e third derivative of -h**9/22680 - h**8/480 + 11*h**7/1890 - 31*h**4/3 - 163*h**2. Let n(x) be the second derivative of i(x). Factor n(v).
-2*v**2*(v - 1)*(v + 22)/3
Suppose -9/4*y**2 + 9/4*y**4 + 1/8*y**5 - 4*y + 0 + 31/8*y**3 = 0. What is y?
-16, -2, -1, 0, 1
Let l be ((-408)/(-45))/(-34)*(-378)/36. What is i in -9/5*i - 1/5*i**2 - l = 0?
-7, -2
Suppose 145/2*w - 23*w**2 - 1/2*w**3 - 49 = 0. What is w?
-49, 1, 2
Let f(o) be the first derivative of -2*o**3/3 + 2342*o**2/9 - 1040*o/9 - 2566. Factor f(w).
-2*(w - 260)*(9*w - 2)/9
Suppose 4*n + 5*g + 18 - 14 = 0, 8 = 7*n + 5*g. Let h(u) be the first derivative of -12/5*u**5 + 0*u + 24*u**2 - 5*u**n + 64/3*u**3 - 23. Factor h(i).
-4*i*(i - 2)*(i + 3)*(3*i + 2)
Suppose 0 = -46*c - 31*c. Let z(h) be the first derivative of 1/12*h**3 + c*h - 45 + 3/4*h**2. What is s in z(s) = 0?
-6, 0
Let h(r) be the third derivative of -9*r**7/490 - 79*r**6/280 + 207*r**5/35 - 45*r**4/14 + 21*r**2 + 20*r. Find f, given that h(f) = 0.
-15, 0, 2/9, 6
Let b(c) be the first derivative of 1/4*c**4 - 1/24*c**6 + 4/3*c**3 - 3/20*c**5 - 66 + 0*c**2 - 4*c. Factor b(o).
-(o - 2)*(o - 1)*(o + 2)**3/4
Let z(l) = -2*l**3 + 174*l**2 + 342*l + 172. Let v(h) = -h**3 - 3*h**2 + h + 1. Let w(m) = -3*v(m) - z(m). Determine a, given that w(a) = 0.
-1, 35
Factor 1610*g - 38*g**2 - 15*g**2 + 1580*g - g**3 - 3292*g.
-g*(g + 2)*(g + 51)
Let k(v) be the second derivative of -v**5/40 + 35*v**4/12 + 71*v**3/12 - 162*v. Suppose k(y) = 0. What is y?
-1, 0, 71
Let i(a) be the first derivative of 2*a**5/25 - 7*a**4/10 - 46*a**3/5 - 113*a**2/5 - 104*a/5 + 299. Determine b, given that i(b) = 0.
-4, -1, 13
What is a in 1/5*a**2 - 316/5 + 156/5*a = 0?
-158, 2
Factor -2*z**2 - 50/3*z + 2/3*z**3 + 50.
2*(z - 5)*(z - 3)*(z + 5)/3
Let v = 1408 + -18302/13. Let d be 2/3*360/130. Factor 72/13 + v*t**2 + d*t.
2*(t + 6)**2/13
Let x be 28/(-5)*(-1625)/520. Let i(g) be the second derivative of 5*g**3 + 0 + 5/12*g**4 + 28*g - x*g**2. Factor i(l).
5*(l - 1)*(l + 7)
Let g(s) = -s**4 - s**2 - 3*s - 2. Let a(z) = 6*z**4 + 78*z**3 + 868*z**2 + 1956*z + 8. Let r(x) = -a(x) - 4*g(x). Find c, given that r(c) = 0.
-18, -3, 0
Let 620/7*d - 204/7*d**2 - 24/7 = 0. What is d?
2/51, 3
Let y(n) be the first derivative of n**5 - 135*n**4/4 - 5*n**3 + 395*n**2/2 + 270*n - 564. Factor y(i).
5*(i - 27)*(i - 2)*(i + 1)**2
Let g be -16 + 14 - (-7892)/18. Let x = g + -436. Find v, given that 0 + 0*v**2 + x*v**4 - 4/9*v**3 + 0*v = 0.
0, 1
Factor -3435*b**3 - 3421*b**3 + 235*b**2 + 6857*b**3.
b**2*(b + 235)
Factor -6*d**3 - 39*d**3 + 159356*d - 530*d**2 - 158651*d - 130.
-5*(d - 1)*(d + 13)*(9*d - 2)
Suppose 3*b - 2*s = -2*b + 48, 16 = -4*s. Factor -268*y**2 + 538*y**2 - 258*y**2 + y**4 - 2*y**4 + b*y**3 - 3*y**4.
