ird derivative of o**5/15 + 13*o**4/6 + 24*o**3 - 520*o**2. Factor x(m).
4*(m + 4)*(m + 9)
Let u be (523 - 83)/(-1 + 3 + -1). Determine o, given that -u*o + 4900 + 4780 - o**2 + 6*o**2 = 0.
44
Let x = -1652907 + 8264538/5. Let 387/5*y**2 + x*y**3 + 16641/5*y + 238521/5 = 0. What is y?
-43
Let p(z) = -4*z**2 - 2502*z - 4986. Let g be p(-2). Determine d so that -2/7*d**g - 156/7*d - 3042/7 = 0.
-39
Let m be 516/(-13760)*256/(-72). Let 0 - 38/5*a + m*a**2 = 0. What is a?
0, 57
Let l(q) = q**4 + q**3 + q - 1. Let x(p) = 10*p**2 - 12*p**2 + 6*p - 6 + 8*p**4 + 6*p**2. Let k(w) = 6*l(w) - x(w). Factor k(i).
-2*i**2*(i - 2)*(i - 1)
Let i = 823 + -37034/45. Let a(l) be the second derivative of 0*l**2 + 1/15*l**5 + 0*l**3 + 0 - 1/18*l**4 + 29*l - i*l**6. Determine x, given that a(x) = 0.
0, 1
Suppose -255*g + 114*g = -564. Let c(n) be the third derivative of 7/54*n**g + 1/270*n**5 - 18*n**2 + 0 + 49/27*n**3 + 0*n. Factor c(s).
2*(s + 7)**2/9
Suppose -3 = 3*l, -5 = -3*z - 2*l + 8. Suppose 0 = 2*c + 4*u + 12, -z*c - 5*u - 12 = 3. Factor 0*q**2 - 9/7*q**4 - 15/7*q**5 + 0*q + 6/7*q**3 + c.
-3*q**3*(q + 1)*(5*q - 2)/7
Let x(t) be the second derivative of -t**4/12 + 53*t**3/3 + 108*t**2 + 1160*t. Find j, given that x(j) = 0.
-2, 108
Factor 4/5*j**3 - 144/5 - 52/5*j**2 + 32*j.
4*(j - 9)*(j - 2)**2/5
Let p(x) = -4*x**2 + 21*x + 23. Let a be p(6). Find f, given that -234 - 17*f**2 + a*f**2 - 4*f**3 + 250 = 0.
-2, 1
Suppose 5*m - 40 = -5*x, 6*m - 4*m = 4*x - 14. Factor -x + 1/2*k**3 + 3/2*k + 3*k**2.
(k - 1)*(k + 2)*(k + 5)/2
Let t(f) be the second derivative of 6 - 29/2*f**3 + 1/4*f**4 + 42*f**2 - 2*f. Suppose t(n) = 0. Calculate n.
1, 28
Let m(b) be the third derivative of 1/8*b**4 + 91*b**2 + 1/80*b**5 + 3/8*b**3 + 0 + 0*b. Factor m(f).
3*(f + 1)*(f + 3)/4
Factor -3/2*c**3 + 1512 + 93/2*c**2 - 468*c.
-3*(c - 12)**2*(c - 7)/2
Factor 60010*s + 21997 + 300*s**3 - 8170*s + 100*s**3 + 83843 - 5*s**4 + 8280*s**2.
-5*(s - 98)*(s + 6)**3
Let h = -19 + 22. Determine u so that 6*u**h + 4*u**2 - 1 - 9 - 2*u**5 + 10 = 0.
-1, 0, 2
Let i(j) be the first derivative of 1/26*j**4 + 67 + 16/13*j**2 + 0*j - 16/39*j**3. Factor i(n).
2*n*(n - 4)**2/13
Let f(m) = m**3 - 47*m**2 - 771*m - 538. Let c be f(60). Let 2/9*i**3 - 242/9 + 286/9*i - 46/9*i**c = 0. What is i?
1, 11
Let j be (1080/378)/(900/756). Let j*d + 0*d**3 - 2/5*d**4 + 14/5*d**2 + 0 = 0. Calculate d.
-2, -1, 0, 3
Let q = 6851 - 6849. Let l(i) be the second derivative of 8/7*i**q + 0*i**3 + 0 - 1/21*i**4 + 25*i. Factor l(h).
-4*(h - 2)*(h + 2)/7
Let y = 16973 - 16970. Let x(g) be the third derivative of -1/180*g**5 + 0*g**y + 0 + 1/24*g**4 + 0*g - 18*g**2. Solve x(k) = 0.
