2/7
Determine n so that 5/8*n**2 - 1/4*n - 1/8*n**3 - 1/4*n**4 + 0 = 0.
-2, 0, 1/2, 1
Let i(y) = -y**2 + 10*y - 10. Let v be i(8). Suppose 4*h = 18 + v. Factor 5*f + f + h*f + 12 - 9*f**2 - 12*f**3 - 3*f**4.
-3*(f - 1)*(f + 1)*(f + 2)**2
Solve -800*p**5 + 9*p**3 + 6*p**4 - 24*p**2 + 15*p + 797*p**5 - 3*p = 0 for p.
-2, 0, 1, 2
Let h be (15 + -14)*1/1*3. Let r(k) be the first derivative of 45/8*k**2 - h*k + k**3 + 1. Factor r(s).
3*(s + 4)*(4*s - 1)/4
Let t(d) be the third derivative of -d**8/168 + 86*d**7/735 + 389*d**6/420 + 214*d**5/105 + 17*d**4/21 - 64*d**3/21 + 3*d**2 - 80. What is s in t(s) = 0?
-2, -1, 2/7, 16
Let w(q) = -q + 3. Let b be w(1). Let -6*s**2 - 3*s - 6*s**3 + 19*s**2 - 4*s**b = 0. Calculate s.
0, 1/2, 1
Let p be (-4)/(-10) - (2534/210 - 12). Let h(j) be the first derivative of -2 + 0*j - j**4 + 2/5*j**5 + 0*j**2 + p*j**6 + 0*j**3. Let h(n) = 0. Calculate n.
-2, 0, 1
Let d(r) be the second derivative of 5/24*r**4 - 5/24*r**3 + 0*r**2 + 1/6*r**6 + 10*r + 0 + 7/16*r**5. Factor d(y).
5*y*(y + 1)**2*(4*y - 1)/4
Let p(i) be the second derivative of -5/3*i**3 + 16*i + 5/12*i**4 + 5/2*i**2 + 0. Factor p(v).
5*(v - 1)**2
Let x(o) = -157*o + 3144. Let q be x(20). Determine u, given that 0*u + 7/5*u**3 + 0 + 2/5*u**q + 2/5*u**2 - 3/5*u**5 = 0.
-1, -1/3, 0, 2
Let d(g) be the second derivative of -g**4/42 + 10*g**3/21 - 24*g**2/7 + 29*g + 4. Factor d(k).
-2*(k - 6)*(k - 4)/7
Let t(p) be the first derivative of 32*p**3/3 + 94*p**2 + 500*p - 9. Let s(x) = 13*x**2 + 75*x + 200. Let u(n) = 12*s(n) - 5*t(n). Factor u(b).
-4*(b + 5)**2
Let u(q) be the second derivative of -4*q - 10 - 1/78*q**4 - 2/39*q**3 + 0*q**2. What is f in u(f) = 0?
-2, 0
Let n(c) be the second derivative of -c**5/30 + c**4/4 - 21*c**2/2 - 14*c. Let s(j) be the first derivative of n(j). Factor s(d).
-2*d*(d - 3)
Let i(z) be the second derivative of z**4/48 + z**3/12 - 3*z**2 - 3*z - 13. Factor i(n).
(n - 4)*(n + 6)/4
Suppose -5*z - 4 = 2*w - 4*w, 7 = -2*z - w. Let l = z + 3. Factor l + d**4 + 4*d - 2*d**2 - 4*d.
(d - 1)**2*(d + 1)**2
Let v(p) be the third derivative of p**7/70 + 7*p**6/40 + 17*p**5/20 + 17*p**4/8 + 3*p**3 + 3*p**2 + 8. Factor v(a).
3*(a + 1)**2*(a + 2)*(a + 3)
Suppose -17 = -6*z + i, 0 = 5*z - 5*i + 14 - 24. Factor -1/4*n**4 - n**z - 1/2*n - 5/4*n**2 + 0.
-n*(n + 1)**2*(n + 2)/4
Let 0 - 16/11*m + 40/11*m**2 - 18/11*m**4 - 12/11*m**3 = 0. Calculate m.
-2, 0, 2/3
Let l(b) be the first derivative of 4*b**3/3 - 6*b**2 - 72*b - 244. Suppose l(i) = 0. What is i?
-3, 6
Let z(l) be the third derivative of l**8/112 + l**7/35 - l**6/20 - 2*l**5/5 - 7*l**4/8 - l**3 - 300*l**2. Factor z(t).
3*(t - 2)*(t + 1)**4
Suppose -o + 274 = 5*r, 0 = 7*o - 2*o - 20. Factor r*h - 40 - 230 - 2*h**2 - h**2 + 27.
