2, 16
Suppose 2*s = -7*s - 441. Let g = s - -51. Factor v - 28 + 28 - 5*v**2 + g*v**2.
-v*(3*v - 1)
Let f(i) be the first derivative of -5*i**3/3 - 265*i**2/2 - 980*i + 4117. Factor f(a).
-5*(a + 4)*(a + 49)
Suppose 19 = 2*i - 5*l - 16, -3*i + 5 = 2*l. Suppose 0 = i*c - 11 - 9. What is q in 10*q - 15*q**3 + 5*q**2 + 82*q**4 + 2*q**5 + 3*q**5 - 87*q**c = 0?
-1, 0, 1, 2
Factor -16*i**2 - 576 + 157*i + 63*i + 32*i**2.
4*(i + 16)*(4*i - 9)
Let z be 15/(-1 + 2)*((-1332)/54 + 25). Let r(h) be the first derivative of 0*h**2 + 0*h**4 + 25 + 0*h + 1/20*h**z + 0*h**3. Factor r(f).
f**4/4
Let j(u) be the first derivative of -2*u**3/15 + u**2 + 3490. Factor j(b).
-2*b*(b - 5)/5
Suppose 4*t - 41 = 2*t + k, 3*t + 4*k = 45. Determine z so that -31*z**4 + 33*z**4 + t*z**3 + 10*z**2 - 11*z**3 + 4*z = 0.
-2, -1, 0
Let i(k) be the first derivative of 5/6*k**4 - 2/15*k**5 - 1/90*k**6 + 0*k - 19 + 0*k**2 - 7/3*k**3. Let b(z) be the third derivative of i(z). Factor b(l).
-4*(l - 1)*(l + 5)
Suppose 0 = -12*a + 6*a + 12. Factor 2*w**5 - 11 + 11*w + 23 - 4*w**5 - 60*w**3 + 80*w**a + 20*w**4 - 61*w.
-2*(w - 6)*(w - 1)**4
Let 0 + 5788/3*r**4 - 698900*r**3 + 696972*r**2 - 4/3*r**5 + 0*r = 0. What is r?
0, 1, 723
Suppose 5*n = -4*c + 187, 2*n + 2*n = 5*c + 125. Let k be -4 + -1 + n/4. Factor -1/4*h**3 - 7/4*h**2 - 9/4 - k*h.
-(h + 1)*(h + 3)**2/4
Let u = -318179 + 20046133/63. Let h = u + -92/7. Factor 2/9*c + h*c**3 - 4/9 + 10/9*c**2.
2*(c + 1)*(c + 2)*(2*c - 1)/9
Let d(y) be the second derivative of y**4/8 - 11*y**3/2 - 69*y**2/4 + 21*y + 11. Suppose d(o) = 0. Calculate o.
-1, 23
Let n(k) = -k**3 + 13*k**2 + 18. Let s be n(13). Solve -4*b**2 - s*b + 3*b**2 - 3 - 78 = 0.
-9
Let r = 1510546/7 + -216957. Let x = r + 1167. Factor 2/7*f**2 + x*f + 32/7.
2*(f + 4)**2/7
Let w = 44181/155099 + 19/22157. Let -120/7 + 118/7*g + w*g**2 = 0. What is g?
-60, 1
Let c(f) be the third derivative of 41*f**2 + 0 + f**3 - 1/24*f**4 + 0*f - 1/60*f**5. Let c(m) = 0. What is m?
-3, 2
Let p(v) = -v**2 - 5*v + 129. Suppose -5*i - 80 = 2*g, 4*i + 69*g + 66 = 67*g. Let n be p(i). Let 0 + 9/4*s**4 - 33/4*s**3 + 9*s**2 - n*s = 0. What is s?
0, 2/3, 1, 2
Let b = -43 - -46. Suppose -3*r + 3 = -b. Factor 11 + r + 4*l**2 - 17 - 4*l**3 + 4*l.
-4*(l - 1)**2*(l + 1)
Suppose 4*r + 3*z - 6 = 0, -5*r - 4*z + 5 = -2. Let k(a) = -a**3 + 20*a**2 - 4*a + 3. Let b be k(0). Let 46*c - 30*c + c**r + 16*c**2 + 3*c**b = 0. Calculate c.
-2, 0
Suppose 44*o - 62*o = -414. Suppose 2*c - o = -3*u, c + 9 + 12 = 5*u. Suppose -46/3*t**3 - 20*t**2 - 10/3*t**c - 8/3*t + 16/3 = 0. Calculate t.
-2, -1, 2/5
Let w be 4/(-7) + 4320/(-84). Let u = -50 - w. Determine a so that -3469 + 3469 + 2*a**3 - u*a = 0.
