h) be the first derivative of o(h). Find j, given that i(j) = 0.
-26, 0
Let f(d) be the first derivative of -d**8/13440 + d**6/960 - d**5/480 - 13*d**3/3 + 2*d + 166. Let h(x) be the third derivative of f(x). Factor h(g).
-g*(g - 1)**2*(g + 2)/8
Let g = -11 - -40. Suppose -3*f - q + 434 = 0, -14*q - 578 = -4*f - 15*q. Factor 32*k - 27*k + k**2 - g*k + f.
(k - 12)**2
Let l(b) be the first derivative of -11*b**6/90 + 7*b**5/15 - b**4/2 - 34*b**3 - 14. Let h(v) be the third derivative of l(v). Suppose h(n) = 0. Calculate n.
3/11, 1
Let i be 34/(-221) - 4*(-118)/1716. Let x(l) be the first derivative of 0*l**2 + 1/22*l**4 - 15 - i*l**3 - 1/33*l**6 + 4/55*l**5 + 0*l. What is y in x(y) = 0?
-1, 0, 1, 2
Let k = -422/23 + 3844/207. Find y, given that -2/9*y**2 - k*y**5 + 2/9*y**3 + 2/9*y**4 + 0 + 0*y = 0.
-1, 0, 1
Let l be 177/(-59) - (-14)/4. Suppose 40*z - 29 = 51. Factor 3/2*c - l - c**z.
-(c - 1)*(2*c - 1)/2
Factor 448/9*w - 2/9*w**2 - 296/3.
-2*(w - 222)*(w - 2)/9
Let j(i) be the first derivative of -2*i**3/3 - 1123*i**2 - 4484*i - 7765. Factor j(t).
-2*(t + 2)*(t + 1121)
What is l in 2/5*l**4 - 18 - 92/5*l**3 + 92/5*l + 88/5*l**2 = 0?
-1, 1, 45
Let q(z) be the second derivative of 9*z**7/70 + 59*z**6/50 + 291*z**5/100 - 39*z**4/20 - 63*z**3/5 + 1390*z - 1. Solve q(w) = 0 for w.
-3, -14/9, 0, 1
Let m(j) be the first derivative of -4/3*j**3 - 10 + 0*j + 2*j**2 + 1/4*j**4. Factor m(v).
v*(v - 2)**2
Let s(d) = -d**2 - d + 1. Suppose 22 = -29*m + 40*m. Let q(h) = -h**3 + 13*h**2 + 32*h + 21. Let t(a) = m*q(a) - 6*s(a). Find r such that t(r) = 0.
-1, 18
Suppose o - 1 = -2*c, 825 = -45*c - o + 955. Suppose -12/13*i + 0 + 2/13*i**2 - 2/13*i**4 + 12/13*i**c = 0. Calculate i.
-1, 0, 1, 6
Let o(f) be the first derivative of f**5/15 - 3*f**4/2 + 2*f**2 + 2*f + 42. Let w(z) be the second derivative of o(z). Let w(d) = 0. Calculate d.
0, 9
Let b be (-2)/(-8) - 3/(36/(-57)). Suppose 5*g = -b*d + 660, -4*g + 125 = -3*d - 403. Factor 160*r - 9*r**4 + 40*r**3 - g*r**2 - 25 - 39 + 5*r**4.
-4*(r - 4)**2*(r - 1)**2
Let r(p) be the second derivative of p**6/6 - 9*p**5/4 + 15*p**4/2 + 10*p**3/3 - 60*p**2 + 1020*p. Suppose r(l) = 0. Calculate l.
-1, 2, 6
Find c, given that 0 - 26/17*c**2 - 14/17*c**3 + 2/17*c**5 + 2/17*c**4 - 12/17*c = 0.
-2, -1, 0, 3
Let p(w) = w**4 + w**3 - w + 1. Let m be (2/(4/(-2)))/(2/72). Let x = m - -40. Let b(n) = 6*n**3 + 14*n**2 + 6*n + 2. Let q(v) = x*p(v) - 2*b(v). Factor q(k).
4*k*(k - 4)*(k + 1)**2
Let f(k) be the third derivative of -k**7/70 + k**6/5 - 6*k**5/5 + 4*k**4 - 8*k**3 + 3*k**2 + 198. Factor f(m).
-3*(m - 2)**4
Let c = -464121 + 464121. Factor 1/5*i**5 + c + 0*i + 7/5*i**3 + i**4 + 3/5*i**2.
i**2*(i + 1)**2*(i + 3)/5
Let x = -191 + 193. What is u in 56*u**x + 204*u**2 + 40*u - 245*u**4 - 5894*u**3 + 6244*u**3 = 0?
