5*c - 16 - c**t - 4*c.
-(c - 4)**2
Let v(m) be the second derivative of -1/24*m**4 - 5*m + 1/2*m**3 - 9/4*m**2 + 0. Factor v(g).
-(g - 3)**2/2
Let a(w) = 2*w**2 - 18*w + 34. Let r(l) = 3*l**2 - 17*l + 35. Let d(q) = -7*a(q) + 6*r(q). Factor d(x).
4*(x - 1)*(x + 7)
Factor -2/3*s - 5/6*s**4 + 7/6*s**3 + 0 + 4/3*s**2.
-s*(s - 2)*(s + 1)*(5*s - 2)/6
Let w(j) be the third derivative of -1/84*j**4 + 1/30*j**5 + 0*j**3 + 13/735*j**7 - 14*j**2 - 1/28*j**6 + 0 + 0*j - 1/294*j**8. Factor w(s).
-2*s*(s - 1)**3*(4*s - 1)/7
Let y(o) = o**2 + 6*o - 13. Let a be y(-8). Let s(k) be the first derivative of 1/6*k**a - 1/2*k + 1/4*k**2 + 3 - 1/8*k**4. Solve s(d) = 0.
-1, 1
Let c(g) = g**3 + g**2 - 4*g + 10. Let l be c(-3). Suppose 25 = -l*s + 5*w, -25 = -4*w - w. Let 3/5*i**2 + 3/5*i**3 + 0*i + s = 0. Calculate i.
-1, 0
Let i(d) = -d**4 - d**3 - d**2 + d - 1. Let t(r) = 5*r**4 + 3*r**3 + r**2 - 3*r + 6. Let o(u) = 12*i(u) + 3*t(u). Find n such that o(n) = 0.
-1, 1, 2
Let u(i) be the third derivative of i**8/1512 + i**7/105 + 7*i**6/180 + 19*i**5/270 + i**4/18 + 2*i**2 - 9*i. Factor u(a).
2*a*(a + 1)**3*(a + 6)/9
Let q be (-5 - 0) + (-50173)/(-8809). Factor 32/23 + 2/23*k**2 - q*k.
2*(k - 4)**2/23
Let h(k) = 5*k**3 + 15*k**2 - 11*k. Let i(p) = -2*p**3 - 6*p**2 + 5*p. Let f(t) = 3*h(t) + 7*i(t). Solve f(c) = 0.
-2, -1, 0
Let k be (1 + -3)/(12/(-18)). What is i in -5*i**2 + i**4 - 3*i**5 + 5*i**4 - 3*i**k + 5*i**2 = 0?
0, 1
Suppose -27/7*r**4 + 6*r**3 - 75/7 + 3/7*r**5 + 102/7*r**2 - 45/7*r = 0. What is r?
-1, 1, 5
Let l(g) = -4*g**3 + 100*g - 216. Let y(x) = -4*x**3 + 98*x - 216. Let r(w) = -5*l(w) + 4*y(w). Factor r(b).
4*(b - 3)**2*(b + 6)
Let o = -75 - -90. Suppose d = -3*y - 10, o = -0*y - 3*y. Factor 126*i**3 - 147/5*i**4 + 24/5*i - 228/5*i**2 + 0 - 1029/5*i**d.
-3*i*(i + 1)*(7*i - 2)**3/5
Let q be 0/(1*(4 - 3)). Suppose q = 5*n - 39 - 1. Factor 2*k**4 + 8*k**3 - n*k**3 - 2*k**2.
2*k**2*(k - 1)*(k + 1)
Determine o so that -9/5*o - 6 + 3/5*o**2 = 0.
-2, 5
Let q(i) be the second derivative of 3*i**5/20 + 15*i**4 + 600*i**3 + 12000*i**2 + 74*i. Factor q(v).
3*(v + 20)**3
Suppose -22*w = -25*w + 6. Let r = 4 - 1. Factor 3*y**2 + 2 + 2*y - y**w - 3*y - r*y**2.
-(y - 1)*(y + 2)
Let x(q) be the second derivative of -q**3/6 - 8*q**2 + 4*q. Let h be x(-17). Factor -5*y + 0 - h + 5*y**2 + 1.
5*y*(y - 1)
Factor -3*r**4 + 3/4*r**5 + 3/2 - 15/4*r + 3*r**3 + 3/2*r**2.
3*(r - 2)*(r - 1)**3*(r + 1)/4
Let f(y) be the first derivative of -y**5/140 + y**3/42 - 16*y + 7. Let t(d) be the first derivative of f(d). Factor t(n).
-n*(n - 1)*(n + 1)/7
Let f(o) = -4 + 6*o**3 + 6*o**2 + 6 + 2 - 16*o + 24*o. Let l(r) = 5*r**3 + 6*r**2 + 7*r + 3. Let g(z) = -3*f(z) + 4*l(z). Determine m, given that g(m) = 0.
