. Let l = -2680 + f. Factor l - 24/5*z + 3/5*z**2.
3*(z - 4)**2/5
Let s = 2762 + -2760. Let n = 144 + -1006/7. Factor -4/7*z**s + n*z**3 - 8/7*z + 16/7.
2*(z - 2)**2*(z + 2)/7
Let u be (474/632)/((1/(-4))/(-1)). Determine k so that -4/5*k**u - 16/5*k**2 - 12/5*k + 0 = 0.
-3, -1, 0
Suppose f + 3*t = 17, -3*t = -f + 4*f - 27. Let y be 14/2 - (1 + 1). Find n, given that 3*n**f - 6*n**3 + y*n + 5*n**2 + 6 - 17*n**2 - 2*n + 6*n**4 = 0.
-2, -1, 1
Let v(h) = 8*h**3 - 10*h**2 - 10*h + 8. Let i(z) = -z**2 - z. Let d(j) = 2*i(j) + v(j). Factor d(l).
4*(l - 2)*(l + 1)*(2*l - 1)
Let p = 31/380 - 3/95. Let q(c) be the second derivative of 1/30*c**6 - 1/6*c**3 - 1/12*c**4 + p*c**5 + 0*c**2 - 4*c + 0. Find k, given that q(k) = 0.
-1, 0, 1
Let f(p) be the third derivative of -5*p**6/32 + 103*p**5/24 + 25*p**4/8 - 35*p**3/3 + 170*p**2 - 2. What is a in f(a) = 0?
-2/3, 2/5, 14
Suppose 0 = -0*b + 7*b - 28. Let y(k) = -2*k. Let c(w) = -w**2. Let d(g) = b*c(g) + 2*y(g). Find z such that d(z) = 0.
-1, 0
Factor -2*o**3 + 3/2*o + 0 - 1/2*o**2.
-o*(o + 1)*(4*o - 3)/2
Let m(s) = -s**2 - 2*s + 1. Let k(i) = 6*i**3 - 300*i**2 + 3332*i + 1166. Let w(o) = 2*k(o) - 28*m(o). Let w(b) = 0. What is b?
-1/3, 24
Let -22/5*q**3 + 0 - 22/5*q**2 + 6*q**4 + 18/5*q**5 - 4/5*q = 0. What is q?
-2, -1/3, 0, 1
Factor 7/3 - 2*f**3 - 1/9*f**4 - 62/9*f + 20/3*f**2.
-(f - 1)**3*(f + 21)/9
Let r be (-2)/6*(-138510)/1995. Factor r*k**4 - 156/7*k + 24/7 - 405/7*k**3 + 54*k**2.
3*(2*k - 1)*(3*k - 2)**3/7
Let v = 2/6851 - -6843/27404. Solve -3/4 + 1/2*n + v*n**2 = 0 for n.
-3, 1
Find c, given that -51/7*c - 14 - 1/7*c**2 = 0.
-49, -2
Let b(l) be the second derivative of l**8/560 - 3*l**7/280 + l**6/60 - 7*l**3/3 + 4*l. Let h(y) be the second derivative of b(y). Find d such that h(d) = 0.
0, 1, 2
Suppose 11 = 5*y + 31. Let l be (-2)/(y/(-12)*-2). Factor 2/3*s**l + 0 + 2/3*s + 4/3*s**2.
2*s*(s + 1)**2/3
Let g(y) be the third derivative of y**7/70 + 2*y**6/5 + 21*y**5/10 + 5*y**4 + 13*y**3/2 + 106*y**2. Solve g(u) = 0 for u.
-13, -1
Factor 84*a + 14 + 3*a**2 - 4 - 37 - 61 + 1.
3*(a - 1)*(a + 29)
Let j be (0/(-20))/((-2)/(-3)*3). Let z(u) be the second derivative of 0*u**3 + 0*u**5 - u**2 + 1/3*u**4 - 9*u + j - 1/15*u**6. Find x, given that z(x) = 0.
-1, 1
Let q(b) be the first derivative of b**4/16 - 7*b**3/6 + 3*b**2 - 10. Suppose q(h) = 0. What is h?
0, 2, 12
Let f(v) be the first derivative of 2*v**6/3 + 48*v**5/5 + 29*v**4 + 24*v**3 + 287. Factor f(y).
4*y**2*(y + 1)*(y + 2)*(y + 9)
Factor -6*p + 5*p**2 - 7*p + 32 + 28 - 27*p.
5*(p - 6)*(p - 2)
Suppose 2*x + 10 = 4*n, 4*x + 3*n + 3 - 27 = 0. Factor 5*g - g**x - g**2 - 3*g + 0*g**3.