-2/7, 0, 2
Suppose 485*k - 449*k - 144 = 0. Let r(w) be the second derivative of 0 + 12*w - 2/15*w**3 + 0*w**2 + 1/30*w**k. Factor r(j).
2*j*(j - 2)/5
Let s(x) be the third derivative of x**7/42 - 9*x**6/4 + 90*x**5 - 1980*x**4 + 25920*x**3 + x**2 + 13. Factor s(g).
5*(g - 18)*(g - 12)**3
Suppose -56 = r + 5*k, -70*r + 73*r = 2*k + 36. Let 11/3*g**r - 155/3*g**2 + 16*g - 95/6*g**3 - 1/6*g**5 + 48 = 0. What is g?
-2, -1, 1, 12
Let x(w) be the second derivative of -w**4/3 + 32*w**2 + 716*w + 1. Factor x(r).
-4*(r - 4)*(r + 4)
Factor -2213*m - 492 + 9/2*m**2.
(m - 492)*(9*m + 2)/2
Let k be 8/3 + 0 + 828/(-1242). Determine p so that 60*p + 176*p**k + 121/3*p**3 + 16/3 = 0.
-4, -2/11
Let y(u) be the second derivative of -2/75*u**6 + 2/5*u**4 + 12/5*u**3 - 2 - 25*u + 0*u**2 - 11/50*u**5 + 1/105*u**7. Factor y(f).
2*f*(f - 3)**2*(f + 2)**2/5
Suppose 2*s - 49 + 35 = 5*b, 16 = 9*s + b. Find y such that 0 - 2/3*y - 2/9*y**3 - 8/9*y**s = 0.
-3, -1, 0
Suppose -f + f = 3*f + 3*f. Determine y, given that 0*y + 2/5*y**3 + f + 0*y**2 - 1/5*y**4 = 0.
0, 2
Let o = 97 - 95. Suppose -o*d + d - 3*d**2 + 5*d - 7*d = 0. Calculate d.
-1, 0
Let s be 19/42 + 220/(-1320). Let h(b) be the first derivative of 0*b + 0*b**2 - 17 + 12/35*b**5 - 15/28*b**4 + s*b**3 - 1/14*b**6. Factor h(r).
-3*r**2*(r - 2)*(r - 1)**2/7
Let t(v) be the first derivative of 3*v**5/20 - 3*v**4/2 + 23*v**3/4 - 21*v**2/2 + 9*v - 785. What is u in t(u) = 0?
1, 2, 3
Let v(l) = 3*l**2 - 2*l - 2. Let i be v(-2). Suppose 30*p**5 - 14*p**5 - i*p**3 - 4*p**4 + 0*p**2 + 2*p**2 - 14*p**5 - 10*p**2 = 0. Calculate p.
-1, 0, 4
Let t(n) = 2*n**2 + 13*n + 28. Let r be t(-6). Suppose 4*c = -5*p - 2 - 4, -r = -3*p + 4*c. Find z, given that p*z - 3*z + 3*z**2 + 5*z + 8*z + 9 = 0.
-3, -1
Suppose -13*i + 24 + 15 = 0. Factor w**i + 15*w**2 + 313*w + 4*w**3 - 333*w - 60.
5*(w - 2)*(w + 2)*(w + 3)
What is r in -345/2*r**2 - 336 + 507*r + 3/2*r**3 = 0?
1, 2, 112
Let t(x) be the second derivative of -13*x**4/48 + 37*x**3/2 - 17*x**2/2 - 1828*x. Factor t(j).
-(j - 34)*(13*j - 2)/4
Suppose 22 = 5*o + 7. Suppose 21 = 5*j + 3*p, -6*j = -3*j + 4*p - 17. Factor -j*d**2 + d**3 + 11*d**2 + 3*d**o + 0*d**3.
4*d**2*(d + 2)
Let s(z) be the third derivative of 5*z**8/48 + 107*z**7/42 - 41*z**6/12 - 8*z**5/3 + 4185*z**2. What is u in s(u) = 0?
-16, -2/7, 0, 1
Let f = 55/589 - -343701/2945. Let s = f - 115. Suppose 3 + s*x**2 - 48/5*x = 0. Calculate x.
1/3, 5
Determine f, given that -55 - 3*f**2 + 31*f + 123*f + 92*f + 594 + 1330 = 0.
-7, 89
Let g be 0*13/104 - (-1574)/2. Let a = -787 + g. Factor a + 0*w - 1/2*w**2 + 1/10*w**3.
w**2*(w - 5)/10
Factor -16665*l + 345*l**4 - 8597*l**2 + 25927*l**2 - 3629*l**3 + 6*l**5 + 5445 - 2821*l**3 - 11*l**5.
-5*(l - 33)**2*(l - 1)**3
Factor 3/7*h**2 - 36/7*h + 60/7.