-3*(h - 9)**2
Let i(g) be the third derivative of g**8/11760 + g**7/4410 + g**4/4 + 3*g**2. Let s(t) be the second derivative of i(t). Determine v, given that s(v) = 0.
-1, 0
Let 2*l**4 + 2*l**5 - 131*l**3 + 119*l**3 + 10*l**5 + 2*l**4 - 4*l**2 = 0. Calculate l.
-1, -1/3, 0, 1
What is x in 4*x**3 - 4*x**3 - 576*x - 5*x**3 + 605 - 139*x + 115*x**2 = 0?
1, 11
Let g(r) be the second derivative of r**8/6048 - r**7/1260 + r**6/1080 + r**5/540 + r**4/3 + 12*r. Let t(o) be the third derivative of g(o). Factor t(v).
2*(v - 1)**2*(5*v + 1)/9
Let m be 2/19 - (4/7 + (-34804)/30723). Factor 0 + m*z - 1/3*z**2.
-z*(z - 2)/3
Let n(x) be the first derivative of 12 + 25/4*x**4 + 0*x + 5/6*x**6 - 15*x**2 - 25/3*x**3 + 5*x**5. Let n(v) = 0. Calculate v.
-3, -2, -1, 0, 1
Let 800/3 - 8240/3*d - 28*d**3 - 1672/3*d**2 = 0. What is d?
-10, 2/21
Let n(s) be the second derivative of -s**6/330 + 43*s**5/220 - 83*s**4/132 + 41*s**3/66 + 3*s - 2. Factor n(t).
-t*(t - 41)*(t - 1)**2/11
Factor -3/5*t**2 - 54/5 - 33/5*t.
-3*(t + 2)*(t + 9)/5
Let m be -9*(-5)/(-360)*-12. Let -3/8*v**5 - 9/8*v**3 + m*v**4 + 3/2*v - 3/2*v**2 + 0 = 0. What is v?
-1, 0, 1, 2
Let k(v) = -v**3 - v + 3. Let h be k(0). Solve 2*l**2 + l**2 + 3*l**h + 2*l**3 + 6*l - 8*l = 0.
-1, 0, 2/5
Let j(r) be the third derivative of -r**6/40 + r**5/20 + r**4/2 - 2*r**3 + r**2 - 6*r. Factor j(n).
-3*(n - 2)*(n - 1)*(n + 2)
Let o(w) be the first derivative of -w**4 - 40*w**3/3 - 56*w**2 - 96*w + 88. Suppose o(k) = 0. What is k?
-6, -2
Suppose -10/3*x + 2 - 14/9*x**4 + 28/9*x**3 - 4/9*x**2 + 2/9*x**5 = 0. Calculate x.
-1, 1, 3
Let s(h) be the first derivative of 5*h**3/3 + 435*h**2 + 37845*h - 395. Determine o so that s(o) = 0.
-87
Let q = 292 - 292. Let m(g) be the first derivative of -1/2*g**6 + 0*g - 3/2*g**2 + 3/2*g**4 + q*g**3 + 0*g**5 + 3. Factor m(j).
-3*j*(j - 1)**2*(j + 1)**2
Let n(y) be the third derivative of 14*y**2 + 1/40*y**6 - 1/20*y**5 + 1/24*y**4 - 1/210*y**7 + 0*y + 0*y**3 + 0. Determine f so that n(f) = 0.
0, 1
Let b be -2 + 8/(-2)*-2. Suppose 15 = 3*h + 4*y, 0 = -2*h - 3*h + 2*y - 1. Suppose -11*u**2 + b*u**2 + h + 6*u**2 - 2*u = 0. Calculate u.
1
Suppose -2 = -5*t + 8. Let l be (0 - (-4)/6)*3. Factor 2*z**3 - 10*z - l*z**2 + 8*z + 0*z**3 + t*z**4.
2*z*(z - 1)*(z + 1)**2
Factor 2 - 1/3*y - 1/9*y**2.
-(y - 3)*(y + 6)/9
Let c(a) = 7*a**3 + 86*a**2 + 77*a - 174. Let y(h) = -20*h**3 - 259*h**2 - 232*h + 522. Let m(d) = -11*c(d) - 4*y(d). Factor m(v).
3*(v - 1)*(v + 2)*(v + 29)
Suppose -8*r + 6 = 118. Let z = r + 16. Factor n + 5/2*n**z + 1/2*n**4 + 0 + 2*n**3.
n*(n + 1)**2*(n + 2)/2
Let w(u) be the first derivative of 2*u**6/9 + 24*u**5/5 - 131*u**4/3 + 400*u**3/3 - 568*u**2/3 + 128*u + 206. Determine q so that w(q) = 0.
-24, 1, 2
Let x(b) be the second derivative of -b**8/53760 + b**7/10080 - b**4/2 + 5*b. Let v(n) be the third derivative of x(n). Factor v(q).
