4*c(g). Find s such that l(s) = 0.
-4, 1, 2
Factor -1/2*f**2 + 0*f - 3/2*f**4 + 3/2*f**3 + 0 + 1/2*f**5.
f**2*(f - 1)**3/2
Let w(n) = -3*n**3 + 206*n**2 - 3531*n - 2450. Let u(h) = -h**2 + 2*h. Let t(l) = -10*u(l) + 5*w(l). Factor t(q).
-5*(q - 35)**2*(3*q + 2)
Let u be 3 - 15/(15/(-3)). What is s in -u*s**2 + 3*s**3 + 2*s - 1 - 3 + 10*s**2 - 5*s**3 = 0?
-1, 1, 2
Let x(r) = -10*r**3 + 15*r**2 - 20*r + 15. Let h(f) be the first derivative of f**4/4 - f**3/3 + f**2/2 - f - 8. Let i(m) = 15*h(m) + x(m). Factor i(o).
5*o*(o - 1)*(o + 1)
Let o = 146 + -146. Let u(p) be the third derivative of 0*p + o + 1/9*p**3 - 1/12*p**4 - 2/45*p**5 - 3*p**2. Determine v, given that u(v) = 0.
-1, 1/4
Let y(d) be the third derivative of -d**5/60 - d**4/3 - 5*d**3/2 + 5*d**2 - d. Let r be y(-3). Factor 0 - 2/3*p**5 + r*p**2 + 0*p**4 - 2/3*p + 4/3*p**3.
-2*p*(p - 1)**2*(p + 1)**2/3
Let i(m) = -23*m**3 + 212*m**2 - 560*m - 17629. Let k(o) = 4*o**3 - 42*o**2 + 112*o + 3526. Let j(b) = 2*i(b) + 11*k(b). Factor j(p).
-2*(p - 9)*(p + 14)**2
Let h(b) be the third derivative of -5/336*b**8 - 5/24*b**4 + 0*b - 1/105*b**7 + 2*b**2 + 1/15*b**5 + 0 + 1/12*b**6 - 1/3*b**3. Find f, given that h(f) = 0.
-1, -2/5, 1
Let l be (20/(-18))/5 - (-34)/153. Factor 0 + 9*c**4 + 2/3*c**2 + l*c - 5*c**3.
c**2*(3*c - 1)*(9*c - 2)/3
Let r(b) be the first derivative of -1/12*b**2 + 1/18*b**3 - b + 13. Determine i so that r(i) = 0.
-2, 3
Let c be 28/5 + 117/(-195). Let f(t) be the third derivative of c*t**2 + 0 + 0*t**3 - 1/210*t**7 + 0*t + 0*t**4 - 1/15*t**5 + 1/30*t**6. What is m in f(m) = 0?
0, 2
Let d(j) = -5*j**3 - 196*j**2 - 4356*j - 31946. Let h(k) = -36*k**3 - 1371*k**2 - 30492*k - 223623. Let b(f) = -15*d(f) + 2*h(f). Solve b(m) = 0 for m.
-22
Factor -131*d - 146*d + 241*d + 228*d - 30276 - 4*d**2 + 504*d.
-4*(d - 87)**2
Let q(a) be the second derivative of a + 0 + 0*a**3 + 0*a**2 + 1/30*a**4. Factor q(m).
2*m**2/5
Find p, given that -25*p**2 + 0 - 5/6*p + 155/6*p**3 = 0.
-1/31, 0, 1
Let m = -180 - -182. Suppose -m*c + 4*t + 3 = 5*t, -5*t = 5. Suppose -2/11*g + 4/11*g**3 + 0 + 2/11*g**c = 0. What is g?
-1, 0, 1/2
Let r be 28 + 5 + (-36)/4. Determine v, given that -30*v - r + 4*v**2 + v**2 + 16*v**2 = 0.
-4/7, 2
Factor 396*b**2 - 37 - 72*b**3 + 405*b + 3*b**2 + 793 + 3*b**4 + 531*b + 138*b**3.
3*(b + 2)*(b + 3)**2*(b + 14)
Let b = 12811 - 12808. What is u in -3/4*u**2 - 3/4*u - 1/4 - 1/4*u**b = 0?
-1
Let y(j) be the third derivative of 0*j - 17/360*j**5 + 14*j**2 + 1/18*j**3 + 0 + 5/48*j**4. Factor y(k).
-(k - 1)*(17*k + 2)/6
Solve -45 - 5*o + o + 5*o**2 + 4*o = 0 for o.
-3, 3
Let x(i) be the second derivative of -i**9/3780 + i**8/336 - 4*i**7/315 + i**6/45 - i**4/6 - 6*i. Let u(v) be the third derivative of x(v). Factor u(p).
