-3*u + 20 = n, 3*u - n = 3*n + 25. Let y(b) = b**2 - 6*b - 5. Let f be y(u). Solve 0 + 2/7*d**f + 2/7*d**3 + 0*d = 0 for d.
-1, 0
Let z(o) be the first derivative of -3*o**4/4 + 2. Factor z(p).
-3*p**3
Let n = -13 - -21. Let q = n + -5. Factor 7*p**2 - p**2 + 0*p**2 - q*p + 3*p**3 - 6*p**3.
-3*p*(p - 1)**2
Factor 5/7*a**3 + 2/7*a + 0 - a**2.
a*(a - 1)*(5*a - 2)/7
Let u(b) be the first derivative of 2*b**6/3 - 4*b**5/5 - b**4 + 4*b**3/3 - 21. Let u(s) = 0. Calculate s.
-1, 0, 1
Let u(r) = 8*r**3 - 14*r**2 + 6*r + 5. Let t(b) = -b**3 + b**2 - 1. Let n(c) = 5*t(c) + u(c). Factor n(f).
3*f*(f - 2)*(f - 1)
Let g = -9 - -11. Let k be g/(-5) + 96/90. What is r in -1/3*r**2 + 1/3*r + k = 0?
-1, 2
Let w be 16/(16/(-4)) + (7 - 0). Determine j so that 1/4 + 3/4*j + 1/4*j**w + 3/4*j**2 = 0.
-1
Let j(u) be the third derivative of -u**9/241920 - u**8/80640 - u**5/60 - 7*u**2. Let l(z) be the third derivative of j(z). Factor l(o).
-o**2*(o + 1)/4
Let b(p) be the second derivative of -p**6/30 + 3*p**5/20 - p**4/4 + p**3/6 - 2*p. Solve b(m) = 0 for m.
0, 1
Let w be 9/15*(-2)/(-3). Let t = -22/13 + 162/65. Let w*o**2 + 0 + t*o = 0. What is o?
-2, 0
Let u(j) be the first derivative of -3*j**5/35 - 3*j**4/28 + 2*j**3/7 - 8. Factor u(a).
-3*a**2*(a - 1)*(a + 2)/7
Let u(a) be the first derivative of a**4/5 + 4*a**3/15 - 2*a**2/5 - 4*a/5 + 9. Find k such that u(k) = 0.
-1, 1
Let 2*t**2 - t + 5 + 9 + 7*t + 10*t = 0. Calculate t.
-7, -1
Factor -1/6*a**3 - 4/3*a - 5/6*a**2 - 2/3.
-(a + 1)*(a + 2)**2/6
Let t(f) be the third derivative of -f**7/490 - f**6/140 + f**5/140 + f**4/28 - 5*f**2. Determine m, given that t(m) = 0.
-2, -1, 0, 1
Let s be (4/11)/(190/209). Determine n, given that s*n**2 + 0 + 6/5*n = 0.
-3, 0
Suppose 0 = 2*f + 4*u + 26, -5*f = 5*u + 35 + 5. Let k be (0 - f)*81/36. Factor -9/2*l - 3/4*l**2 - k.
-3*(l + 3)**2/4
Let b(l) be the third derivative of -l**8/1848 + l**7/231 - l**6/165 - 8*l**5/165 + 8*l**4/33 - 16*l**3/33 - 3*l**2. Find x, given that b(x) = 0.
-2, 1, 2
Let l(y) = 23*y - y**2 + 0*y**3 - y**3 + 0*y**3 + 30*y**2. Let r(m) = -10*m**2 - 8*m. Let o(f) = 6*l(f) + 17*r(f). Factor o(h).
-2*h*(h - 1)*(3*h + 1)
Suppose 0 = -2*u + 3 + 1. Let x(r) = 5*r - 7. Let z be x(u). What is i in 2/7*i**2 + 6/7*i**4 + 0 - 8/7*i**z + 0*i = 0?
0, 1/3, 1
Suppose 3*g**5 - 2*g**3 + 3*g**3 - 2*g**4 - 4*g**5 + 2*g**2 = 0. Calculate g.
-2, -1, 0, 1
Let k(w) be the second derivative of w**5/20 - w**4/24 + w**2/2 - 3*w. Let u(n) be the first derivative of k(n). Suppose u(i) = 0. Calculate i.
0, 1/3
Suppose 0 = -4*j + 16, 6*y = 2*y + j + 20. Suppose 0 = 3*b - y*b + 6. Factor -2/7*u**b + 0*u - 2/7*u**3 + 0.
-2*u**2*(u + 1)/7
Let l(o) = -2*o**3 + 0*o**3 + 144*o**2 - o**3 + 511 + 576*o + 272. Let s(i) = i**3 - 36*i**2 - 144*i - 196. Let z(b) = -4*l(b) - 15*s(b). Factor z(t).
