y - -48. Factor 16*p**2 + 4 + 7*p**3 + 21*p**3 + 12*p**2 - 49*p**4 - 28*p + d*p**2.
-(p - 1)*(p + 1)*(7*p - 2)**2
Let v(w) = -w**2 - 140*w - 4510. Let r be v(-89). Let g(m) be the first derivative of -m**2 + r - 7/3*m**3 + 0*m + m**4. Find f, given that g(f) = 0.
-1/4, 0, 2
Let s(h) be the third derivative of h**6/40 + 107*h**5/20 - 217*h**4/8 + 109*h**3/2 + 796*h**2. Factor s(f).
3*(f - 1)**2*(f + 109)
Let d be (4 - (-19)/(-4))*-4. Let -18*u**2 - 3*u**3 + d*u**3 - 9*u**2 + 3*u**3 - 30*u = 0. What is u?
-1, 0, 10
Let v(f) be the second derivative of 29/6*f**3 + 0*f**2 + 5/16*f**4 + 1/96*f**6 - 11/96*f**5 + 0 - 14*f. Let g(j) be the second derivative of v(j). Factor g(h).
5*(h - 3)*(3*h - 2)/4
Let b(a) be the second derivative of 2*a**7/105 - a**6/10 - 16*a**5/15 - 2*a**4 - 60*a**2 + 280*a. Let g(u) be the first derivative of b(u). Factor g(c).
4*c*(c - 6)*(c + 1)*(c + 2)
Let c(m) be the third derivative of m**5/85 + 371*m**4/204 + 305*m**3/51 - 6637*m**2. Solve c(y) = 0 for y.
-61, -5/6
Let d(w) be the first derivative of -19*w**3/6 + 61*w**2/2 - 84*w + 1373. Factor d(m).
-(m - 2)*(19*m - 84)/2
Suppose -2*v = -4, 2*p + 5 = 10*v + 10 - 21. Let 98/3*x**4 + p*x**5 - 128/3 + 10*x**2 - 416/3*x + 410/3*x**3 = 0. Calculate x.
-8, -1, -1/3, 1
Let b be ((-4)/(-14))/(258/84 - 3). Factor 114*x**3 + 32*x**b - 26*x**3 + 23*x + 4*x**5 + 96*x**2 + 31*x - 18*x.
4*x*(x + 1)**2*(x + 3)**2
Factor 2/7*w**2 - 1578/7*w + 1576/7.
2*(w - 788)*(w - 1)/7
Let s(p) = 6*p**3 - 19*p**2 - 106*p + 29. Let u(i) = 9*i**3 - 28*i**2 - 169*i + 44. Let w(o) = -8*s(o) + 5*u(o). Solve w(z) = 0 for z.
-1, 1, 4
Factor -2/5*c**5 - 13824/5*c**2 - 1776/5*c**3 - 50976/5*c - 104/5*c**4 - 72576/5.
-2*(c + 6)**4*(c + 28)/5
Let a(f) be the first derivative of f**4/54 + 2*f**3 + 81*f**2 - 179*f + 35. Let t(i) be the first derivative of a(i). Determine d so that t(d) = 0.
-27
Let i = -19/4726 - -1933789/212670. Let w = i + 11/45. Let -w*u**2 - 12 + 20*u + 4/3*u**3 = 0. What is u?
1, 3
Let u(c) be the second derivative of 5*c**7/42 - 113*c**6/3 + 449*c**5/4 - 280*c**4/3 + 927*c + 2. Factor u(l).
5*l**2*(l - 224)*(l - 1)**2
Factor -425/2 - 638*l - 853/2*l**2 - l**3.
-(l + 1)*(l + 425)*(2*l + 1)/2
Let d(f) = f**2 + f + 2. Let h(g) = g**5 - 11*g**4 + 22*g**3 + 29*g**2 - 103*g + 66. Let c(m) = -5*d(m) + 5*h(m). What is x in c(x) = 0?
-2, 1, 2, 8
Let n be ((-849)/(-11603))/((-1)/(-41)). Factor 2*o**2 + 2/5*o**n - 16/5*o - 24/5.
2*(o - 2)*(o + 1)*(o + 6)/5
Let i(y) be the second derivative of -1/90*y**6 - 1/6*y**5 + 8*y + 0*y**2 - 4/9*y**3 + 0 - 17/36*y**4. Determine v so that i(v) = 0.
-8, -1, 0
Let m = -210/7673 + 35481422/53711. Solve m + 4/7*r**2 - 272/7*r = 0.
34
Suppose 2*j = 2*y + 1004, -6*y - 20 = -y. Let f be 5/54*8*j/415. Solve -f*v**2 + 4 - 2/3*v + 2/9*v**3 = 0.
