l**2 + l**4 - 782*l.
(l - 22)**2*(l - 6)*(l + 1)
Let m = 15016 + -15004. Let i(l) be the first derivative of 0*l**2 - 2/9*l**6 - m - 2/3*l**4 + 0*l**3 + 0*l + 4/5*l**5. Factor i(r).
-4*r**3*(r - 2)*(r - 1)/3
Let o(q) = 489*q + 1959. Let n be o(-4). Suppose -4*y - 2*m + 168 = 0, 172 = 4*y + 7*m - 3*m. Factor 43 + y*g**n + 28*g**2 - 4*g**2 + 4*g + 15*g**4 - 43.
g*(g + 2)*(3*g + 1)*(5*g + 2)
Let o(i) be the third derivative of i**6/60 - 329*i**5/540 - 245*i**4/216 - 19*i**3/27 + i**2 + 18. Factor o(s).
(s - 19)*(2*s + 1)*(9*s + 2)/9
Suppose 3*m = -91 + 79. Let b be (20/(-15))/(m/6). Factor -q**3 + 2*q**3 + 7*q**5 - 2*q**5 + b*q**4 - 2*q**2 - 6*q**5.
-q**2*(q - 2)*(q - 1)*(q + 1)
Let j(c) = -2*c**2 - 21*c + 13. Let f be j(-11). Suppose -m = f*m - 3*o - 18, -2*o = 2*m - 4. Find g, given that g**3 + g**5 + 34*g**4 - 20*g**m - 16*g**4 = 0.
0, 1
Let y(a) = 26*a**2 + 8782*a + 9653630. Let s(n) = -4*n**2 + n - 2. Let t(f) = 6*s(f) + y(f). Find l such that t(l) = 0.
-2197
Suppose -3*u = 2*g - 12, -3*u - g = 2*u - 13. Solve 26*r - 16*r + 28 - 5*r**2 + 3*r**u = 0.
-2, 7
Let k = 517/10080 + -9/224. Let s(o) be the second derivative of -10*o + 0 + k*o**4 - 2/15*o**3 + 1/3*o**2. Suppose s(u) = 0. What is u?
1, 5
Let b be 26108/(-1098) + ((-22)/18 - -1). Let w be 152/b - 0 - -7. Factor -14/3*z**3 + 32/3*z**2 + 0 + w*z**4 - 8*z.
2*z*(z - 3)*(z - 2)**2/3
Let x(i) be the third derivative of -1/960*i**6 + 61*i**2 + 1/96*i**5 + 0*i + 0*i**3 - 1/48*i**4 + 0. Factor x(a).
-a*(a - 4)*(a - 1)/8
Let x(n) be the first derivative of 9/5*n**2 - 18 + n**3 + 1/50*n**5 + 2*n + 7/30*n**4. Let c(p) be the first derivative of x(p). What is k in c(k) = 0?
-3, -1
Let y(k) be the second derivative of -26*k**6/105 - 31*k**5/7 + 8*k**4 + 3802*k. Find a, given that y(a) = 0.
-168/13, 0, 1
Let n(k) = k**3 + 26*k**2 + 33*k + 23. Let p(m) = -4*m + 24. Let j be p(12). Let f be n(j). Factor -383*r**2 + f*r**2 - 4*r**5.
-4*r**5
Let h(p) = p**3 + p**2 - 1. Let d(w) = 21*w**3 - 24*w**2 - 93*w - 66. Suppose -13*l = -6 - 7. Let q(z) = l*d(z) - 18*h(z). Factor q(u).
3*(u - 16)*(u + 1)**2
Let w(g) be the first derivative of -5*g**4/4 - 310*g**3/3 - 835*g**2/2 + 2950*g + 8378. Factor w(s).
-5*(s - 2)*(s + 5)*(s + 59)
Let c(n) be the first derivative of 2*n**5/15 + 20*n**4/3 + 76*n**3/3 + 112*n**2/3 + 74*n/3 + 648. Solve c(k) = 0 for k.
-37, -1
Let i be (-11)/(-66) - (-10)/12. Let m be (0/(-5))/(i + 1) - 0. Factor 1/4*r**2 - 5/8*r**3 + 0 + m*r - 1/8*r**5 + 1/2*r**4.
-r**2*(r - 2)*(r - 1)**2/8
Let r(v) = -5*v**4 - 10*v**3 - 21*v**2 - 20*v - 1. Let a(d) = 793*d**4 - 6*d + 28*d + 10*d**3 + 22*d**2 - 787*d**4. Let y(w) = -3*a(w) - 4*r(w). Factor y(t).
2*(t + 1)**3*(t + 2)
Let t(h) = 2*h**3 + 34*h**2 - 147*h - 2497. Let d be t(-17). Solve 2/9*r**d + 1682/9 - 116/9*r = 0 for r.
