2/19*w**5 + 0 - 4/19*w**m = 0.
-1, 0, 1
Let c(m) = 4*m**2 - 143*m - 140. Let b(g) = g**2 - 48*g - 47. Let f(u) = 7*b(u) - 2*c(u). Suppose f(l) = 0. What is l?
-49, -1
Let v be 5/(3*2/(-6)). Let a = v - -5. Determine z, given that 10/3*z**3 + 2*z**2 + a - 4/3*z = 0.
-1, 0, 2/5
Let v(f) = 3*f**2 + 6*f - 13. Let i be v(3). Suppose -4*l + 4*a = -i, -4*a + 5 = l - 3. What is s in 14/3*s**3 - 8/3*s + 0 - l*s**2 = 0?
-2/7, 0, 2
Let x(v) be the first derivative of v**4/22 + 6*v**3/11 + 6*v**2/11 - 32*v/11 + 102. Determine r, given that x(r) = 0.
-8, -2, 1
Solve -52*r - 8*r**4 - 17*r**4 + 12*r - 50*r**2 + 2108*r**3 - 1993*r**3 = 0.
-2/5, 0, 1, 4
Let o(i) be the second derivative of -i**5/100 + 37*i**4/60 - 71*i**3/30 + 7*i**2/2 - 120*i. Determine t, given that o(t) = 0.
1, 35
Factor 13/5*k**4 + 36/5*k**2 + 0*k - 1/5*k**5 - 8*k**3 + 0.
-k**2*(k - 9)*(k - 2)**2/5
Let h(z) be the first derivative of -36 - 4/3*z**3 - 16*z + 10*z**2. Let h(b) = 0. Calculate b.
1, 4
Let o = 37 - 18. Let n = -17 + o. Factor 8*d**n - 1 - 4*d + 5 - 2*d**3 - 6*d.
-2*(d - 2)*(d - 1)**2
Let p(t) be the second derivative of -t**8/24640 + t**7/5544 + t**6/495 - t**5/110 - 19*t**4/12 + 4*t. Let j(u) be the third derivative of p(u). Factor j(c).
-(c - 3)*(c + 2)*(3*c - 2)/11
Let x(p) = -p + 10. Let c be x(-3). Suppose -4*j + c = 5. Factor 0*b**3 - 4/11*b**j + 2/11 + 0*b + 2/11*b**4.
2*(b - 1)**2*(b + 1)**2/11
Suppose 6*x = -10*x - 16. Let k be (-176)/80 + -2 + 6 + x. Factor -1/5*a**4 - 1/5 - 6/5*a**2 + 4/5*a + k*a**3.
-(a - 1)**4/5
Factor 1/5*w**2 + 6/5 - 7/5*w.
(w - 6)*(w - 1)/5
Let d(s) be the second derivative of -3*s**5/80 - s**4/24 + 5*s**3/24 - 88*s. Factor d(b).
-b*(b - 1)*(3*b + 5)/4
Let m(o) be the first derivative of -4*o**5/25 - 12*o**4/5 - 128*o**3/15 - 754. Find d such that m(d) = 0.
-8, -4, 0
Let f be (-2)/12*-5 - (-2)/(-4). Suppose 10*j - 17 = 13. Let 2/3*p**j - f + p**2 + 0*p = 0. What is p?
-1, 1/2
Let j(m) be the third derivative of -m**6/240 - 3*m**5/20 - 2*m**4/3 + 69*m**2 - 1. Solve j(b) = 0.
-16, -2, 0
Suppose 0 = -2*f + 2*u + 174, -4*f + 2*u - 42 + 396 = 0. Let c = f - 268/3. Factor -d - c - 1/3*d**2.
-(d + 1)*(d + 2)/3
Let f(j) be the second derivative of -6*j + 0*j**2 + 1/120*j**6 - 1/48*j**4 - 1/160*j**5 + 1/48*j**3 + 0. Determine o, given that f(o) = 0.
-1, 0, 1/2, 1
Let f(n) be the first derivative of 1/18*n**4 - 34 + 0*n + 0*n**3 - 4/45*n**5 + 0*n**2 + 1/27*n**6. Let f(q) = 0. Calculate q.
0, 1
Let b(j) be the third derivative of j**7/210 + j**6/60 - j**5/12 - j**4/4 - 14*j**2 + 2. Factor b(d).
d*(d - 2)*(d + 1)*(d + 3)
Let k(p) = -12*p**2 - 34*p - 30. Let z(c) = -35*c**2 - 103*c - 89. Let r(w) = 17*k(w) - 6*z(w). Factor r(s).