-1, 0, 1
Let h = 78320 + -78317. Determine i, given that 16/3*i**2 - 4/3*i**5 + 16/3*i**4 - 4/3*i + 0 - 8*i**h = 0.
0, 1
Let t(w) be the third derivative of w**6/60 - 113*w**5/15 - 455*w**4/12 - 76*w**3 + 94*w**2 + 2. Determine n so that t(n) = 0.
-1, 228
Let j(q) be the second derivative of 640*q**2 - 80/3*q**3 + 5/12*q**4 - 21*q - 1. Factor j(p).
5*(p - 16)**2
Let f(d) be the second derivative of d**5/130 - d**4/13 - 33*d**3/13 + 8*d**2 - 794*d. What is x in f(x) = 0?
-8, 1, 13
Factor 2308/9 - 1150/9*i - 2/9*i**2.
-2*(i - 2)*(i + 577)/9
Let v(r) be the first derivative of 12*r**5/35 - 53*r**4/14 - 54*r**3/7 + 108*r**2/7 + 40*r/7 - 5151. Determine j, given that v(j) = 0.
-2, -1/6, 1, 10
Let f(d) be the first derivative of d**4/18 + d**3 + 8*d**2/3 + 16*d + 5. Let r(b) be the first derivative of f(b). Factor r(c).
2*(c + 1)*(c + 8)/3
Let g(m) = 10*m**4 + 56*m**3 + 230*m**2 - 8*m + 16. Let w(f) = -f**4 + 3*f**3 - f**2 + f - 2. Let k(l) = -g(l) - 8*w(l). Find i, given that k(i) = 0.
-37, -3, 0
Let u(h) be the first derivative of 5*h**6/24 - 2*h**5/3 + 5*h**4/24 + 5*h**3/3 - 63*h**2/2 + 10. Let s(t) be the second derivative of u(t). Factor s(c).
5*(c - 1)**2*(5*c + 2)
Let l be ((-86)/(-132))/((-12)/312). Let d = 190/11 + l. Factor 1/3*t**5 + 0*t + 0 - 2/3*t**4 + d*t**3 + 0*t**2.
t**3*(t - 1)**2/3
Suppose 3*x = -5*a + 245, 100 = x + 5*a + 15. Let 14 + x*y**5 + 18*y**3 + 145*y**2 - 160*y**4 - 22*y**3 + 1 - 95*y + 19*y**3 = 0. What is y?
-1, 1/4, 3/4, 1
Let r(f) be the first derivative of -162*f**5/65 - 1746*f**4/13 + 6304*f**3/39 - 704*f**2/13 - 892. Factor r(y).
-2*y*(y + 44)*(9*y - 4)**2/13
Let i(b) be the first derivative of 5*b**3/3 - 980*b - 3761. Factor i(k).
5*(k - 14)*(k + 14)
Suppose 3*k + 1 = -3*w - 2, -4*k - 25 = -3*w. Let d be (42/(-7))/(-6) - (k - -3). Factor 9*m**d + 0 + 5/2*m**3 - 4*m.
m*(m + 4)*(5*m - 2)/2
Find q such that 6*q**3 + 9/4*q**4 - 3/4*q**5 - 12*q + 0 - 9*q**2 = 0.
-2, -1, 0, 2, 4
Let r(w) be the third derivative of w**6/60 - 68*w**5/15 - 139*w**4/3 - 560*w**3/3 + 20*w**2 + 33. Factor r(l).
2*(l - 140)*(l + 2)**2
Let z(p) be the second derivative of -5/8*p**4 - 1/40*p**5 - 13/4*p**2 + 0 + 2*p - 9/4*p**3. Find y such that z(y) = 0.
-13, -1
Let s be ((-36)/(-1395))/((-46)/(-333)). Let v = s - 2/155. Suppose 18/23*q**2 + 0 - 4/23*q**3 + v*q - 18/23*q**4 = 0. Calculate q.
-1, -2/9, 0, 1
Let g(u) be the third derivative of 1 + 4/21*u**3 + 0*u - 2*u**2 + 1/28*u**4 - 1/210*u**5. Factor g(z).
-2*(z - 4)*(z + 1)/7
Let g be (21 - 6)/((-6)/18). Let v = -41 - g. Solve -9*u**2 - 1/2*u**v - 4 - 10*u - 7/2*u**3 = 0.
-2, -1
Let a be 210/1960 - -2*((-45)/(-42) + -1). Let n(q) be the second derivative of -11*q**3 - a*q**4 - 363/2*q**2 + 16*q + 0. Factor n(j).