29
Let d(q) be the third derivative of -q**8/20160 + q**6/720 - 89*q**5/60 + 4*q**2 - 7. Let w(o) be the third derivative of d(o). Suppose w(l) = 0. What is l?
-1, 1
Let u be (-2)/(-6) + -2*(-715)/30. What is w in -1 - 46*w + 3*w**2 + u*w - 4*w**2 = 0?
1
Let b(y) be the third derivative of -y**6/200 + 3*y**5/20 + 9*y**4/5 + 38*y**3/5 - 35*y**2 - 13*y. Factor b(d).
-3*(d - 19)*(d + 2)**2/5
Let -109 - 44 - 110 - 60 - 324*v - 332*v**2 + 331*v**2 = 0. What is v?
-323, -1
Suppose -13860729/5*y - 3/5*y**3 - 5733721563/5 - 11169/5*y**2 = 0. Calculate y.
-1241
Let k(q) be the second derivative of -20/3*q**3 + 5/12*q**4 + 40*q**2 + 0 - 280*q. Factor k(p).
5*(p - 4)**2
Solve 0 - 80/3*f + 1/3*f**2 = 0.
0, 80
Factor 30*z**4 - 15 - 14*z**4 - 8*z**4 + 5*z**5 + 15*z + 10*z**2 + 10*z - 3*z**4 - 30*z**3.
5*(z - 1)**3*(z + 1)*(z + 3)
Let b(n) be the third derivative of n**5/140 - 53*n**4/56 - 55*n**3/7 - 2616*n**2. Let b(m) = 0. Calculate m.
-2, 55
Let x(i) be the third derivative of i**5/390 + 563*i**4/78 + 316969*i**3/39 + 5*i**2 + 241. Factor x(w).
2*(w + 563)**2/13
Factor 0*d**2 - 55/2*d**3 + 5/2*d**5 - 25*d**4 + 0*d + 0.
5*d**3*(d - 11)*(d + 1)/2
Let y = -2930 + 43931/15. Let h = y - -391/285. Let -6/19*l + 4/19 + 0*l**2 + h*l**3 = 0. What is l?
-2, 1
Suppose -x + 3*x = 3*a + 20, -2*x = 2*a. Suppose 3*f + 0*s = s + 3, -4*s + 8 = -2*f. Factor 3 - x*j - 4*j + 9*j**f - j - 3*j**3.
-3*(j - 1)**3
Let c(n) = 71*n**3 - 5*n**2 - 346*n - 270. Let w(u) = -11*u**3 + u**2 + 57*u + 45. Let j(a) = -6*c(a) - 39*w(a). Suppose j(l) = 0. What is l?
-5, -1, 9
Determine m so that 152/3*m**2 - 40/3 - 112/3*m**4 + 28*m - 32*m**3 + 4*m**5 = 0.
-1, 1/3, 1, 10
Let x = 175766 + -175766. Find l, given that 28/9*l**3 + 2/9*l**4 + x + 0*l - 10/3*l**2 = 0.
-15, 0, 1
Let g be ((-282)/60 + 3)*-5 + -5 + -3. Determine u, given that 0 + 0*u - g*u**2 = 0.
0
Let j = -34 + 44. Suppose 4 = -2*v + j. Solve 403 - 407 + 7*o - o - 2*o**v = 0.
-2, 1
Let l(r) be the first derivative of r**4/12 - 16*r**3/9 + 10*r**2 + 12864. What is z in l(z) = 0?
0, 6, 10
Let 2/9*t**5 - 17/9*t**4 + 0*t + 22/9*t**3 + 0 - 7/9*t**2 = 0. Calculate t.
0, 1/2, 1, 7
Let u(t) = 66599*t**2 - 900*t + 1. Let b(v) = 332993*v**2 - 4503*v + 4. Let c(x) = 2*b(x) - 11*u(x). Let c(j) = 0. What is j?
1/149
Let o(b) be the second derivative of 1/30*b**5 + 1/30*b**4 + 21*b + 1/225*b**6 + 0*b**2 + 0*b**3 - 5 - 1/315*b**7. What is y in o(y) = 0?
-1, 0, 3
Factor 0*g + 0 + 0*g**2 + g**5 + 33*g**3 + 133/2*g**4.
g**3*(g + 66)*(2*g + 1)/2
Suppose 15 = 19*h - 16*h, -5*u - 2*h + 65 = 0. Suppose -u*j + 266 = 233. Solve -1/2*a**4 - 1/3*a**5 + 1/6*a + 0 + 1/6*a**j + 1/2*a**2 = 0.