-4*p*(p - 2)**2*(p - 1)
Let k = -136 - -128. Let m be (-48)/k + 11/(-2). Suppose 2*j**2 + m*j + 0 = 0. Calculate j.
-1/4, 0
Let k(a) be the first derivative of a**4/3 + 4*a**3 + 16*a**2/3 - 20. Factor k(l).
4*l*(l + 1)*(l + 8)/3
Let r(w) be the third derivative of 1/15*w**5 - 1/15*w**6 + 2/3*w**3 + 0 + 0*w - 4/105*w**7 + 5/12*w**4 - 6*w**2 - 1/168*w**8. Determine l, given that r(l) = 0.
-2, -1, 1
Let j = -1304 - -13041/10. Let t(q) be the third derivative of 2/3*q**3 - 5/12*q**4 + 0*q + 0 - j*q**5 - 7*q**2. What is l in t(l) = 0?
-2, 1/3
Let q(x) be the third derivative of -x**6/180 - x**5/90 + x**4/9 + 4*x**3/9 - 76*x**2. Factor q(o).
-2*(o - 2)*(o + 1)*(o + 2)/3
Find u, given that 44*u**2 - 13*u**2 + 17*u**2 - 3*u**4 - 45*u**3 = 0.
-16, 0, 1
Let c(y) be the second derivative of -y**10/7560 - y**9/1890 - y**8/1680 - y**4/6 + 3*y. Let x(g) be the third derivative of c(g). Determine m so that x(m) = 0.
-1, 0
Let y = 458 + -452. Let o(i) be the second derivative of -10*i + 0*i**2 + 1/10*i**4 + 0*i**5 + 2/15*i**3 - 1/75*i**y + 0. Factor o(u).
-2*u*(u - 2)*(u + 1)**2/5
Let k = 130 + -127. Factor -80*v**5 + 22*v**2 - 120*v**4 - 3*v + 8*v**2 - 2*v - 5*v**k.
-5*v*(v + 1)**2*(4*v - 1)**2
Let n(i) = -i + 41. Let q be n(-19). Let v = q + -58. Factor -1/2*a**v + 0 - 3/2*a.
-a*(a + 3)/2
Let j(f) be the first derivative of 0*f**3 + 1/16*f**4 - 11/2*f**2 - 1 + 1/120*f**5 + 0*f. Let a(h) be the second derivative of j(h). Factor a(b).
b*(b + 3)/2
Let o(r) be the first derivative of -4*r**3/3 - 16*r**2/3 - 16*r/3 - 450. Factor o(s).
-4*(s + 2)*(3*s + 2)/3
Let b be 6/40*(-530)/12 + 7. Find p such that -1/8*p**3 + 1/8 + b*p**2 - 3/8*p = 0.
1
Suppose -3*z - a + 1 + 3 = 0, 0 = 2*z + 2*a. Let t(w) = -w**2 - 13*w - 38. Let k be t(-5). Factor 0*o - 4/5*o**k - z*o**3 + 0.
-2*o**2*(5*o + 2)/5
Suppose -5*h + 3 + 22 = 0. Suppose -8 = h*o - 9*o. Factor -5*u**2 + u**2 + 4*u**2 - 2*u - o + 4*u**2.
2*(u - 1)*(2*u + 1)
Suppose 0 = 7*o - 12 - 9. Factor 15 - 20*f**2 + 5*f + 0*f - 10*f**o + 7*f + 5*f**4 - 2*f.
5*(f - 3)*(f - 1)*(f + 1)**2
Let h(j) be the first derivative of 0*j + 45/2*j**2 - 85/4*j**4 + 9 + 35*j**3 + 3*j**5. What is l in h(l) = 0?
-1/3, 0, 3
Let z(a) = 4*a**2 - 6*a - 2. Let s(o) = -5*o**2 + 6*o + 2. Let c(p) = 5*s(p) + 6*z(p). Let b be c(-5). Determine d so that -d**2 + 2*d**2 - b*d**2 + 2*d = 0.
0, 1
Suppose -3*b + 8*m = 7*m + 15, -18 = 3*b - 2*m. Let j be (b + -1 - -7) + -2. Let 0*p**2 + j*p**3 + 3/5*p**4 + 0 + 0*p = 0. What is p?
0
Factor 0*v + 0*v**2 - 1/2*v**5 - 2*v**4 + 0 - 2*v**3.
-v**3*(v + 2)**2/2
Let a(f) be the second derivative of -f**5/230 + 7*f**4/138 - 11*f**3/69 + 5*f**2/23 - 231*f. Factor a(u).
-2*(u - 5)*(u - 1)**2/23
Let u be (12/8)/(0 + 3). Let n = 1555/2 - 777. Factor -n*o**3 - 1/2*o**2 + u + 1/2*o.