2*(s + 6)*(3*s + 2)
Let t(f) be the first derivative of -4/9*f**3 + 0*f**2 + 21 + 16/3*f. Determine n so that t(n) = 0.
-2, 2
Let a(v) = 34*v**2 - 2*v + 3. Let r be a(2). Let z = r - 135. Factor 2/7*q**2 - 1/7*q**3 + z + 0*q.
-q**2*(q - 2)/7
Let v(f) = 2*f - 2. Let w be v(11). Let 105*u**4 + 77*u + 12 - 2*u - 2 + w*u**5 + 205*u**3 + 185*u**2 = 0. Calculate u.
-2, -1, -1/4
Let n(a) = -2*a**5 - 106*a**4 - 185*a**3 - 93*a**2. Let f(s) = 5*s**5 + 210*s**4 + 370*s**3 + 185*s**2. Let d(x) = -3*f(x) - 5*n(x). Factor d(k).
-5*k**2*(k + 1)**2*(k + 18)
Let k(n) be the first derivative of 2*n**3/39 - 20*n**2/13 - 160. Factor k(c).
2*c*(c - 20)/13
Suppose -44 = -21*w - 2. Let o(y) be the third derivative of 1/14*y**3 + 3/140*y**5 + 1/14*y**4 + 0 + 0*y + 3*y**w. What is i in o(i) = 0?
-1, -1/3
Let g(b) be the second derivative of 0*b**2 + 16/3*b**3 - 3*b**4 + 1/5*b**5 + 0 + 43*b. Factor g(w).
4*w*(w - 8)*(w - 1)
Let i(l) be the first derivative of 2*l**3/15 + 132*l**2/5 + 8712*l/5 + 54. Suppose i(s) = 0. Calculate s.
-66
Let g(d) be the first derivative of 1/3*d**6 - 10 + 4/3*d**3 + 0*d - d**2 - 4/5*d**5 + 0*d**4. Factor g(u).
2*u*(u - 1)**3*(u + 1)
Suppose 2*n - 5*n = 72. Let q be (-4)/n*-21*24/(-70). Factor 0 + 0*v + q*v**2 - 3/5*v**3.
-3*v**2*(v - 2)/5
Let l = 2855 - 17129/6. Find h, given that l*h - 1/6*h**2 + 0 - 1/6*h**3 + 1/6*h**4 = 0.
-1, 0, 1
Let m be 764/10 + -1 + 0. Let s = -75 + m. Factor 6/5*k**3 - 6/5*k**2 - s*k**4 + 0 + 2/5*k.
-2*k*(k - 1)**3/5
Let s(n) = -40*n**2 + 20*n + 8. Let c(o) = -o**2. Let z be (-35)/(3/(-9)*3). Suppose -z - 1 = 3*g. Let f(u) = g*c(u) + s(u). Suppose f(q) = 0. Calculate q.
-2/7, 1
Let t be 50/(-9)*((-24796)/4928 - -5). Let z = t + 1/168. Determine y so that -z*y**2 + 0*y + 2/11 = 0.
-1, 1
Let q(l) be the second derivative of 5*l**4/12 + 95*l**3/3 - 200*l**2 + 143*l. Factor q(r).
5*(r - 2)*(r + 40)
Let d(y) = -14*y**2 - 7*y - 25. Let v(z) = 3*z**2 + z + 2. Let f(s) = d(s) + 5*v(s). Factor f(i).
(i - 5)*(i + 3)
Let v(s) be the second derivative of -s**7/168 + s**6/120 + s**5/16 + s**4/16 + 453*s. Determine k, given that v(k) = 0.
-1, 0, 3
Factor 56/5*l + 4/5*l**2 + 196/5.
4*(l + 7)**2/5
Let h = -2/21125 + 71542/443625. Let f = h - 2/273. Solve 2/13*i**2 + f - 4/13*i = 0.
1
Factor 5/3*u**3 + 4/3 - 2*u**2 - u.
(u - 1)**2*(5*u + 4)/3
Let r(a) be the second derivative of -4/21*a**3 - 9*a + 0 - 3/35*a**5 + 11/42*a**4 - 1/7*a**2. Factor r(d).
-2*(d - 1)**2*(6*d + 1)/7
Let i(c) be the third derivative of c**8/2800 - c**6/600 - 3*c**3/2 + 8*c**2. Let x(g) be the first derivative of i(g). Determine v so that x(v) = 0.
-1, 0, 1
Let i(w) be the second derivative of w**4/30 - 4*w**3/3 + 20*w**2 - 10*w - 1. Suppose i(q) = 0. What is q?
10
Let z = -226 - -235. Let p be (-7)/(-12) + (-6)/z*-1. Solve p*r + 1/2 + 1/2*r**2 = 0 for r.
