- 5206 = -5241. Let l(r) be the first derivative of 0*r + 2*r**2 - r**4 - 10 + 8/5*r**d - 8/3*r**3. Factor l(n).
4*n*(n - 1)*(n + 1)*(2*n - 1)
Factor 0 + 1/2*p**4 + 311/2*p**3 + 0*p + 0*p**2.
p**3*(p + 311)/2
Suppose 12*v**2 + 15*v**4 - 51/2*v**3 + 0*v - 3/2*v**5 + 0 = 0. Calculate v.
0, 1, 8
Let c(h) be the first derivative of h**3/5 - 324*h**2/5 + 129*h - 1000. Factor c(s).
3*(s - 215)*(s - 1)/5
Factor 22/9*d - 28/9*d**2 + 2/9*d**3 + 52/9.
2*(d - 13)*(d - 2)*(d + 1)/9
Let g(s) = 4*s + 41. Let a be g(-9). Factor 68*f + a - 12*f**2 - 4 - 5 + 4*f**3 - 56*f.
4*(f - 1)**3
Let v(m) = -599*m - 19764. Let q be v(-33). Factor 30*h**2 + 3/2*h**4 + 12*h**q + 24*h + 0.
3*h*(h + 2)**2*(h + 4)/2
Let n(t) be the first derivative of -106 + 4/3*t**2 + 8/9*t**3 - 1/2*t**4 + 1/9*t**6 - 4/15*t**5 + 0*t. Let n(b) = 0. What is b?
-1, 0, 2
Let q(t) be the second derivative of t**5/20 + t**4/2 - 3*t**3/2 + 2*t**2 - 16*t. Let n be q(-7). Factor 0 - n*p**2 - 8 - 9*p**2 + 20*p + 19*p**2.
-4*(p - 2)*(2*p - 1)
Let i be ((-9)/2 + 7)/(9/(-6)). Let z = -7/9 - i. Factor -2/3 + 4/9*n**2 - z*n + 2/9*n**4 + 8/9*n**3.
2*(n - 1)*(n + 1)**2*(n + 3)/9
Let d(w) = -1. Let v(o) be the second derivative of -o**4/3 + 4*o**3/3 + 2*o**2 + 46*o. Let y(l) = 4*d(l) + v(l). Solve y(k) = 0.
0, 2
Let n(o) = 5*o**2 + 115*o + 296. Let u(x) = -2. Let q(r) = -n(r) + 2*u(r). Suppose q(y) = 0. What is y?
-20, -3
Let w be 586638/486 - (2 + (-208)/108). Let m = w - 1205. Factor 0*i + 3/7*i**m + 0.
3*i**2/7
Let o(n) be the third derivative of 0*n - 20*n**3 - 1/12*n**5 + 18 + 2*n**2 - 35/12*n**4. Factor o(p).
-5*(p + 2)*(p + 12)
Let o = 160 - 82. Suppose 21 - o = -3*g. What is j in -g*j + j**2 - 2 + 25*j - 6 + j**2 = 0?
-4, 1
Suppose 695 = 4*h + 683. Let l(s) be the first derivative of 3/5*s**2 + 7 + 1/10*s**4 - 2/5*s**h - 2/5*s. Factor l(b).
2*(b - 1)**3/5
Let n(m) = -4*m**4 + 56*m**3 + 6*m**2 - 54*m - 2. Let h(i) = 5*i**4 - 56*i**3 - 8*i**2 + 53*i + 3. Let k(d) = 2*h(d) + 3*n(d). Factor k(f).
-2*f*(f - 28)*(f - 1)*(f + 1)
Suppose 164/5*b - 102 + 2/5*b**2 = 0. Calculate b.
-85, 3
Let t(o) = -25*o - 496. Let q be t(-21). Suppose -9*j + 190 = q*j. Factor -2/7*d + 0 + 0*d**4 + 4/7*d**3 - 2/7*d**j + 0*d**2.
-2*d*(d - 1)**2*(d + 1)**2/7
Let s = -658 + 1119. Let g = s - 3225/7. Factor 4/7 + g*u - 2/7*u**2.
-2*(u - 2)*(u + 1)/7
Let w(j) = 13*j + 159. Suppose 54 = -4*z + 5*l - 2*l, 3*l - 42 = 3*z. Let o be w(z). Factor -3/4*k + 11/4*k**o - 3/4*k**4 + 0 - 5/4*k**2.
-k*(k - 3)*(k - 1)*(3*k + 1)/4
Let r(c) = 3*c**3 + 365*c**2 + 4*c - 6. Let s(j) = 12*j**3 + 1461*j**2 + 18*j - 27. Let x(b) = 9*r(b) - 2*s(b). Suppose x(v) = 0. Calculate v.