-3*(t + 4)**3
Let d be (-22)/24*(-45)/(-51). Let g = d - -18/17. Factor -1/4*p**2 - g - 1/2*p.
-(p + 1)**2/4
Let z(p) = p**3 + 13*p**2 - 9*p. Let q(a) = 2*a**3 + 20*a**2 - 14*a. Let o = -7 - -12. Let g be (-2 - 0)/((-1)/(-4)). Let j(h) = g*z(h) + o*q(h). Factor j(v).
2*v*(v - 1)**2
Suppose -3 = -3*c + 2*c. Let 9/2*m**4 + 0*m + 0*m**2 - m**c + 0 = 0. Calculate m.
0, 2/9
Let i(d) = -d**3 - d**2 + 1. Let n(o) = -o**2 - 2*o + 7*o + 7*o**2 - 4 - 7*o - 2*o**4 + 6*o**3. Let z(g) = 4*i(g) + n(g). Factor z(q).
-2*q*(q - 1)**2*(q + 1)
Let x = 29 + -17. Let k be (4/9)/(8/x). Suppose -2/3*p**3 + 2/3 + k*p - 2/3*p**2 = 0. Calculate p.
-1, 1
Let b(q) be the third derivative of -q**5/360 + q**4/8 - 9*q**3/4 + 19*q**2. Find s such that b(s) = 0.
9
Factor 4/5*o + 14/5*o**2 + 0.
2*o*(7*o + 2)/5
Let d(v) = v**3 + v**2 - v + 1. Let n(y) = 78*y**3 + 33*y**2 + 3. Let m(c) = 3*d(c) - n(c). Let m(l) = 0. What is l?
-1/5, 0
Let p = 67/219 - -2/73. Factor -1/3*h**2 - 2/3*h - p.
-(h + 1)**2/3
Factor -5*v**2 + 0*v**2 - v**2 + 3*v - 3*v**3 + 6.
-3*(v - 1)*(v + 1)*(v + 2)
Let y be -3 + 10 + (-38)/6. Factor -1/3*j**2 + y*j - 1/3.
-(j - 1)**2/3
Let n be (-31)/14 - 320/(-128). Solve 6/7*r**3 - 2/7 + 10/7*r**2 + n*r = 0 for r.
-1, 1/3
Suppose -k - k + 3*u = 11, -3*k - 2*u - 23 = 0. Let a(o) = 3*o + 21. Let q be a(k). Solve 0*w**2 + q*w + 0 + 2/11*w**3 = 0 for w.
0
Let z(x) = -5*x**2 + 3*x**2 + x**2 - 8*x. Let r be z(-8). Solve -2/3*i**3 + 4/3*i**2 - 2/3*i + r = 0 for i.
0, 1
Let t be (-2)/6*(8 - 7)*-1. Let n(d) be the third derivative of -t*d**4 + 0 + 4/3*d**3 - 2*d**2 + 0*d + 1/30*d**5. Factor n(y).
2*(y - 2)**2
Let b(y) = -15*y**2 - 290*y + 280. Let z(g) = 2*g**2 + 36*g - 35. Let c(a) = 3*b(a) + 25*z(a). Find i such that c(i) = 0.
-7, 1
Suppose 0 = 4*p + 3 - 15. What is t in p*t**5 + t**5 + 3*t**3 + 12*t**2 - 12*t**4 - 6*t**3 - t**3 = 0?
-1, 0, 1, 3
Let v(j) = -j**3 - 3*j**2 - 2*j - 4. Let b be v(-3). Suppose -2*z = 118 - 118. Determine d, given that -1/3*d**b + z*d + 0 = 0.
0
Let j = -3 - -5. Factor a**2 + a + a**4 - 2*a - j*a**2 + a**3.
a*(a - 1)*(a + 1)**2
Suppose 2*h - 6 = -h - r, 2*r + 8 = 4*h. Suppose 0 + 0*t**4 + 0*t**h + 2/9*t - 4/9*t**3 + 2/9*t**5 = 0. What is t?
-1, 0, 1
Factor 0 - 4/11*n**4 + 1/11*n**5 - 2/11*n**2 + 0*n + 5/11*n**3.
n**2*(n - 2)*(n - 1)**2/11
Find n such that -1/6*n**3 + 1/3*n + 1/6*n**2 + 0 = 0.
-1, 0, 2
Let m be (-301)/(-63) + (-6)/(-27). Determine c, given that -22*c + 0*c**2 + 4*c**2 - m - 3 + 18*c = 0.
-1, 2
Suppose 4*r - 3*z - 74 = 0, -3*r - 2*z = -r - 30. Determine c so that 3*c**5 - 3*c**3 - c**2 + 14*c**4 - r*c**4 + 4*c**2 = 0.