-g*(g - 1)*(g + 2)
Let i = -335 - -340. Let j(z) be the third derivative of 0 - 1/42*z**4 + 1/70*z**i + 0*z + 0*z**3 + 5*z**2. Factor j(l).
2*l*(3*l - 2)/7
Let s = -267 - -267. Let d(c) be the second derivative of -4/105*c**6 + 3*c + 0*c**3 + 0*c**2 - 1/42*c**4 - 1/14*c**5 + s. Factor d(n).
-2*n**2*(n + 1)*(4*n + 1)/7
Let t(z) = -3*z + 124. Let w be t(38). Let l(k) be the first derivative of -25/3*k**3 + 15*k - w*k**2 - 5 + 5/2*k**4. Factor l(p).
5*(p - 3)*(p + 1)*(2*p - 1)
Let f(u) = -13*u**4 - 76*u**3 + 103*u**2 - 7*u. Let p(c) = 6*c**4 + 39*c**3 - 51*c**2 + 3*c. Let y(v) = 3*f(v) + 7*p(v). What is b in y(b) = 0?
-16, 0, 1
Factor -5*m**3 + 8*m**2 + 2*m - 2 + 6*m**2 - 12*m + 3*m.
-(m - 2)*(m - 1)*(5*m + 1)
Let s(a) = -a**2 + 2. Let n be s(0). Suppose 4*z = 2*c + 6, -4*c = -z + 3*z - 8. Factor 4 + 163*y**n + 28*y + 0 - 155*y**z + 8.
4*(y + 3)*(2*y + 1)
Let t = -70/93 + 583/651. Factor 4/7 + 3/7*n - t*n**2.
-(n - 4)*(n + 1)/7
Let k(i) be the second derivative of 5*i**2 + 4 - 5/4*i**5 + 1/6*i**6 - 35/6*i**3 + 15/4*i**4 + i. What is r in k(r) = 0?
1, 2
Let b = 24325 - 218903/9. Factor -b*q + 2/9*q**2 + 0.
2*q*(q - 11)/9
Determine j so that -35*j**3 + 3*j**3 + 10*j**2 - 17*j**2 - 13*j**2 - 23*j**3 + 5*j**4 + 220*j = 0.
-2, 0, 2, 11
Let g(r) = 5*r**2 - 7*r - 4. Let p(m) = 11*m**2 - 15*m - 9. Let b(s) = s + 4. Let o be b(-17). Let x(z) = o*g(z) + 6*p(z). Let x(w) = 0. Calculate w.
-2, 1
Suppose 4*s - 2*j = 2, 0 = -3*s + j - 79 + 82. Let r(x) be the first derivative of x**s + 4 + 0*x + 2/3*x**3. Factor r(y).
2*y*(y + 1)
Let k = -1/119 + 52/119. Factor 0*f - k + 3/7*f**2.
3*(f - 1)*(f + 1)/7
Let d(p) be the first derivative of -3*p**4/4 + 5*p**3 + 123*p**2/2 - 135*p - 276. Factor d(s).
-3*(s - 9)*(s - 1)*(s + 5)
Let m(l) be the second derivative of l**4/24 + 26*l**3/3 + 676*l**2 + 2*l + 10. Factor m(x).
(x + 52)**2/2
Let d = -51 + 54. Find b, given that -3 - 27*b**4 + 0*b**5 - 6*b**d + 0*b**4 + 19*b**5 + 30*b**2 - 9*b - 4*b**5 = 0.
-1, -1/5, 1
Suppose -2 - 16 = -6*r. Let v = 10 - 10. Solve -3 - 1 + 5*b**2 + b - r*b**4 + 2 - b**3 + v*b**4 = 0 for b.
-1, 2/3, 1
Let g(b) be the third derivative of b**6/200 + 21*b**5/50 + 441*b**4/40 + 4*b**2. Find r, given that g(r) = 0.
-21, 0
Suppose 0 = -4*k + 5*i + 18, -12*i + 8*i - 8 = 0. Suppose 0 + 2/5*p**3 + 4/5*p - 6/5*p**k = 0. Calculate p.
0, 1, 2
Let f be ((-1)/2)/((-22)/(6336/60)). Suppose -4/5*t**4 - 4*t**3 - f*t**2 + 0*t + 4/5*t**5 + 0 = 0. What is t?
-1, 0, 3
Let c(q) be the first derivative of q**6/10 + 33*q**5/20 + 27*q**4/4 + 25*q**3/2 + 12*q**2 - 31*q - 27. Let u(i) be the first derivative of c(i). Factor u(x).
3*(x + 1)**3*(x + 8)
Let n(r) = -r - 1. Let m be 2/(-5)*(-9 - -4). Let w(f) = 3 + 30*f - 5 + 21 + 3*f**m + 8. Let l(u) = -18*n(u) - w(u). Factor l(g).