-121, 0
Let s be (-10)/80*((2 + -4)*3 - -3). Let t(b) be the first derivative of 0*b - s*b**4 + 20 + 0*b**2 - b**3. Find p such that t(p) = 0.
-2, 0
Let y(w) = 3*w**4 - 24*w**2 + 15. Let g = -166 - -159. Let x(o) = 3*o**4 - o**3 - 26*o**2 + o + 16. Let h(q) = g*y(q) + 6*x(q). Factor h(s).
-3*(s - 1)**2*(s + 1)*(s + 3)
Let l(x) be the first derivative of -x**4/84 + 5*x**3/42 + x**2 + 96*x - 103. Let u(n) be the first derivative of l(n). What is b in u(b) = 0?
-2, 7
What is c in -4*c**2 + 7*c + 111*c + 275 + 6*c + 91 + 194 = 0?
-4, 35
Let c(g) be the first derivative of g**3/18 - 59*g**2/6 - 121*g/2 - 3028. Factor c(y).
(y - 121)*(y + 3)/6
Factor -50 + 5*w**2 + 1279 + 360*w + 131.
5*(w + 4)*(w + 68)
Suppose 0 = 3*n - 12 - 18 + 24. Suppose -4*i - 6 = -18. Factor 3*s**3 + 162*s**4 - 8 + 5*s**3 + 54*s**5 + 64*s - 146*s**n + s**i + 9*s**3.
2*(s + 2)**2*(3*s - 1)**3
Suppose 3*x + x - 5*k - 33 = 0, 0 = -3*x + 4*k + 25. Suppose -4*l - x + 79 = 0. Determine f so that -2 + 6*f**3 - 23*f**2 - 33*f - 16*f**2 - 4 - l*f**3 = 0.
-2, -1, -1/4
Solve 13*b**3 + 13/4*b**4 - 3/2*b**5 - 21/4*b**2 - 23/2*b + 2 = 0.
-2, -1, 1/6, 1, 4
Let i(d) be the first derivative of -d**9/1512 - d**8/210 + d**7/60 + d**6/18 + 7*d**3/3 - 9*d + 91. Let l(y) be the third derivative of i(y). Solve l(g) = 0.
-5, -1, 0, 2
Let a(m) be the first derivative of 3*m**4/28 + 29*m**3/7 + 825*m**2/14 + 363*m + 7966. Factor a(b).
3*(b + 7)*(b + 11)**2/7
Let c(a) be the second derivative of a**5/60 - a**4/4 + 4*a**3/3 - 8*a**2/3 + 4*a + 110. Factor c(q).
(q - 4)**2*(q - 1)/3
Factor -14004/5*v - 4085667/5*v**2 - 12/5.
-3*(1167*v + 2)**2/5
Suppose 105 = 7*y + 91. Solve 10 - 28*h - 7*h - 183*h**y + 198*h**2 = 0 for h.
1/3, 2
Let r(y) = 9*y**4 + 7*y**3 + y**2 - 10*y + 7. Let b = 51 - 48. Let c(o) = 4*o**4 + 3*o**3 - 4*o + 3. Let x(i) = b*r(i) - 7*c(i). Factor x(h).
-h*(h - 1)**2*(h + 2)
Let b be 10/12 + (-163523)/204. Let p = b - -801. Factor p*j**2 + 1/4*j**3 - 1/4*j - 1/4.
(j - 1)*(j + 1)**2/4
Let a(u) = -4*u**3 + 63*u**2 - 1323*u + 9258. Let o(b) = 4*b**2 + b**3 + 1 - 13*b**2 + 9*b**2. Let j(m) = -2*a(m) - 6*o(m). Factor j(l).
2*(l - 21)**3
Let b(m) = -m**3 + m**2. Let s = -210 - -214. Let g(y) = 15*y**4 + 36*y**3 + 19*y**2 - 10*y. Let i(u) = s*b(u) - g(u). Find a such that i(a) = 0.
-2, -1, 0, 1/3
Let r(x) be the first derivative of 1/40*x**5 - 1/8*x**3 - 1/2*x - 1/16*x**4 - 8 + 1/2*x**2. Factor r(c).
(c - 2)*(c - 1)**2*(c + 2)/8
Let o(m) = -3*m - 4. Let b be o(-3). Let r = -3 + b. Factor 3*f**2 + 17*f**r + 4*f - 18*f**2.
2*f*(f + 2)
Let w be (10/30)/((-2)/(-12)). Suppose 3*b = -2*b - 5*m + 5, -22 = -4*b + 5*m. Factor 24*d - 3*d**2 + 8 - 4*d**b - 3*d**2 - w*d**2 - 20*d.
-4*(d - 1)*(d + 1)*(d + 2)
Factor 0 + 938*a**3 - 819 + 17965*a**4 - 2448*a**2 - 17962*a**4 - 128*a**3 + 2454*a.