-2, -1, 0
Let q(p) = p**3 - p**2 - 3*p - 3. Let b(d) be the first derivative of d**2/2 - 24. Let r(t) = 10*b(t) - 5*q(t). What is c in r(c) = 0?
-1, 3
Let u(o) be the third derivative of 5*o**8/672 + 17*o**7/840 + o**6/160 - o**5/48 - o**4/96 + 137*o**2 + 1. Find b such that u(b) = 0.
-1, -1/5, 0, 1/2
Let n = 1078 - 3230/3. Suppose -8/3*p**2 - n*p + 4/3*p**3 + 8/3 = 0. Calculate p.
-1, 1, 2
Let t(m) be the second derivative of m**6/10 + 9*m**5/10 - 12*m**4 + 37*m**3 - 99*m**2/2 + 37*m. Factor t(q).
3*(q - 3)*(q - 1)**2*(q + 11)
Factor 801/2*f**2 + 2114907/2 - 71289/2*f - 3/2*f**3.
-3*(f - 89)**3/2
Let t(j) be the first derivative of j**5/35 - j**4/14 - 4*j**3/7 - j**2 - 5*j/7 - 688. Determine x so that t(x) = 0.
-1, 5
Let g(n) be the first derivative of n**5/60 - 11*n**4/12 + 121*n**3/6 - 12*n**2 + 38. Let u(v) be the second derivative of g(v). Factor u(d).
(d - 11)**2
Suppose 67*p - 82*p = -60. Let n(b) be the second derivative of 2*b**3 + 9/4*b**2 - 1/20*b**6 + 0*b**5 - 5*b + 0 + 3/4*b**p. Find q, given that n(q) = 0.
-1, 3
Let v = -2503 - -2506. Let m(p) be the second derivative of 0*p**2 + 0 + 1/3*p**v - 6*p + 1/6*p**4. Suppose m(d) = 0. What is d?
-1, 0
Suppose 4*w = 5*k - 2, 3*k + 0 = 5*w - 4. Factor 160*m**3 + 64*m**4 + 40*m + 1 - 4*m**k + 3 + 136*m**2.
4*(m + 1)**2*(4*m + 1)**2
Find l, given that -48*l**2 - 3*l**3 - l**4 + 42*l**2 + 0*l**3 - 2*l**3 = 0.
-3, -2, 0
Suppose -3*h + 14 + 13 = 2*y, -y = 2*h - 15. Factor 5*c**4 + c**3 - 7*c**3 - 5*c**2 + 5*c**5 + 12*c - y*c**3 - 2*c.
5*c*(c - 1)**2*(c + 1)*(c + 2)
Suppose 4*k + 35 = 11*k. Suppose 2*n - r = 0, 3*n - 5 = -3*r + 13. Find g such that 2/3*g**4 + 1/3*g - 2/3*g**n + 0 - 1/3*g**k + 0*g**3 = 0.
-1, 0, 1
Let s(v) be the first derivative of 4*v**6 - 228*v**5/5 + 345*v**4/2 - 241*v**3 + 156*v**2 - 48*v + 51. Factor s(h).
3*(h - 4)**2*(2*h - 1)**3
Let c(p) = 19*p**3 + 134*p**2 + 286*p + 136. Let r(v) = -8*v**3 - 68*v**2 - 142*v - 68. Let f(b) = -2*c(b) - 5*r(b). Determine j, given that f(j) = 0.
-34, -1
Let i(r) = 2*r - r + 3*r. Let h be i(8). Find p such that 6*p**3 - p**3 + h*p**2 + 28*p + 5*p**3 + 8 + 2*p**3 = 0.
-1, -2/3
Let t(l) be the third derivative of -1/24*l**3 + 5/96*l**4 + 0*l - 1/96*l**6 + 0 + 1/240*l**5 + 20*l**2. Suppose t(i) = 0. What is i?
-1, 1/5, 1
Let m(t) = -34*t**4 - 8*t**3 + 4*t - 4. Let u(h) = 2*h**5 + h - 1. Let c(g) = m(g) - 4*u(g). Factor c(l).
-2*l**3*(l + 4)*(4*l + 1)
Let o be 116/110 + (-16)/(-40). Let l = -498 + 501. Let -o*u - 2/11*u**l + 8/11 + 10/11*u**2 = 0. What is u?
1, 2
Let y(a) be the first derivative of 4*a**3/9 - 28*a**2/3 + 128. Factor y(u).
4*u*(u - 14)/3
Let j(y) be the first derivative of -y**5 + 15*y**4/2 - 55*y**3/3 + 15*y**2 - 119. Suppose j(u) = 0. What is u?