0, 3
Let s(u) = 647*u - 3867. Let c be s(6). Let w(z) be the second derivative of -1/30*z**4 + 2/15*z**3 + 1/75*z**6 - 1/25*z**5 - c*z + 0 + 0*z**2. Factor w(t).
2*t*(t - 2)*(t - 1)*(t + 1)/5
Let d be (-12816)/2403*(-1 + -1 - (-8)/7). Solve -d*w - 128/21*w**2 - 6/7 = 0.
-3/8
Let h(b) be the third derivative of 49/12*b**8 + 0 - 82*b**2 - 72/5*b**5 - 224/15*b**7 + 9/2*b**4 + 0*b**3 + 21*b**6 + 0*b. Let h(k) = 0. Calculate k.
0, 3/7, 1
Let o(r) be the third derivative of -r**5/36 + 95*r**4/9 - 755*r**3/18 - 4*r**2 + 35*r. Factor o(p).
-5*(p - 151)*(p - 1)/3
Let l(t) be the first derivative of 2*t**3/3 - 127*t**2 + 500*t - 1761. Suppose l(w) = 0. What is w?
2, 125
Let c(r) be the first derivative of 2*r**3/15 + 39*r**2/5 + 496*r/5 + 7780. Let c(l) = 0. What is l?
-31, -8
Let n = 3297 + -3295. Let j(t) be the first derivative of 0*t + 3*t**3 + 3/2*t**4 + 1/5*t**5 - 10 + 2*t**n. Solve j(y) = 0 for y.
-4, -1, 0
Let l(n) = 7*n**2 + n. Let o(y) be the second derivative of 13*y**4/12 + y**3/6 - y**2/2 - 76*y. Let f(d) = -11*l(d) + 6*o(d). Factor f(g).
(g - 6)*(g + 1)
Let v = -60301/7 + 180917/21. Let -v*o**4 - 40/3*o**3 - 512/3 - 640/3*o - 88*o**2 = 0. Calculate o.
-8, -2
Let h(m) be the third derivative of -m**6/120 - m**5/8 - 3*m**4/4 + 89*m**3/6 - 9*m**2. Let b(d) be the first derivative of h(d). Suppose b(i) = 0. Calculate i.
-3, -2
Factor 2*a**3 - 5*a**3 - 25*a - 195*a**2 - 44*a + 150 + 117*a**2.
-3*(a - 1)*(a + 2)*(a + 25)
Let o = 49652 + -49650. Let -9/2 + 3*f**o + 3/4*f**3 + 3/4*f = 0. What is f?
-3, -2, 1
Suppose 8*g - 3*g - 4*u - 908 = 0, 2*g = 2*u + 364. Suppose -3*x = -9*x + g. Determine i, given that -12 - 19 - 5*i**2 + x*i - 14 = 0.
3
Suppose -80 = -46*y + 42*y. Let m be ((-4)/22)/(3*y/(-165)). Suppose -8 - 4*r - m*r**2 = 0. Calculate r.
-4
Suppose -3*q + j + 31 = 0, 3*j - 2 = -2*q + 15. Find y, given that 12 + q*y - 1/2*y**3 + y**2 = 0.
-2, 6
Let u(z) be the first derivative of -z**4/4 - 870*z**3 - 1135350*z**2 - 658503000*z + 7861. Determine r so that u(r) = 0.
-870
Let d(y) be the third derivative of 0*y + 1/72*y**4 - 1/360*y**6 + 0 - 2/9*y**3 + 1/45*y**5 - 20*y**2. Let d(t) = 0. What is t?
-1, 1, 4
Factor 1 + 7 - 128*g**2 + 60*g**2 - 9*g + 69*g**2.
(g - 8)*(g - 1)
Let k(o) be the third derivative of 17*o**6/10 - 79*o**5/15 + 4*o**4 + 8*o**3/3 - 4*o**2 - 111. Factor k(x).
4*(x - 1)*(3*x - 2)*(17*x + 2)
Let f(q) be the first derivative of 0*q**2 - 72 - 1/5*q**3 + 0*q - 3/20*q**4. Factor f(a).
-3*a**2*(a + 1)/5
Let f be (-23 + -11 + 34)/3. Let f*c**2 + 0 + 8/9*c**3 - 4/9*c + 0*c**4 - 4/9*c**5 = 0. What is c?
-1, 0, 1
Let p(k) = 10*k**4 - 2*k**3 + 23*k**2 - 223*k - 180. Let m(x) = -5*x**4 - x**3 - 11*x**2 + 111*x + 90. Let y(v) = -13*m(v) - 6*p(v). Factor y(g).