-1, 0, 1
Let z(u) be the first derivative of -3*u**4/14 - 6*u**3/7 + 21. Find h, given that z(h) = 0.
-3, 0
Let y(x) be the first derivative of 2*x**3/3 + 2*x**2/3 + 2*x/9 + 6. Let y(b) = 0. Calculate b.
-1/3
Let y be (-15990)/(-252) - 4/6. Let r = y + -125/2. Factor 0*g**2 + 6/7*g + 4/7 - r*g**3.
-2*(g - 2)*(g + 1)**2/7
Let f(w) be the second derivative of 2*w + 2/5*w**2 - 1/100*w**5 - 4/15*w**3 + 1/12*w**4 + 0. Factor f(g).
-(g - 2)**2*(g - 1)/5
What is f in -5*f**2 + 32*f + 37*f - 74*f = 0?
-1, 0
Let b(w) be the third derivative of w**7/490 + w**6/280 + 35*w**2. Factor b(x).
3*x**3*(x + 1)/7
Let u(b) = -3*b**3 - 2*b**3 + 3 + b - 2 - b**2. Let v be u(-1). Factor -i**4 + 2*i**2 - 4*i**v - i + 3*i**4 + i**3.
-i*(i - 1)*(i + 1)*(2*i - 1)
Let w(h) be the first derivative of -1/12*h**3 + 3/8*h**2 - 1/2*h - 3. Suppose w(t) = 0. Calculate t.
1, 2
Factor -2*d + 0 + 1/2*d**2.
d*(d - 4)/2
Let y = -775 + 775. Solve 1/2*f**4 + 0 + 1/2*f**2 + y*f - f**3 = 0 for f.
0, 1
Let m(y) be the third derivative of -y**8/2688 + y**7/840 + y**6/320 - y**5/120 - y**4/48 - 14*y**2. Determine h so that m(h) = 0.
-1, 0, 2
Find x such that 7/2*x**3 + x + 9/2*x**2 + 0 = 0.
-1, -2/7, 0
Let y(f) = -2*f**3 - 5*f**2 + 2*f + 1. Let q be y(-3). Let g(v) be the first derivative of -2/3*v**3 + 0*v + 0*v**2 + 1/4*v**q + 3. Find x, given that g(x) = 0.
0, 2
Let o(q) be the second derivative of -q**8/33600 + q**7/4200 - q**6/1800 - q**4/6 + 2*q. Let s(c) be the third derivative of o(c). Factor s(h).
-h*(h - 2)*(h - 1)/5
Let r(s) = 6*s**5 - 4*s**4 + 2*s**3 - 4*s**2 + 8. Let m(t) = -t**5 + t**2 - 1. Let v(f) = -8*m(f) - r(f). Factor v(p).
2*p**2*(p - 1)*(p + 1)*(p + 2)
Let p(a) be the third derivative of a**8/84 + 2*a**7/21 + 3*a**6/10 + 7*a**5/15 + a**4/3 - 13*a**2. Factor p(h).
4*h*(h + 1)**3*(h + 2)
Let b(k) be the first derivative of -k**3/18 - k**2/6 - 29. Factor b(h).
-h*(h + 2)/6
Let i(p) be the third derivative of -125*p**8/336 - 355*p**7/42 - 1579*p**6/24 - 1685*p**5/12 + 1375*p**4/3 - 1250*p**3/3 + 54*p**2. Factor i(q).
-5*(q + 5)**3*(5*q - 2)**2
Let p(z) = -9*z**2 - 16*z + 7. Let h(i) = -1. Let g(x) = 3*h(x) + p(x). Solve g(u) = 0.
-2, 2/9
Let g be 2/8 + (-7)/(-4). Let d be (-1 - g)*1*-1. Factor -2*i**2 + d*i**3 + 4*i + 2*i**2 + 8*i**2.
i*(i + 2)*(3*i + 2)
Let u(r) = 72*r - 4. Let f be u(2). Let b(p) be the first derivative of 44*p**2 + 346/3*p**3 - 2 + f*p**4 + 294/5*p**5 + 8*p. Determine s so that b(s) = 0.
-1, -1/3, -2/7
Let p be 3/1*(-5 + 6). Let 12*t**2 - 6 - 11 - 4*t**4 + 2*t**p - 16*t + 6*t**3 + 1 = 0. What is t?
-1, 2
Suppose 0 = -3*x - 4*x + 42. Let c(v) be the first derivative of 0*v**4 + 0*v - 2 - 2/45*v**5 + 0*v**2 + 0*v**3 - 1/27*v**x. Factor c(f).
-2*f**4*(f + 1)/9
Factor 2/5*q**2 + 0*q - 8/5.
2*(q - 2)*(q + 2)/5
Let g(y) be the third derivative of y**7/735 + y**6/210 - y**5/210 - y**4/42 