0, 1, 2, 3
Let t(g) be the first derivative of -4/5*g**2 - g - 2/25*g**5 + 11 - 4/5*g**3 + 1/2*g**4. Let f(m) be the first derivative of t(m). Factor f(r).
-2*(r - 2)**2*(4*r + 1)/5
Let n(j) be the second derivative of -j**7/147 - 2*j**6/35 - 4*j**5/35 + j**4/7 + 3*j**3/7 - 53*j. Solve n(y) = 0 for y.
-3, -1, 0, 1
Let m(y) be the first derivative of -9*y**4/14 + 40*y**3/7 + 3*y**2 - 210. Factor m(s).
-6*s*(s - 7)*(3*s + 1)/7
Let t(g) be the third derivative of g**7/105 - 17*g**6/60 + 8*g**5/3 - 16*g**4/3 - 2*g**2 + 149. Solve t(j) = 0 for j.
0, 1, 8
Factor -69/5*t**4 + 0 + 3/5*t**5 + 96*t**3 + 0*t - 180*t**2.
3*t**2*(t - 10)**2*(t - 3)/5
Let l(i) = -18*i**2 + 18*i - 24. Let j(m) = -m**2 + 15*m + 15. Let d be j(16). Let c(o) = o**2 + o. Let y(s) = d*l(s) - 10*c(s). Factor y(k).
4*(k - 2)*(2*k - 3)
Solve 23/2*o**4 + 74*o**2 + 0 - 49*o**3 - 1/2*o**5 - 36*o = 0.
0, 1, 2, 18
Factor -2/9*u**2 + 2/9*u**4 + 26/3*u + 0 - 26/3*u**3.
2*u*(u - 39)*(u - 1)*(u + 1)/9
Let g(w) be the second derivative of w**7/42 - 2*w**6/5 + 9*w**5/5 - 791*w. Find l, given that g(l) = 0.
0, 6
Suppose 0 = 4*c + 2*n - 24, 4*n - 21 + 8 = -c. Let q(j) be the first derivative of 0*j**3 - 1/6*j**6 - 6 - 1/2*j**2 + 0*j + 1/2*j**4 + 0*j**c. Factor q(d).
-d*(d - 1)**2*(d + 1)**2
Suppose -14 = -c + 1. Factor 11*f - c*f**2 - 26*f - 8 - 5*f**3 + 3.
-5*(f + 1)**3
Let f be (-2)/(0 + -8 - 0). Let -h - h**3 + 3/2*h**2 + f + 1/4*h**4 = 0. What is h?
1
Suppose 46*x = 43*x. Let v(l) be the second derivative of 2*l + 1/4*l**4 + 0 + 1/3*l**3 - 1/30*l**6 + 0*l**5 + x*l**2. Suppose v(f) = 0. What is f?
-1, 0, 2
Let g(w) be the third derivative of 1/60*w**6 + 0*w**5 - 1/210*w**7 - 19*w**2 + 0*w**4 - 1/336*w**8 + 0*w + 0*w**3 + 0. Suppose g(t) = 0. What is t?
-2, 0, 1
Suppose 0 = -2*a - 4*s + s + 8, -3*s = 0. Let f be a + 2 - (4 - 0). Determine y, given that -2*y**2 + 4*y**2 + y - 5*y**f + 4*y**2 = 0.
-1, 0
Let x(k) = -k**3 - 2*k**2. Let c(o) = -3*o**4 + 6*o**3 - 6*o**2. Let v(d) = -c(d) + 3*x(d). Factor v(h).
3*h**3*(h - 3)
Let g(b) be the second derivative of b**4/12 - b**2 - 2*b. Let c(f) = 13. Let i(a) = 37. Let u(r) = 17*c(r) - 6*i(r). Let w(n) = 3*g(n) - 6*u(n). Factor w(h).
3*h**2
Suppose 3*s - 7 = -p, -p = -s + 16 - 7. Suppose l = 3*o - 8, 12 = s*o + l - 3*l. Factor -11*h - 6*h**3 + 7*h - 2*h**4 - o*h**3 - 10*h**2.
-2*h*(h + 1)**2*(h + 2)
Let d(v) be the second derivative of -v**4/72 - v**3/2 - 27*v**2/4 + v. Factor d(t).
-(t + 9)**2/6
Let z be ((-32)/18)/((-406)/609). Determine w so that 0 + 2*w + z*w**2 + 2/3*w**3 = 0.
-3, -1, 0
Let m = -45 - -47. Suppose -5*d**3 - 5*d - 2*d**2 + 10*d**3 + 8 - 3 - 3*d**m = 0. Calculate d.
-1, 1
Let c(n) be the first derivative of n**5/20 - n**4/8 + 5*n**2 + 6. Let l(k) be the second derivative of c(k). Solve l(q) = 0.
0, 1
Let k(q) =