5*(g - 2)*(g + 1)*(g + 3)**2
Let x be (-18)/21 + 1643/651. Let w = x - -25/21. Suppose -w*p + 4/7*p**3 + 12/7*p**2 - 4/7*p**4 + 8/7 = 0. Calculate p.
-2, 1
Let r(b) = -3*b**2 - 133*b - 150. Let p(y) = y**2 + 27*y. Let z(k) = 20*p(k) + 5*r(k). Factor z(o).
5*(o - 30)*(o + 5)
Suppose 0 = b + 4*n + 45, b + 23 = 6*n + 98. Factor -4/3*u**b - 20*u + 28/3 + 12*u**2.
-4*(u - 7)*(u - 1)**2/3
Let c be 7/(-294)*(-36)/6. Let i be (-3 - (-33)/9)/((-1)/(-6)). Determine w, given that 5/7*w - 2/7 + 1/7*w**i - 3/7*w**2 - c*w**3 = 0.
-2, 1
Suppose 40 = 43*c - 48*c. Let b be c/(-28) + (-1674)/(-21). Factor 66*v + v**2 + 4*v**2 - 26*v + b.
5*(v + 4)**2
Let s(l) be the second derivative of l**6/240 - 9*l**5/160 - 31*l**4/48 - 9*l**3/4 - 7*l**2/2 + 5086*l. Suppose s(p) = 0. Calculate p.
-2, -1, 14
Let b(h) = -5*h**3 + 27*h**2 + 29*h - 53. Let f(x) = -7*x**3 + 26*x**2 + 33*x - 60. Let c(z) = 6*b(z) - 5*f(z). Find t, given that c(t) = 0.
-6, -1, 3/5
Let y be (-3)/(((-27)/6)/3). Let h be 3/(-1170)*-10*1080/20. Solve 80/13*i**y + h + 24/13*i**3 + 6*i = 0.
-3/2, -1/3
Let q(n) = -4*n - 6*n + 0 + 12*n - 18. Let i be q(7). Let h(g) = g - 1. Let z(u) = 16*u**3 + 24*u**2 + 11*u - 2. Let f(b) = i*h(b) + 2*z(b). Factor f(r).
2*r*(4*r + 3)**2
Let u(q) be the second derivative of -5/18*q**3 - 1/72*q**4 - 26*q - 1 + 0*q**2. Determine f so that u(f) = 0.
-10, 0
Suppose 5*k - 60*n = -62*n + 97, -3*k + 75 = 4*n. Let f(h) be the first derivative of -h**3 + 3/2*h**2 - k + 0*h. Determine i, given that f(i) = 0.
0, 1
Suppose -938515*o + 102 = -938464*o. Find r such that -22/9*r + 4/3 + 2/3*r**o = 0.
2/3, 3
Let y be ((-110)/(-440))/((-189)/(-2352)). Find t such that 2/9*t**2 + 0 - y*t = 0.
0, 14
Let h(w) = w**2 - 8*w - 55. Let i(n) = -3*n - 27. Let k(l) = -3*h(l) + 5*i(l). Factor k(c).
-3*(c - 5)*(c + 2)
Let n(x) be the third derivative of -x**5/90 + 305*x**4/18 - 93025*x**3/9 + 160*x**2 + x. Factor n(o).
-2*(o - 305)**2/3
Let d(a) be the first derivative of a**6/90 - 2*a**5/5 + 2*a**2 + 8*a - 141. Let n(g) be the second derivative of d(g). Let n(o) = 0. Calculate o.
0, 18
Suppose 8*c = -1000 + 1016. Let g(r) be the first derivative of -r**c + 16 + 12/7*r + 2/21*r**3. Factor g(m).
2*(m - 6)*(m - 1)/7
Let f(m) be the second derivative of 3*m**5/20 - 9*m**4/4 - 32*m**3 - 126*m**2 + m + 45. Factor f(k).
3*(k - 14)*(k + 2)*(k + 3)
Factor 289485*d**2 - 144741*d**2 - 870 + 175*d - 144749*d**2.
-5*(d - 29)*(d - 6)
Let o(j) be the first derivative of -3*j**4/8 - 26*j**3 - 441*j**2/4 + 1436. Let o(c) = 0. What is c?
-49, -3, 0
Let v(h) be the third derivative of h**6/24 + 35*h**5/12 + 1715*h**4/24 + 1715*h**3/2 - 2*h**2 - 8*h. Find l, given that v(l) = 0.
-21, -7
Let r(f) = -5*f**2 - 90*f - 2. Let b(z) = -10*z**2 - 190*z - 5. Let p(o) = 2*b(o) - 5*r(o). Determine k so that p(k) = 0.
-14, 0
Let x(w) be the third derivative of -w**5/270 - 16