-4*y**2*(y - 3)*(y + 1)
Let l(m) be the third derivative of 2*m**7/105 + 38*m**6/15 + 1108*m**5/15 - 2128*m**4 + 18816*m**3 + 1621*m**2 - 2. Determine s, given that l(s) = 0.
-42, 4
Suppose -111*o = -119*o - 104. Let f be ((-1778)/154 - o) + 12/22. Find v such that -1/4*v**f + 3*v - 9 = 0.
6
Let d(a) be the first derivative of -a**6/40 + 7*a**5/20 + 93*a**2/2 + 189. Let y(m) be the second derivative of d(m). Suppose y(o) = 0. Calculate o.
0, 7
Let b be (100/(-5) - -20)/(-10). Solve b - 72/7*l - 96/7*l**2 - 26/7*l**3 - 2/7*l**4 = 0.
-6, -1, 0
Suppose 3*k + 44 = g + 8*k, 8 = 3*k - 2*k. Find i, given that 5/3*i**3 - 5/3*i - 5/6*i**2 + 5/6*i**g + 0 = 0.
-2, -1, 0, 1
Let r be 6 + (1 - 6 - (23 - 31)). Let t be (4/r*51)/2. Factor -t*g - 10/3*g**2 - 4.
-2*(g + 3)*(5*g + 2)/3
Suppose -10 = 5*y + 4*c - 9*c, 4 = -4*y + 3*c. Let z be (-2 + 1 + y)*(-6)/(-2). Suppose -w**5 - 9*w**4 - 15*w**z - w**5 - 8*w**2 - w**4 - w**3 = 0. Calculate w.
-2, -1, 0
Let f(g) be the second derivative of -3 + 0*g**2 + 3*g - 25/2*g**4 + 625/2*g**3 + 3/20*g**5. Factor f(b).
3*b*(b - 25)**2
Let l(p) be the third derivative of -p**5/100 - 377*p**4/40 - 5392*p**2. Factor l(j).
-3*j*(j + 377)/5
Let r(n) be the first derivative of n**6/24 - 4*n**5/3 + 385*n**4/24 - 245*n**3/3 + 7*n**2/2 + 3*n - 97. Let i(o) be the second derivative of r(o). Factor i(l).
5*(l - 7)**2*(l - 2)
Let m(z) = -z - 6*z + 13*z**2 + 4 - 12*z**2. Let u be m(7). Factor 0*o**3 - 19*o**2 - 3*o + 16*o**2 + 0*o**3 + 3*o**u + 3*o**3.
3*o*(o - 1)*(o + 1)**2
Determine p so that 140/3*p + 22 + 2*p**4 + 55/6*p**3 - 331/6*p**2 = 0.
-33/4, -1/3, 2
Let t(b) = -5*b**2 - 232*b + 1753. Let i be t(-53). Let -2/3*y**i - 4/3*y**3 + 0 - 2/3*y**2 + 0*y = 0. What is y?
-1, 0
Let d(n) = n**2 - 25*n + 6. Let h(u) = u**2 + 26*u - 8. Let y be (-1232)/660 + (-4)/30. Let p(f) = y*d(f) - 3*h(f). Factor p(t).
-(t + 6)*(5*t - 2)
Let t be -10 - ((-5)/3 - (-4)/(780/(-14261))). Find g, given that 396/5*g**3 + 4/5*g**5 + t*g**2 + 76/5*g**4 + 0 + 0*g = 0.
-9, -1, 0
Suppose 3*l + 4 = 118. Suppose 10 = -4*t + l. Factor t*p**3 - 9*p**3 - 16 + 16*p + 4*p**2 - 2*p**3.
-4*(p - 2)*(p - 1)*(p + 2)
Determine a, given that 4/7*a**5 + 48/7*a**2 + 0 - 12/7*a**4 + 0*a - 16/7*a**3 = 0.
-2, 0, 2, 3
Let h(y) be the second derivative of y**9/52920 - y**8/7840 + y**7/2940 - y**6/2520 - 4*y**4 - 58*y. Let q(r) be the third derivative of h(r). Factor q(j).
2*j*(j - 1)**3/7
Suppose 4*x + 5*u + 10 = 0, 2 = 2*x + 2*x - u. Let h(j) = -7*j**2 - 140*j - 446. Let t be h(-16). Find k, given that x*k + 2/9*k**t + 0 = 0.
0
Determine y, given that -4*y**2 + 300759*y**3 + y**2 + 3*y**4 - 300726*y**3 - 7*y - 26*y = 0.
-11, -1, 0, 1
Let l(v) be the third derivative of 0*v - 25/12*v**3 - 11/120*v**5 + 1/240*v**6 + 1 + 21*v**2 + 35/48*v**4. Factor l(a).