-1, -1/2, 0, 1
Let w be 1/(-3 + 35/10). Suppose 0*r - 26 = -r + 2*c, 3*r = w*c + 74. Factor -10 + 0*x - 56*x**2 - 4*x**5 + 26*x + 18*x + 4*x**4 - 2 + r*x**3.
-4*(x - 1)**4*(x + 3)
Let v(d) be the first derivative of -1/9*d**3 + 46/3*d**2 + 3 - 2116/3*d. Find w such that v(w) = 0.
46
Let n(f) be the first derivative of -605*f**3/3 - 85800*f**2 - 12168000*f - 7972. Find l, given that n(l) = 0.
-1560/11
Let h = 464 - 450. Suppose 103*a - h = 96*a. Factor 3*c**a + 0*c + 0 + 3/2*c**3.
3*c**2*(c + 2)/2
Let r be (-64)/(-320) - 44/(-30). Suppose p**3 + 2/3*p + 0 + r*p**2 = 0. Calculate p.
-1, -2/3, 0
Let m(v) be the second derivative of -v**5/4 - 25*v**4/3 - 55*v**3/2 + 135*v**2 - 279*v - 2. Let m(c) = 0. What is c?
-18, -3, 1
Suppose 0 = -505*w + 508*w. Suppose -j = 5*z + j, w = -3*z - 3*j - 9. Solve -z*n**2 + 0*n + 8/3 + 2/3*n**3 = 0 for n.
-1, 2
Let w = -58 + 121. Let k = 71 - w. Find c, given that 1 - 264*c - 1 - 2 + 276*c - 18*c**2 + k*c**3 = 0.
1/4, 1
Suppose -2*c - 2*i = -12, -c + 7 = -0*c + 2*i. Suppose 0 = 5*z - 7*z + 4*n + 20, n = -c*z + 6. Factor 6/5 - 3/5*u**3 + 0*u**z + 9/5*u.
-3*(u - 2)*(u + 1)**2/5
Factor -1/4*u**3 + 19/2*u**2 + 289 - 425/4*u.
-(u - 17)**2*(u - 4)/4
Let f = -7/726 + 34/1815. Let o(i) be the third derivative of 1/660*i**6 + 0*i**4 - 16*i**2 + 0*i + 2 + 4/33*i**3 - f*i**5. Factor o(s).
2*(s - 2)**2*(s + 1)/11
Let v(u) be the third derivative of -u**6/60 - 41*u**5/15 + u**4/12 + 82*u**3/3 + 2019*u**2. Let v(t) = 0. Calculate t.
-82, -1, 1
Let h(p) be the second derivative of 75*p + 0*p**3 - 2 - 7/48*p**4 - 3/40*p**5 + 0*p**2. Solve h(g) = 0 for g.
-7/6, 0
Factor -46*q + 24*q**3 - 21*q**2 - 453*q**4 + 1041*q**4 - 589*q**4.
-q*(q - 23)*(q - 2)*(q + 1)
Let i(a) be the first derivative of -2*a**5/5 + 21*a**4/2 + 140*a**3/3 + 48*a**2 - 2233. Let i(y) = 0. What is y?
-2, -1, 0, 24
Let x(o) = -o**3 + 29*o**2 - 27*o - 29. Let q be x(28). Let j be (-4 + 2)*((-85)/(-90) + q). Find f such that 0 - j*f**3 + 1/9*f**2 + 0*f = 0.
0, 1
Let f(x) = -168*x + 7397. Let w be f(44). Let i(p) be the second derivative of 1/4*p**5 + w*p**2 + 0 - 5/6*p**3 - 25*p - 5/6*p**4. Factor i(n).
5*(n - 2)*(n - 1)*(n + 1)
Let k = -2483459/180 - -13797. Let a(m) be the third derivative of 24*m**2 - 1/18*m**4 + 0*m + 0 - 1/6*m**3 - k*m**5. Factor a(q).
-(q + 1)*(q + 3)/3
Let x(i) be the second derivative of -3*i**5/160 - 149*i**4/32 + 227*i**3/8 - 57*i**2 + 228*i. Factor x(c).
-3*(c - 2)*(c - 1)*(c + 152)/8
Factor 11/2*i + 1/4*i**2 + 24.
(i + 6)*(i + 16)/4
Let t(n) = -397*n**2 - 406 + 17 - 869*n - 94*n**2. Let f(l) = -737*l**2 - 1304*l - 584. Let w(g) = 5*f(g) - 8*t(g). Suppose w(u) = 0. What is u?
-8/9
Let n(x) be the first derivative of -2/5*x**4 + 0*x - 1/5*x**2 + 3 - 2/3*x**3. Let n(k) = 0. What is k?
-1, -1/4, 0
Let z(f) be the first derivative of 1/5*f**5 + 41 - 9/2