2*u**2 - 4. Determine m, given that c(m) = 0.
-2, -1, 0, 1
Suppose 5*s + k = 16, -2*s + 12 = 3*k + 3. Suppose 7*j - 3*j - 8 = 0. Factor 1/4*d**4 + 0*d + 0 + 1/2*d**s + 1/4*d**j.
d**2*(d + 1)**2/4
Let r(x) be the third derivative of -1/120*x**4 + 0*x**3 - 1/150*x**5 + 0 + 1/525*x**7 + 5*x**2 + 1/600*x**6 + 0*x. Factor r(d).
d*(d - 1)*(d + 1)*(2*d + 1)/5
Factor -6*x**5 + 3*x**5 - 15*x**4 - 27*x**3 - 6*x - 79*x**2 + 58*x**2.
-3*x*(x + 1)**3*(x + 2)
Let q(w) be the third derivative of -w**6/360 + 11*w**5/180 - 19*w**4/72 + w**3/2 + 4*w**2 + 5*w. Determine f, given that q(f) = 0.
1, 9
Let w(l) be the third derivative of 1/60*l**6 - 1/3*l**3 + 0*l - 1/12*l**4 + 0 - 2*l**2 + 1/30*l**5. What is s in w(s) = 0?
-1, 1
Let p(k) be the first derivative of 2 - 3*k + 0*k**2 + 1/18*k**4 + 0*k**3 - 1/30*k**5. Let r(j) be the first derivative of p(j). Factor r(q).
-2*q**2*(q - 1)/3
Let d(p) be the third derivative of p**5/60 - p**4/12 + p**3/6 - 39*p**2. Find u, given that d(u) = 0.
1
Let x = -15 - -91/5. Let i(g) be the first derivative of 12/5*g**2 + 2 + x*g + 4/5*g**3 + 1/10*g**4. Factor i(t).
2*(t + 2)**3/5
Let b be (-874)/(-18) + 1/(-3). Let c = b + -48. Suppose -4/9*z**3 - 2/9*z**4 - 2/9 + c*z**5 + 2/9*z + 4/9*z**2 = 0. What is z?
-1, 1
Let a(s) = -10*s**5 + 30*s**4 - 30*s**3 + 15*s**2 - 5. Let c(n) = -5*n**5 + 15*n**4 - 15*n**3 + 7*n**2 - 2. Let k(p) = 2*a(p) - 5*c(p). Factor k(g).
5*g**2*(g - 1)**3
Suppose 9 = 5*z - 11. Factor -4*h**3 - 2*h**3 + 4*h**3 - 2*h + z*h**2.
-2*h*(h - 1)**2
Let h = 538451/44 - 12237. Let v = -1/44 + h. Suppose v*n**5 - 1/2*n**4 - 1/2 + 1/2*n + n**2 - n**3 = 0. Calculate n.
-1, 1
Let v(g) = g**4 - g**3 + g**2 - g. Let l(y) = 229*y**4 + 171*y**3 + 51*y**2 - y. Suppose -10 = 3*n + 5. Let z(r) = n*v(r) + l(r). Find j such that z(j) = 0.
-2/7, -1/4, 0
Let j(w) be the first derivative of -w**8/840 - w**7/210 - w**6/180 + w**3/3 + 1. Let k(q) be the third derivative of j(q). Factor k(s).
-2*s**2*(s + 1)**2
Let f(l) be the third derivative of -1/16*l**4 + 0 - 1/6*l**3 + 3*l**2 + 0*l - 1/120*l**5. Suppose f(r) = 0. What is r?
-2, -1
Let r be (-2 - 6/(-4))*-8. Determine z so that -28*z**2 - 14*z**4 + 2*z + 26*z - 14*z**r - 90*z**3 + 44*z - 16 = 0.
-2, 2/7, 1/2
Let r be (-73)/(-36) - 2*1/(-9). Find q, given that -r*q**2 - 9/4*q - 3/4 - 3/4*q**3 = 0.
-1
Suppose -10*r + 15*r = 2*b - 33, 3*r + 3 = -3*b. Let p(a) be the first derivative of 4*a**2 + 25/2*a**4 + 40/3*a**3 + b + 0*a. Let p(s) = 0. What is s?
-2/5, 0
Let n(y) be the third derivative of -1/8*y**3 - 1/48*y**4 - 5*y**2 + 0 + 0*y + 1/240*y**5. Solve n(a) = 0 for a.
-1, 3
Let q(b) be the second derivative of 8/5*b**6 - b + 0 + 7/10*b**5 - b**2 - 23/6*b**4 + 3*b**3 - 16/21*b**7. Solve q(z) = 0.
-1, 1/4, 1
Let k(j) = -j**2 + 17*j - 66. Let h be k(11). Factor 2/15*c + 2/5*c**2 + h.
