e third derivative of d(f). Factor w(p).
4*(p + 1)*(p + 13)
Factor -23/4*u + 1/2 - 53/4*u**3 + 17/4*u**4 + 57/4*u**2.
(u - 1)**3*(17*u - 2)/4
Let f(z) be the second derivative of -5*z**4/6 + 11*z**3/3 - 6*z**2 + 4*z + 20. Factor f(j).
-2*(j - 1)*(5*j - 6)
Let n = -379 - -379. Let k(r) be the second derivative of -6*r + 1/12*r**3 + 0*r**5 - 1/16*r**4 + 1/120*r**6 + 0 + n*r**2. Determine s, given that k(s) = 0.
-2, 0, 1
Let s(c) = -c**2 + 10*c + 4. Let q be s(10). Suppose -3*i = -q*i + 2. Factor -3*n**2 + 8 + n**3 - 10 - n + 5*n**i.
(n - 1)*(n + 1)*(n + 2)
Suppose 0 = 10*l + 506 - 536. Let k(q) be the first derivative of -3 + q + 5/8*q**2 + 1/12*q**l. Determine v, given that k(v) = 0.
-4, -1
Let m = 4900 - 4900. Let k = 235/1353 + 1/123. Let 2/11*h**2 + m - k*h = 0. What is h?
0, 1
Let p(s) be the second derivative of 0 + 2/51*s**4 + 31*s - 6/17*s**2 + 1/170*s**5 + 1/51*s**3. Determine o so that p(o) = 0.
-3, -2, 1
Let c(h) be the first derivative of h**4/2 + 19*h**3/2 - 89*h**2/8 + 15*h/4 - 107. Suppose c(j) = 0. What is j?
-15, 1/4, 1/2
Suppose -2*k = 20*k - 66. Let x(q) be the second derivative of -12*q + 0 + 1/16*q**4 + 6*q**2 - q**k. Factor x(r).
3*(r - 4)**2/4
Let m(v) be the first derivative of -1/50*v**5 + 0*v - 1/300*v**6 - 1/30*v**4 + 0*v**3 - 2*v**2 + 3. Let a(n) be the second derivative of m(n). Factor a(q).
-2*q*(q + 1)*(q + 2)/5
Let k = -4 - -4. Suppose h = 3*o + 17, h + h + 1 = -o. Determine z, given that -2/5*z**h + k + 0*z + 1/5*z**3 = 0.
0, 2
Suppose -6*t - 5 = -9*t - 2*x, -t - 5 = 2*x. Let p(n) be the second derivative of -1/50*n**t + 1/5*n**3 + 2/5*n**2 + 3*n + 0*n**4 + 0. Factor p(m).
-2*(m - 2)*(m + 1)**2/5
Suppose p + 22 + 43 = 2*a, p + 73 = -2*a. Let o be (p/(-9))/((-4)/(-12)). Find t, given that 6 + 8*t**4 - 13*t - 21*t**2 + 7*t**4 + o*t + 9*t**3 - 19*t = 0.
-1, 2/5, 1
Let 6*i**2 + i**2 - 10*i**2 + 6*i - 3 + 5*i**2 - 77 = 0. What is i?
-8, 5
Let p(f) be the first derivative of -f**3/12 + 3*f**2/4 - 9*f/4 + 219. Solve p(i) = 0 for i.
3
Suppose -797*l**2 - 4 + 21*l - 20 + 800*l**2 = 0. What is l?
-8, 1
Let g(c) = -49*c**2 + 32*c**2 + 4*c - 6*c - 6*c. Let i(x) = 4*x - 4*x**2 - 3*x + 0*x - 3*x. Let t(l) = 6*g(l) - 26*i(l). Find q such that t(q) = 0.
-2, 0
Let h(o) be the first derivative of 0*o**3 - 1/27*o**6 - 4 + 0*o + 8/45*o**5 + 0*o**2 - 2/9*o**4. Suppose h(f) = 0. What is f?
0, 2
Suppose -5*p + 61*n + 18 = 60*n, 2*n = -3*p - 10. Find j such that 0 - 6*j**p - 24/5*j + 9/5*j**3 = 0.
-2/3, 0, 4
Let h(q) = q**2 - 23*q - 35. Let o be h(25). Let m be (-9)/(-10) - o/30. Suppose 8/5 - m*i**2 + 0*i = 0. Calculate i.
-2, 2
Let d = -380 + 799/2. Let o(x) be the first derivative of 24*x**3 + 6*x - d*x**2 - 27/4*x**4 + 2. Find w such that o(w) = 0.
1/3, 2
Let r(m) be the second derivative of -m**4/6 + 42*m**3 - 3969*m**2 - m - 18. Factor r(q).