-3*(j + 11)**2
Let r(b) be the third derivative of b**11/92400 + b**10/25200 - b**9/25200 + 9*b**5/20 - 6*b**2 - 3. Let g(t) be the third derivative of r(t). Factor g(m).
6*m**3*(m + 2)*(3*m - 1)/5
Find m such that 64*m - 56*m**2 + 56443*m**3 - 112892*m**3 + 2*m**4 + 56439*m**3 = 0.
-4, 0, 1, 8
Suppose 42*s = 7*s + 70. Factor 1004*v**2 + 1004*v**s + 36*v - 2012*v**2 + 88.
-4*(v - 11)*(v + 2)
Let j(c) be the second derivative of -c**5/4 - 65*c**4/12 + 5*c**3/6 + 65*c**2/2 + 548*c. Find d such that j(d) = 0.
-13, -1, 1
Factor 40/11 - 2/11*o**3 - 10/11*o**2 + 8/11*o.
-2*(o - 2)*(o + 2)*(o + 5)/11
Let x(p) be the second derivative of 0 - 1/3*p**3 + 8/9*p**2 + 100*p + 1/54*p**4. Factor x(z).
2*(z - 8)*(z - 1)/9
Let b be (-6)/4 + (-55)/(-10). Let v be (-4)/(-3)*(66/b - 3). Suppose v*t**2 - 6*t + 67*t**4 - 12*t**3 - 3*t**2 - 64*t**4 = 0. What is t?
0, 1, 2
Let b(i) be the second derivative of -i**7/210 + i**6/50 - i**4/15 + 98*i - 2. What is s in b(s) = 0?
-1, 0, 2
Suppose -5*b = x + 12, -2*b + 0*b = 6. Let u = 21 + -18. Factor -u + 4 - l**4 + 4*l + 2*l**x - 6*l + 0.
-(l - 1)**3*(l + 1)
Let t(s) = -s**3 + 7*s**2 - 2*s - 16. Let p be t(6). Factor -17*u - 8*u**2 + 19*u + 0*u**3 - 2*u**3 + p*u.
-2*u*(u - 1)*(u + 5)
Let c(t) be the second derivative of t**4/72 - 673*t**3/18 + 452929*t**2/12 + 2*t - 124. Factor c(h).
(h - 673)**2/6
Let c(t) be the second derivative of -t**4/3 - 4628*t**3/3 - 2677298*t**2 - 53*t - 1. Factor c(g).
-4*(g + 1157)**2
Find g such that -4/5*g**3 + 0*g**2 + 3888/5*g - 46656/5 = 0.
-36, 18
Let j(u) be the second derivative of -4*u**4/9 + 76*u**3 - 9747*u**2/2 - 138*u + 2. Suppose j(n) = 0. Calculate n.
171/4
Let n(m) be the third derivative of m**8/1176 - 13*m**7/735 + m**6/14 + 10*m**5/21 - 34*m**4/21 - 64*m**3/7 - 6130*m**2. Solve n(y) = 0 for y.
-2, -1, 2, 6, 8
Let q(z) be the third derivative of -z**5/75 + z**4/6 + 16*z**3/5 + 790*z**2. Factor q(d).
-4*(d - 8)*(d + 3)/5
Let g(n) = -n - 3*n + 0 + 4*n**3 + 8. Let v(d) = -d**2 + 28*d - 124. Let f be v(6). Let m(y) = -y**3 + y**2 - 1. Let r(x) = f*m(x) + g(x). Factor r(j).
-4*j*(j - 1)**2
Let r = -7174 + 7176. Let i(w) be the second derivative of 0 - 8/57*w**3 - 7/114*w**4 + 1/38*w**5 + 4/19*w**r - 13*w. Solve i(o) = 0 for o.
-1, 2/5, 2
Let v = -439 - -668. Let l = -1602/7 + v. Determine t so that -l*t**4 - 3/7*t**3 - 3/7*t**2 + 0 - 1/7*t = 0.
-1, 0
Factor -726 + 14*b**2 + 24275*b + 3842 - 13365*b.
2*(b + 779)*(7*b + 2)
Let v be 12 - (-189*(-11)/165 + (0 - 1)). Factor v*x**2 - 16/5 - 4/5*x.
2*(x - 4)*(x + 2)/5
Suppose -9*r**3 - 653*r**2 + r**5 + 625*r**2 + r**4 + 8*r + 6*r**3 - 11*r**3 + 32 = 0. Calculate r.
-2, 1, 4
Let a(z) = -z + 217. Let t be a(-46). What is g in -3 + 257*g + 3*g**4 + 12*g**3 - t*g - 6*g**3 = 0?
-1, 1
Let z(o) be the second derivative of -o**4/3 + 2540*o**3/3 - 806450*o**2 - 1562*