-2, 3
Solve -43/3*d + 44/3 - 1/3*d**2 = 0.
-44, 1
Factor -20*a + 240*a**2 - 5*a**4 - 230 + 117 - 207 - 65*a**3.
-5*(a - 2)**2*(a + 1)*(a + 16)
Let r(k) be the first derivative of 11*k**6/60 - k**5/2 + 4*k**4/11 - 4*k**3/33 + k**2 - 42*k - 15. Let z(g) be the second derivative of r(g). Solve z(n) = 0.
2/11, 1
Solve 0 - 2/11*b**2 + 800/11*b = 0 for b.
0, 400
Let h(i) be the second derivative of 1/2*i**2 + 0 + 6*i + 1/72*i**4 + 5/36*i**3. Factor h(z).
(z + 2)*(z + 3)/6
Let t(r) be the second derivative of r**6/60 - 73*r**5/5 + 10511*r**4/3 + 28616*r**3 + 86436*r**2 - 9629*r. Let t(q) = 0. What is q?
-2, 294
Suppose 0*w - 2*w - 4*v = 14, 2*v + 6 = 0. Let r = w + 17. Let -2*d**3 + 3*d**3 + d + 7*d**2 - r*d**2 + 7*d**2 = 0. What is d?
0, 1
Let o(m) be the first derivative of -3*m**4/8 - 11*m**3/4 + 129*m**2/4 - 30*m + 1286. What is n in o(n) = 0?
-10, 1/2, 4
Let u(c) be the second derivative of -c**9/3780 + 11*c**7/630 + c**6/10 + 4*c**5/15 + 24*c**4 - 57*c. Let n(y) be the third derivative of u(y). Factor n(h).
-4*(h - 4)*(h + 1)**2*(h + 2)
Let y be -1*7*(-9)/18 + (-4)/8. Let u be 1*(-5)/(5/(-4)). Find p such that -20/11*p**y - 10/11*p**2 + 2/11*p**u + 16/11*p + 8/11 + 4/11*p**5 = 0.
-2, -1, -1/2, 1, 2
Let y(w) be the third derivative of 0 - w + 2/3*w**3 + 30*w**2 - 11/36*w**4 + 1/60*w**6 - 1/315*w**7 + 1/30*w**5. Let y(z) = 0. What is z?
-2, 1, 3
Let b(a) be the first derivative of -17*a - 12/7*a**2 + 10/21*a**3 + 1/21*a**4 + 15. Let x(k) be the first derivative of b(k). Factor x(n).
4*(n - 1)*(n + 6)/7
Let l(n) be the second derivative of 184*n + 1/10*n**6 + 0*n**2 + 20*n**4 + 0 + 57/20*n**5 - 50*n**3. Factor l(z).
3*z*(z - 1)*(z + 10)**2
Let z(h) be the second derivative of 22*h + 4/15*h**5 + 3/2*h**3 - 15/2*h**2 - h**4 + 0. Let c(p) be the first derivative of z(p). Factor c(a).
(4*a - 3)**2
Let q(z) be the first derivative of -2*z**6/3 + 228*z**5/5 + 61*z**4 - 676*z**3/3 - 576*z**2 - 464*z + 1017. Factor q(r).
-4*(r - 58)*(r - 2)*(r + 1)**3
Suppose 2*h = 5*p - 1710, -4*h - 1461 = 2*p + 1959. Let g = h - -855. Factor 1/4*s**3 + g + 1/2*s + 3/4*s**2.
s*(s + 1)*(s + 2)/4
Factor -1922/3*k + 3836/3 + 2/3*k**2.
2*(k - 959)*(k - 2)/3
Let n(a) be the first derivative of 2*a**6/3 - 49*a**5/20 + 3*a**4/16 - 1878. Suppose n(i) = 0. What is i?
0, 1/16, 3
Let z be (-252)/45 + 4 + ((-30)/(-6) - 3). Find f such that 6/5*f**3 - 6/5*f + z*f**4 + 2/5*f**2 - 4/5 = 0.
-2, -1, 1
Let j(k) be the second derivative of -1/4*k**4 - 1/20*k**6 + 0*k**3 + 0 + 0*k**2 + 159*k + 9/40*k**5. Let j(g) = 0. Calculate g.
0, 1, 2
Factor -3*t**3 + 281*t**2 + 4*t**4 - 205*t**2 + 64*t + 14*t**3 - 5*t**4.
-t*(t - 16)*(t + 1)*(t + 4)
Let -2*o**2 + o**5 + 24*o**2 + 8*o - 3*o**3 - o**4 - 5*o**3 + 2*o**3 - 18*o**2 = 0. What is o?