2*c*(3*c + 1)/15
Let p(f) be the first derivative of -f**4/16 - f**3/12 + f**2/4 + 32. Solve p(y) = 0 for y.
-2, 0, 1
Let n(z) = 8*z**3 - 6*z**2 - 6*z + 4. Let d(x) = 23*x**3 - 17*x**2 - 18*x + 12. Let u(i) = -6*d(i) + 17*n(i). Factor u(t).
-2*(t - 1)**2*(t + 2)
Let g = 6 - 4. Suppose 4*m - 15 = -m + 3*t, 0 = -2*t. What is i in -2/7*i**m - 2/7*i**g + 0*i + 0 = 0?
-1, 0
Let l be 15/60 - (-5)/(-28). Let y(z) be the second derivative of 0*z**5 + 0*z**4 + 0*z**2 + 1/10*z**6 + 0 + 0*z**3 + 3*z - l*z**7. Solve y(x) = 0 for x.
0, 1
Let d(r) be the first derivative of -r**4/12 + 2*r**2/3 + 12. Factor d(i).
-i*(i - 2)*(i + 2)/3
Let x(c) = -c**3 - 23*c**2. Let p be x(-23). Factor 3/2*j + 1/2*j**2 + p.
j*(j + 3)/2
Let q(s) be the second derivative of -s**7/147 - 2*s**6/105 + s**4/21 + s**3/21 - 5*s. Factor q(c).
-2*c*(c - 1)*(c + 1)**3/7
Let h(k) be the second derivative of -1/36*k**4 + 0 + 4*k + 0*k**2 - 1/18*k**3. Determine f, given that h(f) = 0.
-1, 0
Let y(i) be the second derivative of 4*i + 1/8*i**3 + 0*i**2 + 1/32*i**4 + 0. Determine m so that y(m) = 0.
-2, 0
Let z(x) be the second derivative of -1/2*x**4 - 3/20*x**5 + 4/5*x**6 + 0*x**2 - 6*x + 0 - 5/14*x**7 + 0*x**3. Factor z(n).
-3*n**2*(n - 1)**2*(5*n + 2)
Let u(c) be the third derivative of -c**8/1344 + c**7/168 - 3*c**6/160 + 7*c**5/240 - c**4/48 - 6*c**2. Factor u(v).
-v*(v - 2)*(v - 1)**3/4
Let z be 18/(-81) + (-2)/18*-2. Let v be ((-92)/(-22) - 2) + -2. Factor -v*n - 4/11*n**2 + 4/11*n**4 + 2/11*n**5 + z + 0*n**3.
2*n*(n - 1)*(n + 1)**3/11
Let h be (-1 - 2) + 9 + -1. Suppose 10 = h*q - 0. Factor 0*n - 1/4 + 1/4*n**q.
(n - 1)*(n + 1)/4
Let u(w) = w**3 + 3*w**2 + 3*w + 6. Let l(s) = 4*s**3 + 8*s**2 + 8*s + 16. Let a(z) = -3*l(z) + 8*u(z). Solve a(i) = 0.
0
Let j(v) be the first derivative of -v**5/40 - v**4/12 + v**3/3 + 2*v**2 - v - 5. Let x(z) be the first derivative of j(z). Solve x(t) = 0 for t.
-2, 2
Let n be 2 - 12/16*2. Let w(z) be the first derivative of n*z**4 + 1 + 0*z + 2/3*z**3 + 0*z**2. Factor w(j).
2*j**2*(j + 1)
Factor -8/13*m + 2/13*m**2 + 8/13.
2*(m - 2)**2/13
Let x(d) = d**3 - 6*d**2 + 8*d - 4. Let b be x(5). What is g in 19*g**4 - 4*g**4 + 24*g**3 + 3*g**2 - b*g + 5*g = 0?
-1, 0, 2/5
Let i(y) be the third derivative of -1/180*y**6 - 1/72*y**4 + 0 + 0*y**3 + 3*y**2 - 1/60*y**5 + 0*y. Factor i(z).
-z*(z + 1)*(2*z + 1)/3
Let d be 0*(2 + 10/(-4)). Let l be 1/(3 + 4/8). Factor d*q - 2/7 + l*q**2.
2*(q - 1)*(q + 1)/7
Let f(t) be the first derivative of 3*t**4/8 - 5*t**3/2 + 6*t**2 - 6*t - 40. Factor f(d).
3*(d - 2)**2*(d - 1)/2
Let g(a) be the third derivative of -a**6/36 - a**5/10 + a**4/18 - 16*a**2. Factor g(f).
-2*f*(f + 2)*(5*f - 1)/3
Suppose -2*h**3 - 2*h**3 + 2*h**3 + 26*h**5 - 24*h**5 = 0. What is h?