-2, -1/2
Let b(v) be the second derivative of 2*v**6/15 - 7*v**5/5 + 10*v**4/3 - 113*v. Factor b(a).
4*a**2*(a - 5)*(a - 2)
Let u(c) be the second derivative of 0*c**4 + 0*c**5 + 0*c**3 + 0 - 1/378*c**7 + 0*c**2 - 12*c - 1/270*c**6. What is k in u(k) = 0?
-1, 0
Let v(j) = -100*j**4 - 815*j**3 - 1330*j**2 - 660*j + 90. Let k(h) = -9*h**4 - 74*h**3 - 121*h**2 - 60*h + 8. Let r(g) = 45*k(g) - 4*v(g). Factor r(f).
-5*f*(f + 1)**2*(f + 12)
Let j(a) be the third derivative of -a**8/4032 - a**7/504 - a**6/144 - 4*a**5/15 - 14*a**2. Let g(f) be the third derivative of j(f). Factor g(w).
-5*(w + 1)**2
Let n(h) be the third derivative of -h**7/42 + 19*h**6/24 + 7*h**5/4 - 95*h**4/24 - 50*h**3/3 + 15*h**2 - 2*h. Factor n(c).
-5*(c - 20)*(c - 1)*(c + 1)**2
Let b(o) be the first derivative of o**6/40 - o**5/60 - o**4/3 - 2*o**3/3 - 9*o**2 - 11. Let i(q) be the second derivative of b(q). Factor i(d).
(d - 2)*(d + 1)*(3*d + 2)
Let a(w) be the second derivative of w**4/28 - 9*w**3/14 + 27*w**2/7 - 10*w - 4. Factor a(v).
3*(v - 6)*(v - 3)/7
Let b(x) be the second derivative of 3*x**5/80 - 5*x**4/12 - 3*x**3/8 + 7*x**2/4 - 2*x + 118. Factor b(t).
(t - 7)*(t + 1)*(3*t - 2)/4
Let j(k) be the second derivative of -k**6/20 - 33*k**5/40 - 27*k**4/8 - 25*k**3/4 - 6*k**2 - 25*k - 1. Let j(c) = 0. What is c?
-8, -1
Let k(d) be the third derivative of -d**7/150 - 2*d**6/5 - 17*d**5/75 - 269*d**2. Factor k(q).
-q**2*(q + 34)*(7*q + 2)/5
Factor 5/4*c**5 + 13/8*c**2 + 31/8*c**4 + 0 + 1/8*c + 33/8*c**3.
c*(c + 1)**3*(10*c + 1)/8
Let c(o) be the second derivative of o**8/420 + o**7/105 - o**5/15 - o**4/6 - 5*o**3/3 - 2*o. Let u(g) be the second derivative of c(g). Factor u(k).
4*(k - 1)*(k + 1)**3
Let y(o) = -o**5 + o**4 + 3*o**3 - 9*o**2 - 2*o + 2. Let m(j) = -j**5 + 4*j**3 - 10*j**2 - 3*j + 1. Let s(u) = -2*m(u) + 3*y(u). Factor s(f).
-(f - 2)**2*(f - 1)*(f + 1)**2
Factor -28/3*v - 8/3*v**2 - 80/9 - 1/9*v**3.
-(v + 2)**2*(v + 20)/9
Factor -88/13*h - 2/13*h**2 - 86/13.
-2*(h + 1)*(h + 43)/13
Let l(z) be the second derivative of 0 - 2*z + 1/80*z**5 + 1/32*z**4 + z**2 + 0*z**3. Let w(y) be the first derivative of l(y). Find p, given that w(p) = 0.
-1, 0
Suppose 6*q = 4*q - 5*r + 3, -3*q = 2*r - 10. Find t such that 4/3 - 1/3*t**2 + 8/3*t**3 - t**q - 8/3*t = 0.
-1, 2/3, 1, 2
Let f(j) be the third derivative of j**8/1120 + 2*j**7/525 - j**5/60 - j**4/80 + j**3/30 - 147*j**2. What is p in f(p) = 0?
-2, -1, 1/3, 1
Let c(a) be the second derivative of a**6/3 - 7*a**5/4 + 5*a**4/4 - 11*a - 2. Factor c(t).
5*t**2*(t - 3)*(2*t - 1)
Let c = -24 + 48. Suppose -6 + 2*t - c*t**4 + 30*t**2 + 0*t**3 + 3*t**3 + 9*t**3 - 15*t**5 + t = 0. Calculate t.
-1, 2/5, 1
Let q(o) be the third derivative of 9/140*o**6 - 5*o**2 + 1/42*o**4 + 1/168*o**8