-2, -1, 0, 2
Let v = 6244 - 6244. Let b(p) be the third derivative of -1/120*p**6 + 5*p**2 + 0*p + 2/3*p**3 - 1/3*p**4 + 1/12*p**5 + v. Solve b(u) = 0 for u.
1, 2
Suppose -2533*q + 120 + 58 = -2444*q. Factor -2/15*r**q + 2/5*r + 4/3.
-2*(r - 5)*(r + 2)/15
Determine c so that -1/4*c**5 - 55/2 - 151/2*c**2 - 31*c**3 - 307/4*c - 5*c**4 = 0.
-11, -5, -2, -1
Let a(l) be the third derivative of 2*l**7/945 - 14*l**6/27 + 137*l**5/135 + 139*l**4/27 + 1097*l**2. Find m such that a(m) = 0.
-1, 0, 2, 139
Let o(b) be the first derivative of -b**6/2 + 192*b**5/5 + 3*b**4/2 - 128*b**3 - 3*b**2/2 + 192*b - 3980. Let o(c) = 0. Calculate c.
-1, 1, 64
Let h = 12 + -28. Let q be (h/10)/(2/(-5)). Factor 15*d**2 - d**3 - 18*d**2 + q*d**3.
3*d**2*(d - 1)
Let u = 2114 - 14794/7. Let n(j) be the first derivative of -u*j**2 - 1/14*j**4 + 0*j + 11 + 8/21*j**3. Factor n(h).
-2*h*(h - 2)**2/7
Let i be 13 + (392/(-24) - -8). Let m(t) be the third derivative of 13/120*t**6 + i*t**4 + t**5 + 1/210*t**7 - 12*t**2 + 0 + 0*t + 32/3*t**3. Factor m(k).
(k + 1)*(k + 4)**3
Suppose 103 = 3*y + 2*i - 90, -y - 5*i + 60 = 0. Suppose 5*q - 6*k + 2*k = 38, 5*k - y = -5*q. Factor 20 - 6*u**2 + u**2 + q*u**2 + 25*u.
5*(u + 1)*(u + 4)
Let o be (9/(-24)*-3)/(4410/1960*(-2)/(-6)). Solve 21 + o*y**3 + 24*y**2 + 87/2*y = 0 for y.
-14, -1
Let n = -169517 + 339039/2. Factor -3/2 - 2*j + n*j**2 + j**3.
(j - 1)*(j + 3)*(2*j + 1)/2
Let j(t) be the third derivative of 0*t + 0 + 0*t**3 + 1/60*t**5 - 65*t**2 - 1/6*t**4. Factor j(n).
n*(n - 4)
Suppose -5*q + 1348 = 538. Let l = q + -160. Solve 4/5*b**3 + 0*b**4 - 2/5*b + 0*b**l + 0 - 2/5*b**5 = 0 for b.
-1, 0, 1
Let u be 1/(4/480*84). Find d such that -8/7*d**2 + 2/7*d**3 - 4/7 + u*d = 0.
1, 2
Let u(d) = 48*d**2 - 137 + 178*d + 557*d + 384 + 473. Let w(z) = 3*z**2 + 46*z + 45. Let r(x) = 2*u(x) - 33*w(x). Factor r(g).
-3*(g + 1)*(g + 15)
Let a be (((-19)/(-8))/19)/((-4)/(-64)). Let r(d) be the first derivative of 21 + 0*d**a + 0*d - 5/4*d**4 + 5/3*d**3. Factor r(s).
-5*s**2*(s - 1)
Let o be ((-1395)/(-120))/((-6)/8) + 16. Let -o*t**2 - 9/2 - 3*t = 0. Calculate t.
-3
Suppose 0 = 28*b - 130 + 46. Suppose w - 87 = 57. Let b*m**3 + 24*m**2 + 12*m**2 + 192 - 6*m**3 - w*m = 0. What is m?
4
Let i(f) be the third derivative of -f**6/60 + 2*f**5/3 - 47*f**4/12 - 68*f**3/3 + 3288*f**2 + 1. Factor i(m).
-2*(m - 17)*(m - 4)*(m + 1)
Suppose 15/2 - 39/2*i**4 - 75/2*i**3 + 21/4*i**5 + 12*i**2 + 129/4*i = 0. Calculate i.
-1, -2/7, 1, 5
Let z = 89 + 340. Suppose 301 + 3*k**3 - 95*k**2 - z*k - 6*k**3 + 206 + 20*k**2 = 0. Calculate k.
-13, 1
Suppose -22*m - 56 = -50*m. Let v be 2 + 1/((-12)/8). Solve -j + v - 1/3*j**m = 0.
-4, 1
Factor 194688/7 + 2/7*z**2 - 1248/7*z.
2*(z - 3