-1, 0, 1
Let f = 3 - 0. Suppose -11 = -f*s + 1. Factor a**2 + 3*a**2 + 2*a - 4*a**2 + s*a**2 - 2*a**3 - 4.
-2*(a - 2)*(a - 1)*(a + 1)
Factor 2/7*k**3 + 162/7 + 38/7*k**2 + 198/7*k.
2*(k + 1)*(k + 9)**2/7
Suppose 8/3*c + 2/9*c**2 + 8 = 0. Calculate c.
-6
Factor -15/2*v**2 - 3*v + 0 - 9/2*v**3 + 3/2*v**5 + 3/2*v**4.
3*v*(v - 2)*(v + 1)**3/2
Factor -21*d**2 - 6 - 20*d + 39*d**2 - 23*d**2 + 31.
-5*(d - 1)*(d + 5)
Let j(x) be the third derivative of -x**6/420 + x**5/105 - x**4/84 + 4*x**2. What is y in j(y) = 0?
0, 1
Let l = 220 + -216. Determine s, given that -1/7*s**l + 0*s**2 + 0 + 3/7*s**3 - 4/7*s = 0.
-1, 0, 2
Let q(h) be the first derivative of 5*h**4 + 4*h**3/3 + 18. What is c in q(c) = 0?
-1/5, 0
Let l(g) be the first derivative of g**7/420 - g**6/80 + g**5/40 - g**4/48 + 7*g**2/2 + 8. Let q(k) be the second derivative of l(k). Let q(m) = 0. What is m?
0, 1
Let s be (-8)/10*(-20)/8. Factor 0*g**s - 3/5*g**4 + 0*g + 0 - 3/5*g**3.
-3*g**3*(g + 1)/5
Suppose 0*v + 0*v**2 + 0 + 1/5*v**3 - 1/5*v**4 = 0. Calculate v.
0, 1
Suppose -4 + 4*v**2 - 18*v + 7*v + 15*v - 4*v**3 = 0. Calculate v.
-1, 1
Let i(c) be the second derivative of -c**7/462 + c**5/110 - c**3/66 - 18*c. Solve i(q) = 0.
-1, 0, 1
Let y(s) be the second derivative of s**7/630 + s**6/360 - 2*s**2 + s. Let k(a) be the first derivative of y(a). Factor k(i).
i**3*(i + 1)/3
Let j(a) be the second derivative of a**7/42 + 13*a**6/120 + 3*a**5/16 + 7*a**4/48 + a**3/24 - 13*a. Determine k, given that j(k) = 0.
-1, -1/4, 0
Let n = 17 + -5. Factor -11*i**3 + 0*i**4 + 0 - 8*i + 2*i**4 + 3*i**3 + n*i**2 + 2.
2*(i - 1)**4
Suppose 27*u - 16 = 19*u. Let z(b) be the first derivative of 2/21*b**3 + 0*b**4 + 1 + 1/42*b**6 - 1/14*b**u - 2/35*b**5 + 0*b. Factor z(t).
t*(t - 1)**3*(t + 1)/7
Let h be 3/(-9) + 2/6. Let d(n) be the second derivative of 1/21*n**3 + 2*n + 1/21*n**4 + 1/70*n**5 + h + 0*n**2. Determine p, given that d(p) = 0.
-1, 0
Let w(d) be the first derivative of 3*d**4/28 - 6*d**3/7 + 33*d**2/14 - 18*d/7 + 68. Factor w(n).
3*(n - 3)*(n - 2)*(n - 1)/7
Let v be 3/(12/46)*-6. Let m = 211/3 + v. Determine x so that m*x + 0 - 2/3*x**2 = 0.
0, 2
Suppose -2*j - 3*p + 26 = 0, -j + 3*j = -2*p + 28. Suppose -j = -6*h - 4. Determine m, given that -m + 0 - 1/2*m**h = 0.
-2, 0
Let -67*j**3 + 0*j**2 + j**2 + j**4 + 69*j**3 = 0. Calculate j.
-1, 0
Find c such that -1/2*c**2 + 4 - c = 0.
-4, 2
Let z(d) = -14*d**3 + 4*d**2 + 2. Let o(w) = -5 - 3*w - 8*w**2 - 8*w + 28*w**3 + 11*w. Let a(p) = 2*o(p) + 5*z(p). Factor a(q).
-2*q**2*(7*q - 2)
Suppose 6*n + 8 = 5*n. Let b(c) = c + 8. Let t be b(n). Factor 1/3*k**4 + 0*k**2 + 0*k**3 + t + 0*k.
k**4/3
Factor -4/7*a**3 + 0*a + 0 + 0*a**2.
-4*a**3/7
Solve 4 - 