-3*(g + 1)*(g + 3)
Suppose 3*a - 2 = -4*w, -297*w + 294*w + 3*a = -12. Find z such that 3 + 3/4*z**w + 9/4*z**3 - 6*z = 0.
-2, 2/3, 1
Let a(b) be the second derivative of 5*b**7/42 - b**6/6 - 3*b**5/4 + 25*b**4/12 - 5*b**3/3 - 129*b. Factor a(h).
5*h*(h - 1)**3*(h + 2)
Let l(y) = y**4 - 2*y**2 + 4*y + 5. Let j(n) = -n**3 - n**2 - n - 1. Let u(g) = -2*j(g) - l(g). Find x such that u(x) = 0.
-1, 1, 3
Let a(c) be the first derivative of c**4/4 - 2*c**3 + 6*c**2 - 18*c + 14. Let b(g) be the first derivative of a(g). Solve b(x) = 0.
2
Suppose -m - 2*a - 20 = 0, -4*m - m - 90 = 5*a. Let l be m/(-18)*((-3)/(-4))/1. Suppose -l*x**2 + 8/3*x - 8/3 = 0. What is x?
2
Let l(w) be the first derivative of w**5/20 - 37*w**4/16 - 13*w**3/4 + 37*w**2/8 + 19*w/2 + 65. Suppose l(g) = 0. What is g?
-1, 1, 38
Suppose -1 = -k - 0*k. Suppose k = 4*o - 11. What is l in -2*l**2 - 3 + o - 4*l - 2 = 0?
-1
Let z(p) be the first derivative of 5*p**4/12 - 95*p**3/9 + 200*p**2/3 + 500*p/3 - 223. What is b in z(b) = 0?
-1, 10
Let a = -2940 - -2943. Suppose -18/13*i**4 + 16/13*i**2 - 4/13*i**a + 12/13*i + 2/13 - 8/13*i**5 = 0. What is i?
-1, -1/4, 1
Let b(z) = -26*z**2 + 71*z - 20. Let r(a) = -6*a**2 + 17*a - 5. Let i(u) = 2*b(u) - 9*r(u). Factor i(m).
(m - 5)*(2*m - 1)
Let q(y) be the first derivative of -1/12*y**3 + 1/2*y - 1/8*y**2 + 6. Determine x so that q(x) = 0.
-2, 1
Let q(n) be the first derivative of 3/5*n + 2/5*n**3 - 1/25*n**5 + 0*n**4 - 38 + 4/5*n**2. Find m such that q(m) = 0.
-1, 3
Let i(j) be the second derivative of -j**4/24 - 5*j**3/6 - 21*j**2/4 + 54*j. Find k, given that i(k) = 0.
-7, -3
Suppose 2*j - 4*u - 122 = 0, -u + 6*u + 295 = 5*j. Let n = -57 + j. Factor n*f + 0 + 0*f**3 + 4/3*f**4 + 0*f**2 + 2/3*f**5.
2*f**4*(f + 2)/3
Let h = 35 - 36. Let t be (h + 1)/(3*5/(-15)). Factor -2/9*w**2 + t - 10/9*w**3 + 0*w - 8/9*w**4.
-2*w**2*(w + 1)*(4*w + 1)/9
Let v(y) be the first derivative of -y**5 - y**4/2 - y**3/15 - 251. Factor v(p).
-p**2*(5*p + 1)**2/5
Let -3/5*j**2 + 9/5*j - 3/5*j**4 + 6/5 - 9/5*j**3 = 0. What is j?
-2, -1, 1
Suppose -8*q + 7*q = 0. Suppose -5*z + 25 = -5*v - q*v, 4*z + v = 15. Let z*g**2 - 3*g + g**2 - 2*g**2 = 0. Calculate g.
0, 1
Let j = -244 + 246. Let g(u) be the first derivative of -4 + 1/5*u**3 - 1/10*u**j + 1/20*u**4 - 3/25*u**5 + 0*u. Factor g(h).
-h*(h - 1)*(h + 1)*(3*h - 1)/5
Let t(j) be the third derivative of j**7/5040 - j**6/1440 + 11*j**4/12 - 24*j**2. Let v(z) be the second derivative of t(z). Factor v(r).
r*(r - 1)/2
Let o(t) be the second derivative of -t**5/5 - 2*t**4/3 + 10*t**3/3 + 12*t**2 + 548*t + 2. Let o(x) = 0. What is x?
-3, -1, 2
Let j(i) = -18*i**2 + 32*i - 59. Let r(a) = 21*a**2 - 33*a + 60. Let w(l) = 6*j(l) + 5*r(l). Let w(x) = 0. What is x?
3, 6
Let l(g) be the first derivative of 4*g**5/35 + 3*g**4/14 - 2*g**3/21 - 3*g**2/7 - 2*g/7