)
Let l(n) = n**2 + 1. Let p(c) be the third derivative of c**6/40 - c**5/12 - c**4/8 - 5*c**3/6 + c**2. Let x(f) = -5*l(f) - p(f). Factor x(r).
-3*r*(r - 1)*(r + 1)
Let v(n) be the second derivative of n**7/42 - n**6/30 - n**5/10 + 4*n. Factor v(o).
o**3*(o - 2)*(o + 1)
Find b, given that -9/7*b**4 + 51/7*b**3 + 4*b + 0 + 80/7*b**2 = 0.
-2/3, 0, 7
Let c = 1/5 + 2/15. Let y(w) be the third derivative of 0*w - 2*w**2 + 0 + 1/30*w**5 + 1/6*w**4 + c*w**3. Find x such that y(x) = 0.
-1
Let o(y) be the third derivative of y**5/210 + y**4/84 - 2*y**3/2