(a - 5)**2*(a - 1)/2
Let o(z) be the second derivative of z**9/20160 - z**8/8960 - z**4/6 - 35*z**3/3 + 3*z + 7. Let b(q) be the third derivative of o(q). Factor b(u).
3*u**3*(u - 1)/4
Let m(f) be the second derivative of -1/48*f**4 - 3/8*f**3 + 7*f - 3 + 0*f**2. Find h, given that m(h) = 0.
-9, 0
Let w be 5*(-370)/(-600) - (-4 - -7). Let g(j) be the first derivative of 1/4*j**2 - 28 + 0*j + w*j**3. Factor g(n).
n*(n + 2)/4
Let b = 74 + -116. Let y = -39 - b. Factor -13*f + 3*f**2 - f**4 + 7 - 11 + 9*f + 2*f**y.
-(f - 2)**2*(f + 1)**2
Suppose 0 = 3*t + 3*b + 1 + 2, 2*b - 1 = t. Let j be 1/t - (-180)/75. Determine u, given that -9/5*u**3 - 1/5*u**5 - j*u**2 - u**4 - 2/5*u + 0 = 0.
-2, -1, 0
Let r be (-3 - -2 - -1)*(85/(-20))/17. Let b(o) be the third derivative of -5*o**2 - 1/156*o**4 + r*o + 0 - 2/39*o**3 + 1/390*o**5. Factor b(a).
2*(a - 2)*(a + 1)/13
Let u(j) be the first derivative of 2*j**6/3 + 24*j**5/5 + 37*j**4/4 - 3*j**3 - 16*j**2 + 12*j - 1391. Let u(n) = 0. What is n?
-3, -2, 1/2
Solve -126 - 1/10*u**2 - 319/10*u = 0 for u.
-315, -4
Let t(w) = w**3 + 24*w**2 + 48*w - 18. Let c be t(-21). Let j = -1479/5 + c. Suppose 4/5*m + j - 2/5*m**2 = 0. Calculate m.
-1, 3
Let u(b) be the second derivative of 25/9*b**3 + 5/18*b**4 + 0 - 5*b**2 - 2*b + 1/90*b**5. Let k(c) be the first derivative of u(c). Factor k(z).
2*(z + 5)**2/3
Let y(q) be the third derivative of q**7/1365 + 41*q**6/780 + 4*q**5/39 - 956*q**2. Solve y(u) = 0.
-40, -1, 0
Let f(s) be the first derivative of s**6/12 - s**5 + 13*s**4/8 + 16*s**3/3 - 17*s**2 + 16*s + 9695. What is u in f(u) = 0?
-2, 1, 2, 8
Let h(l) be the third derivative of -12308679*l**6/160 + 110889*l**5/40 - 333*l**4/8 + l**3/3 - 17*l**2 - 30*l. Factor h(d).
-(333*d - 2)**3/4
Factor 4/7*j**2 + 0 - 36*j.
4*j*(j - 63)/7
Let h(u) = 7*u**2 - 922*u + 5. Let i(l) = -8*l**2 + 932*l - 6. Let n(g) = -6*h(g) - 5*i(g). Determine o so that n(o) = 0.
0, 436
Let p be (-6 + (-7 - (-1 + -9)))*7/(-42). Solve p*s**5 - s**2 + 1/2*s**4 - s**3 + 1/2 + 1/2*s = 0.
-1, 1
Let s be 6 - (6 + (-72)/27). Let c be (2 - (-36)/(-21))/((-30)/(-70)). Suppose 0*i**4 - 4/3*i**2 + s*i**3 + 4/3 - c*i**5 - 2*i = 0. What is i?
-2, -1, 1
Let g = 0 + 0. Suppose 0 = -59*l + 189 - 75 + 4. Factor -2/21*y**5 - 4/21*y**4 + 0 + 0*y**l - 2/21*y**3 + g*y.
-2*y**3*(y + 1)**2/21
Let k = 44883 + -8976599/200. Let g(c) be the third derivative of -7/100*c**5 - k*c**6 + 2 - 1/5*c**4 - 6*c**2 + 8/5*c**3 + 0*c. Determine u so that g(u) = 0.
-4, 1
Let x(f) be the third derivative of -13/24*f**4 + 0*f - 62*f**2 + 1/4*f**3 + 0 + 23/120*f**5. Factor x(q).
(q - 1)*(23*q - 3)/2
Suppose 50 = -3*z + 4*o, -z + 28*o = 32*o + 22. Let d be z/171 + (-230)/(-380). Find p such that 1/4*p - d - 1/