-2*(q - 63)**2
Let y(i) be the third derivative of -i**5/30 - 31*i**4/12 + 32*i**3/3 + 21*i**2. Let y(z) = 0. What is z?
-32, 1
Let v(d) be the second derivative of -2*d**4/13 + 11*d**3/39 - 2*d**2/13 + 2*d - 26. Let v(g) = 0. Calculate g.
1/4, 2/3
Let b(n) be the first derivative of 0*n**2 - 8 + 1/3*n**3 - 1/4*n**4 + 0*n. Find v, given that b(v) = 0.
0, 1
Let h(u) be the first derivative of u**4/22 + 8*u**3/33 - 19*u**2/11 + 28*u/11 - 145. Factor h(g).
2*(g - 2)*(g - 1)*(g + 7)/11
Suppose 18 - 15/2*z - 3/4*z**2 = 0. Calculate z.
-12, 2
Let m(y) be the third derivative of y**6/660 - y**5/330 - y**4/22 + 339*y**2. Suppose m(a) = 0. What is a?
-2, 0, 3
Let f(y) be the third derivative of -y**5/480 - 13*y**4/96 - 11*y**3/6 + 283*y**2. Suppose f(u) = 0. What is u?
-22, -4
Determine f, given that -190*f - 30*f**4 - 245/2*f**3 - 60 - 5/2*f**5 - 225*f**2 = 0.
-6, -2, -1
Factor -12*v**4 + 6*v**3 + 10*v**4 - 8*v**3.
-2*v**3*(v + 1)
Let k(x) be the second derivative of 2*x**3 + 1/4*x**4 + 0*x**2 + 0 - 20*x. What is y in k(y) = 0?
-4, 0
Let a(b) be the third derivative of -1/270*b**6 - 24*b**2 + 0*b**3 + 2/27*b**4 + 2/315*b**7 + 0 + 0*b - 4/45*b**5. Find h such that a(h) = 0.
-2, 0, 1/3, 2
Let i = -9821/3 - -3283. Find o, given that -16/3*o - i*o**2 + 16/3*o**3 + 4*o**4 + 16/3 = 0.
-2, -1, 2/3, 1
Let n(y) be the first derivative of y**4/30 + 82*y**3/15 + 248*y**2 - 7688*y/15 + 480. Factor n(a).
2*(a - 1)*(a + 62)**2/15
Let n(m) be the second derivative of -m**5/2 + 3*m**4 - 19*m**3/3 + 6*m**2 + 104*m. Factor n(y).
-2*(y - 2)*(y - 1)*(5*y - 3)
Suppose 0 = -2*q - 4*d + 24, -2*q - 7 = -5*d + 5. Let j(o) = o**2 - 5*o + 6. Let s be j(q). What is a in -15 + 11 - 4*a**s + 8 = 0?
-1, 1
Suppose -520 - 452 = -18*i. Let k = i + -54. Determine m, given that 1/5*m**5 - 1/5*m - 2/5*m**4 + 0*m**3 + 2/5*m**2 + k = 0.
-1, 0, 1
Let m(w) be the second derivative of -21*w + 5/18*w**4 - 7/45*w**6 + 0 + 2/3*w**2 + 3/10*w**5 - w**3. Determine z so that m(z) = 0.
-1, 2/7, 1
Let s(i) be the second derivative of -i**4/30 + 4*i**3/15 + 21*i**2/5 + 8*i + 2. Find q, given that s(q) = 0.
-3, 7
Suppose 0 = 4*p - 8*p - 16. Let t be ((-14)/(-3) + p)*(-6)/(-20). Find n such that -t*n**2 - 16/5 + 8/5*n = 0.
4
Let n(q) be the first derivative of -2/35*q**5 - 4/7*q**2 - 1/21*q**6 + 10/21*q**3 + 5/14*q**4 - 9 - 8/7*q. Solve n(r) = 0.
-2, -1, 1, 2
Let p be (-9*1/5)/(-10 + 228/24). Factor 3/5*l**2 + p*l + 3.
3*(l + 1)*(l + 5)/5
Let v(r) be the second derivative of r**6/80 - 3*r**5/8 - 21*r**4/32 - 10*r - 12. Factor v(i).
3*i**2*(i - 21)*(i + 1)/8
Let s = -3025 + 3028. Factor -4*x - 4/3 - 5/3*x**2 + 3*x**4 + 4*x**s.
(x - 1)*(x + 1)*(3*x + 2)**2/3
Let u(y) be the first derivative of y**5/35 + 2*y**4/21 - 2*y**3/7 - 27*y - 7. Let i(c) be the first derivative of u(c). Factor i(o).