3*(h - 10)*(h - 2)/7
Let z(i) be the first derivative of i**5 + 355*i**4/2 + 5425*i**3/3 + 4370*i**2 + 4020*i + 6975. Factor z(j).
5*(j + 1)**2*(j + 6)*(j + 134)
Let o(v) be the third derivative of -76*v**2 + 63/2*v**7 + 39/4*v**5 + 10/3*v**3 - 63*v**6 + 0 + 0*v + 85/6*v**4. Let o(j) = 0. Calculate j.
-2/21, 1/3, 1
Suppose 2*c = -4*s + 18, -s = -22*c + 28 + 80. Let y(j) be the third derivative of 0*j - 2/105*j**c + 2/7*j**3 + 0 - 19*j**2 + 5/84*j**4. Solve y(a) = 0 for a.
-3/4, 2
Let w(o) = -o**4 - 3*o**3 - o**2 + o - 1. Let l(k) = k**4 + 53*k**3 + 301*k**2 + 619*k + 446. Let h(s) = -l(s) + 4*w(s). Solve h(d) = 0.
-5, -3, -2
Suppose 8*l - 3*l = 5*b + 140, -4*b - 88 = -3*l. Suppose l*o - 15 = 21*o. Let -5/2*p**3 + 1/4*p**5 - 1 - 15/4*p + 0*p**4 - o*p**2 = 0. Calculate p.
-1, 4
Let s(i) = -32*i**2 + 10674*i - 7104. Let g(v) = 28*v**2 - 10672*v + 7104. Let l(r) = -5*g(r) - 4*s(r). Factor l(y).
-4*(y - 888)*(3*y - 2)
Suppose -3*d + 18 = 3*o, -2*o - 3 = 3*d - 19. Suppose -5*w - 10 = -5*y - w, 8 = d*y - 4*w. Suppose 6*k**y - 47 + 2*k**3 + 12*k**2 - 3 + 30*k = 0. Calculate k.
-5, 1
Suppose -39*w = -35*w - 1616. Let k = w + 236. Factor -z**4 + 28*z**2 + 358 - k*z + 3*z**4 + 308*z**2 - 46*z**3 - 1382.
2*(z - 8)**3*(z + 1)
Let j(n) be the second derivative of -1/15*n**6 + 1 - 4/9*n**4 - 1/3*n**2 + 31*n + 7/30*n**5 + 1/2*n**3 + 1/126*n**7. Find u, given that j(u) = 0.
1, 2
Let c(l) = 15*l**3 - 125*l**2 + 955*l - 2010. Let o(x) = -17*x**3 + 124*x**2 - 961*x + 2012. Let y(k) = -6*c(k) - 5*o(k). Factor y(a).
-5*(a - 16)*(a - 5)**2
Suppose 12*g = 2*g - 10. Let f(i) = 3*i**5 - 9*i**4 + 2*i**3 + 8*i**2 - 4*i - 8. Let m(t) = -t**3 + 2*t**2 - t - 2. Let q(n) = g*f(n) + 4*m(n). Factor q(b).
-3*b**3*(b - 2)*(b - 1)
Let k be 2/(3/(6 + 3)). Let y be 3/((-6 - (-6 + 3)) + k). Find v, given that 6*v + 5*v - 2*v**3 - 3*v**4 + 4*v**2 - y + 0*v - 9*v = 0.
-1, 1/3, 1
Factor 15*i**2 - i**2 + 102 + 38*i + 30 - 16*i**2.
-2*(i - 22)*(i + 3)
Let o(b) = -b**2 - 13*b - 36. Let j = -73 + 65. Let u be o(j). Factor 2*k + 2*k + 5*k**3 - k**u - 8*k**2 + 0*k**2 + 0*k**4.
-k*(k - 2)**2*(k - 1)
Let m = -48 - -73. Let i(c) = 8*c + 3. Let x be i(1). Find j such that 21*j**2 - x*j - m*j**2 - j - 8 = 0.
-2, -1
Determine j so that -4/5*j**4 + 0 + 176/5*j**2 + 4/5*j**3 - 336/5*j = 0.
-7, 0, 2, 6
Let g = -55 + 57. Let x(r) = -5*r**2 + 36*r - 52. Let o(i) = -i**2 + 12*i - 17. Let m(p) = g*x(p) - 7*o(p). Factor m(f).
-3*(f - 1)*(f + 5)
Suppose 50*p + 5740 = 43*p. Let g = 823 + p. Let 3/5*z**2 + 3/5*z**g - 12/5 - 12/5*z = 0. Calculate z.
-2, -1, 2
Let u(j) = -j**2 + 3. Let d be u(0). Factor -15*y**3 - 6*y**4 + 3*y**d - 2*y**5 - 4*y**4.
-2*y**3*(y + 2)*(y + 3)