3*(a - 1)**3*(a + 273)
Suppose 5*z + 5*t - 225 = 0, t = -z + 4*t + 25. Let q = -8 + 36. Suppose -6*f + 16 + 30*f + z*f + q*f**2 = 0. Calculate f.
-2, -2/7
Let w(r) be the second derivative of r**6/1080 - r**5/90 + 63*r**3/2 - 172*r. Let f(x) be the second derivative of w(x). Solve f(u) = 0 for u.
0, 4
Let t(y) be the second derivative of -28/9*y**3 + 0 - 16/3*y**2 - 7/9*y**4 - 1/15*y**5 - 172*y. Factor t(j).
-4*(j + 1)*(j + 2)*(j + 4)/3
Let n = 65 + -63. Suppose -o - 6 = -4*o. Let -3*m**3 - o*m**3 - 8*m**n - 20*m + 28*m**2 + 0*m**3 = 0. What is m?
0, 2
Let f(v) be the second derivative of v**3/3 - 13*v**2 - 2*v + 106. Let j be f(13). Let 0*n - 3/2*n**2 + j - 1/2*n**4 + 2*n**3 = 0. Calculate n.
0, 1, 3
Let c be -2 + 34/8 + 2/(-8). Let n be 18 + (-708)/39 - (-82)/26. Find r, given that n - c*r**2 + 23/2*r = 0.
-1/4, 6
Let l(t) be the second derivative of -t**6/120 + 7*t**5/8 - 17*t**4/4 + t**3 + 8*t**2 + 6*t + 28. Let p(k) be the second derivative of l(k). Factor p(s).
-3*(s - 34)*(s - 1)
Let n(m) be the second derivative of -3*m**5/40 - 321*m**4/8 - 34347*m**3/4 - 3675129*m**2/4 - 459*m. Factor n(u).
-3*(u + 107)**3/2
Solve -135*g**2 + 21 - 124*g**2 + 8*g**3 - 122*g + 19 + 105*g**2 = 0.
-1, 1/4, 20
Let v = 373992 - 373988. Let 4/9*x**2 + 56/9 + v*x = 0. Calculate x.
-7, -2
Find q, given that -1078/17*q**2 - 288120/17*q + 4321800/17 + 2/17*q**4 + 196/17*q**3 = 0.
-70, 21
Factor -17/2 + 53/4*h + 1/4*h**3 - 5*h**2.
(h - 17)*(h - 2)*(h - 1)/4
Solve -16*c**3 - 7*c**2 - 27*c**3 + 75*c**3 - 104 - 18*c**3 + 70*c - 15*c**3 = 0.
-13, 2, 4
Let h(a) = -121804*a**2 + 707*a - 16. Let f(p) = 243607*p**2 - 1411*p + 27. Let u(y) = -3*f(y) - 5*h(y). Solve u(s) = 0.
1/349
Let q(s) = 6*s**3 + 33*s**2 + 121*s - 380. Let c(m) = -20*m**3 - 98*m**2 - 368*m + 1141. Let b(z) = -2*c(z) - 7*q(z). Factor b(h).
-(h - 2)*(h + 9)*(2*h + 21)
Let k be 2/(-7) - (-132)/(-77). Let v be (90/8)/5 + k/8. Determine h so that 0*h**3 - 284*h**v + h**3 + 285*h**2 = 0.
-1, 0
Suppose 100*l**3 + 2*l**4 - 333*l + 572*l**2 + 2*l**4 + 434*l - 777*l = 0. Calculate l.
-13, 0, 1
Suppose -3*c = -2870 - 3040. Factor -40*r**2 + c + 4*r**4 - 1970 + 12*r**3.
4*r**2*(r - 2)*(r + 5)
Let f = -727935 - -727937. Solve 26/3*y - 8*y**f - 3 + 2*y**3 + 1/3*y**4 = 0 for y.
-9, 1
Let u = 18017/4 - 4503. Let z(x) be the first derivative of -25/12*x**3 - u*x**4 - 1/4*x**5 + 0*x - 5/4*x**2 - 17. Factor z(p).
-5*p*(p + 1)**2*(p + 2)/4
Let c(j) = -j**2 + 12*j - 8. Let d be c(5). Factor 405 + 93*s + 24*s + 5*s**2 - d*s.
5*(s + 9)**2
Let h(o) = o**4 - 113*o**3 - 344*o**2 - 4. Let u(x) = -3*x**4 + 456*x**3 + 1377*x**2 + 18. Let t(k) = -9*h(k) - 2*u(k). Suppose t(f) = 0. What is f?
-3, 0, 38
Suppose -19 = -s - 14. Let h(a) = a**2 - 17*a + 15. Let b(t) = -t**2 + 18*t - 18. Let l(y) = s*b(y) + 6*h(y). Let l(z) = 0. What is z?
0, 12