4*o*(o - 1)*(o + 3)/7
Let o(q) be the first derivative of -8/3*q + 1 - 2*q**6 - 4*q**2 - 62/15*q**5 + 70/9*q**3 + 5*q**4. Suppose o(n) = 0. What is n?
-2, -1, -2/9, 1/2, 1
Let a(o) be the first derivative of 0*o**2 - 19 + 0*o + 5/2*o**4 - 5/3*o**3 + 3*o**5. Determine q so that a(q) = 0.
-1, 0, 1/3
Factor 8*j**2 - 3*j**3 + 36*j**3 - 18 + 97*j**2 + 123*j**2 + 177*j.
3*(j + 1)*(j + 6)*(11*j - 1)
Let f(h) = 30*h**3 - 75*h**2 + 80*h - 15. Let l(b) = -b**3 - b**2. Let m(i) = f(i) + 10*l(i). Factor m(p).
5*(p - 3)*(p - 1)*(4*p - 1)
Let z(f) be the third derivative of 1/2*f**4 + 4/3*f**3 - 10*f**2 - 1/48*f**8 + 0*f - 5/6*f**5 + 5/24*f**6 + 2/35*f**7 + 0. What is w in z(w) = 0?
-2, -2/7, 1, 2
Let x = -12614/3 - -4205. Factor 0 - 1/6*d**5 + x*d**4 + 0*d**2 + 0*d + 0*d**3.
-d**4*(d - 2)/6
Let q(m) = -m**2 + 0 - 2*m - m**3 + 1 - 2. Let f(i) = 2*i**3 - 58*i**2 + 89*i - 48. Let n(o) = -f(o) + 3*q(o). Factor n(v).
-5*(v - 9)*(v - 1)**2
Let c(g) = -6*g**5 + g**4 + 61*g**3 + 80*g**2 - g. Let n(p) = -p**5 + p**4 + p**3 - p. Let b(j) = c(j) - n(j). Factor b(y).
-5*y**2*(y - 4)*(y + 2)**2
Let f(y) be the first derivative of y**3/18 - 53*y**2/12 - 657. Suppose f(w) = 0. What is w?
0, 53
Factor -12 + 75*z**3 - 5*z**4 + 56*z - 51 + 91*z + 38*z - 195*z**2 + 3.
-5*(z - 12)*(z - 1)**3
Let n(u) be the third derivative of 7*u**6/120 + 88*u**5/15 + 4475*u**4/24 + 625*u**3/3 + 42*u**2 + 2*u. Determine v, given that n(v) = 0.
-25, -2/7
Let n(j) be the third derivative of j**8/112 - j**7/70 - j**6/40 + j**5/20 - 18*j**2 + j. Solve n(u) = 0.
-1, 0, 1
Let j be (-6)/(-5)*(2 + 1 - -2). Factor 21*v**3 + 27*v - j*v**2 + 18 + 42*v**2 - 102*v.
3*(v - 1)*(v + 3)*(7*v - 2)
Suppose 2*m - 2 = 0, 0 = -3*f - 0*f + 4*m - 43. Let t be (-13 - f)/(1 + -2). Solve 1 - 15/4*w**3 - 19/4*w**2 + t*w = 0.
-1, -2/3, 2/5
Let w(j) be the second derivative of 7*j**4/30 + j**3/5 - 11*j. Find n, given that w(n) = 0.
-3/7, 0
Let z(v) be the first derivative of 25/33*v**6 - 10 + 32/11*v - 2/11*v**5 + 64/11*v**2 - 58/11*v**4 + 32/33*v**3. Determine n, given that z(n) = 0.
-2, -2/5, 1, 2
Let q(a) be the first derivative of -a**4/12 + a**3/3 - 12*a - 21. Let v(u) be the first derivative of q(u). Find w such that v(w) = 0.
0, 2
Let v(j) = -12*j**2 - 3*j - 6. Let u be v(-2). Let a = -48 - u. Let -1/5*b**2 + 0*b + a = 0. Calculate b.
0
Let u(s) be the second derivative of s**6/15 - 2*s**5/5 + 5*s**4/6 - 2*s**3/3 + 2*s - 3. Solve u(n) = 0 for n.
0, 1, 2
Let w(u) = u**3 + 5*u**2 - 5*u - 13. Let o be w(-5). Factor -39*y**4 - 51*y**4 + 8*y**2 - 28*y**5 + 42*y**4 - o*y**3.
-4*y**2*(y + 1)**2*(7*y - 2)
Suppose 3*b = -3 - 3, 0 = 2*u - 2*b - 2