-(o - 1)*(o + 1)**2/2
Let n(s) = s**3 + 4*s**2 - 7*s - 6. Let t be n(-5). Factor 3*i**t - 20*i + 46*i**3 - 18*i**4 - 11*i**3.
-5*i*(i - 2)*(i - 1)*(3*i + 2)
Let q be (-16)/5 - (-16 - (32 - 44)). Factor 12/5*z**2 - q*z**3 + 0*z + 0.
-4*z**2*(z - 3)/5
Let i = -132 + 134. Let n(z) be the second derivative of 0*z**3 - 3*z + 0*z**i + 0*z**4 + 1/100*z**5 + 0. Determine k so that n(k) = 0.
0
Let q be 4/18 + ((-145)/45 - -5). Find r such that -35*r**3 - 4*r**4 - 2*r**2 + 27*r**3 + 8*r + 6*r**q = 0.
-2, -1, 0, 1
Factor 15*c**2 - 9*c**3 + 8*c**2 + 6*c**3 - 8*c**2 - 18*c.
-3*c*(c - 3)*(c - 2)
Let p(f) = -f**5 + f**4 - 4*f**3 + 6*f**2 - 9*f - 7. Let s = 16 - 18. Let w(d) = -d**3 + d**2 - d - 1. Let u(h) = s*p(h) + 14*w(h). Factor u(o).
2*o*(o - 2)*(o - 1)*(o + 1)**2
Let o(d) = -8*d + 160. Let k be o(20). Factor 0*p + k - 2/3*p**2 + 4/3*p**3 - 2/3*p**4.
-2*p**2*(p - 1)**2/3
Let q(i) be the second derivative of -i**7/336 + 7*i**6/240 - 7*i**5/80 + i**4/12 - 86*i. Determine c, given that q(c) = 0.
0, 1, 2, 4
Let r(u) be the third derivative of u**5/20 + u**4/2 - 6*u**3 - 595*u**2. Solve r(s) = 0 for s.
-6, 2
Let y(q) be the third derivative of q**9/5040 - q**7/840 - 31*q**4/24 + 10*q**2. Let b(c) be the second derivative of y(c). Suppose b(h) = 0. Calculate h.
-1, 0, 1
Let h = 2647 + -2640. Let g(v) be the second derivative of 3*v + 1/6*v**3 + 0*v**2 - 2/15*v**6 - 1/3*v**4 + 1/42*v**h + 3/10*v**5 + 0. Solve g(u) = 0.
0, 1
Suppose -m + 347 = 3*z + m, 0 = 2*z + 2*m - 230. Let l = 119 - z. Determine k, given that 8/3*k**l + 2*k**4 + 8/15*k + 0 + 62/15*k**3 = 0.
-1, -2/3, -2/5, 0
Let v = -30453 + 334987/11. Let 2/11*o**2 + 2/11 + v*o = 0. Calculate o.
-1
Let l(s) be the second derivative of s**5/20 + s**4/3 - 2*s**3/3 + 7*s**2/2 - 3*s. Let o be l(-5). Factor 2*k**o + k**2 - k - 5*k.
3*k*(k - 2)
Let k = -9019/56 + 1067/7. Let r = 361/40 + k. Let 6/5*m**2 + 0 - r*m**3 - 4/5*m = 0. Calculate m.
0, 1, 2
Let b(h) be the third derivative of -h**7/630 + h**6/180 + h**5/15 - 3*h**4/8 - 20*h**2. Let x(n) be the second derivative of b(n). Factor x(t).
-4*(t - 2)*(t + 1)
Let g(f) be the third derivative of f**7/840 - f**5/40 + f**4/12 + 2*f**3/3 - 3*f**2. Let t(o) be the first derivative of g(o). Factor t(j).
(j - 1)**2*(j + 2)
Determine i so that -8*i**3 + 96*i + 0*i**4 + 84*i**2 - 3*i**4 - 13*i**3 + 10*i**3 + 23*i**3 = 0.
-2, 0, 8
Let k(b) be the second derivative of -b**5/5 - 2*b**4/3 + 10*b**3/3 + 12*b**2 + 46*b + 2. Let k(p) = 0. What is p?
-3, -1, 2
Let z be 2*1*((3 - 5) + 4). Find m, given that -8*m**5 + 18*m**4 + 12*m - z*m**3 - 2 + 12*m**5 - 16*m**2 - m**5 - 11*m**5 = 0.
-1, 1/4, 1
Let x be 12/(-72)*(-37 + (-5 - -10)). Determine u, given that x*u + 14/3*u**4 + 12*u**3 + 40/3*u**2 + 