-q**2*(q - 2)/8
Suppose -25*a = -15*a. Suppose a = 5*c - c - 16. Factor 0*q + 0 + 1/2*q**5 + 1/2*q**c - 1/2*q**3 - 1/2*q**2.
q**2*(q - 1)*(q + 1)**2/2
Let k(c) be the second derivative of c**4/4 + 5*c**3/2 + 24*c + 2. Find v, given that k(v) = 0.
-5, 0
Let j(u) be the second derivative of -u**4/48 - 2*u**3/3 - 15*u**2/8 - 63*u. Factor j(b).
-(b + 1)*(b + 15)/4
Let c(i) be the second derivative of i**7/56 - i**6/5 - 3*i**5/40 + i**4 + i**3/8 - 3*i**2 - 2*i + 106. Solve c(n) = 0 for n.
-1, 1, 8
Let j(n) = 9*n + 4*n + 2*n + 50 + 0*n. Let z be j(-3). Factor -2/9*q**z + 8/9*q**4 + 0*q**2 - 8/9*q**3 + 0*q + 0.
-2*q**3*(q - 2)**2/9
Let g(v) = -v**4 + v**3 - 2*v**2 + v - 1. Let o(y) = 24*y**4 - 75*y**3 - 129*y**2 - 18. Let d(b) = -18*g(b) + o(b). Let d(i) = 0. Calculate i.
-1/2, -2/7, 0, 3
Let a(p) = 2*p**3 - 2*p**2 + 2*p. Let h be a(2). Let v = h + -9. Find c, given that -7*c**4 + c**4 + 9*c**5 + 6*c**2 - 5*c**v - 4*c**3 = 0.
-1, 0, 2/3, 1
Solve 13*q**2 - 48 - 20*q**3 - 22*q**2 + 128*q - 3*q**2 = 0.
-3, 2/5, 2
Let l(q) be the third derivative of -q**8/1008 + 23*q**7/315 - 131*q**6/60 + 299*q**5/9 - 18421*q**4/72 + 2197*q**3/3 - q**2 + 197*q. What is u in l(u) = 0?
1, 6, 13
Factor 1/2*u**3 - 9/2*u**2 - 5*u + 0.
u*(u - 10)*(u + 1)/2
Let q(b) be the third derivative of b**5/240 + 11*b**4/96 + 5*b**3/4 - 447*b**2. Solve q(y) = 0.
-6, -5
Determine t so that -80/3*t - 94/9*t**4 - 8 + 14/9*t**5 + 94/9*t**2 + 154/9*t**3 = 0.
-1, -2/7, 2, 3
Let q(z) be the first derivative of 5*z**3/12 - 45*z**2/8 - 25*z/2 - 13. Determine u so that q(u) = 0.
-1, 10
Let n = 7666 + -7664. Factor -10/3*b - 25/3 - 1/3*b**n.
-(b + 5)**2/3
Let o be 4/(-42) - 363/(-1386). Suppose -3*i + 2*n + 2 + 4 = 0, 5*n = -3*i - 15. Factor -1/3*s**2 + 1/6*s + i + o*s**3.
s*(s - 1)**2/6
Factor 15*z**2 - 22 + 10*z**2 + 2*z**2 - 5*z**3 + 60*z - 14 - z**3.
-3*(z - 6)*(z + 2)*(2*z - 1)
Determine p so that 0 + 1/2*p**4 - p - 3/2*p**2 + 0*p**3 = 0.
-1, 0, 2
Suppose 4*b - 3*m + 0 = 5, 8 = 5*b - 2*m. Let a(o) be the second derivative of 1/39*o**3 + 0*o**b - 4*o + 0 + 1/78*o**4. Factor a(q).
2*q*(q + 1)/13
Factor 7 - 1 - v**2 + 1 - v**3 - 1 + 3 + 9*v.
-(v - 3)*(v + 1)*(v + 3)
Let f be 10 - (-2 + 0 + 5). Let g(r) be the third derivative of -1/15*r**5 + 0 + 0*r + 4/3*r**3 - 1/6*r**4 - f*r**2. Factor g(y).
-4*(y - 1)*(y + 2)
Suppose -5*j**2 + 16*j + 0*j**3 - j**3 - 11*j**2 + j**4 + 3*j**4 - 3*j**3 = 0. What is j?
-2, 0, 1, 2
Let g(x) = -x - x**2 - 3*x + 4*x + 1. Let u be (4 + -4)/(-3) + -2. Let f(m) = 5*m**4 - 22*m**3 + 31*m**2 - 20*m + 6. Let b(v) = u*g(v) + f(v). Factor b(s).
(s - 2)*(s - 1)**2*(5*s - 2)
Let o(d) = 36*d**5 - 27*d*