 + 58*f**3 - f**2 - 58*f. Let h(s) = 102*s**4 + 231*s**3 - 3*s**2 - 231*s. Let b(t) = 2*h(t) - 9*i(t). What is a in b(a) = 0?
-20, -1, 0, 1
Suppose -3*r - 3*z + 320 = r, -3*r = 3*z - 240. Let n = 5 + -3. Factor 4*w**3 - 7*w**3 + 8*w**3 - 40*w**n + r*w.
5*w*(w - 4)**2
Let h(q) be the first derivative of -37 + 1/16*q**4 + 54*q**2 + 3*q**3 + 432*q. Determine r, given that h(r) = 0.
-12
Determine n, given that -2640/7*n**4 - 4250/7*n + 250 + 890/7*n**2 + 4178/7*n**3 + 72/7*n**5 = 0.
-1, 5/6, 1, 35
Factor 0*m - 134/3*m**4 - 2/3*m**5 + 0 + 2312/3*m**2 - 2176/3*m**3.
-2*m**2*(m - 1)*(m + 34)**2/3
Let v be (-1 + 0)/((-10)/(-80)). Let t(n) = -4*n - 14. Let y be t(v). Factor -3*o**2 + 6*o**4 - 4*o**4 - 30*o**3 + y*o - 11*o**4.
-3*o*(o + 1)*(o + 3)*(3*o - 2)
Suppose -9*u = u - 480. Determine c so that -56*c**2 - u*c**2 + 101*c**2 + 12 - 9*c = 0.
-4, 1
Let p(r) = -r**5 - 7*r**3 + r**2 + 1. Let a(n) = 128*n**5 - 3400*n**4 + 26166*n**3 - 39693*n**2 - 3. Let o(c) = a(c) + 3*p(c). Factor o(q).
5*q**2*(q - 2)*(5*q - 63)**2
Let z = -1168025 + 1168028. Determine u, given that 2/9*u**4 + 2*u**z - 2/9*u**5 - 16/9*u - 26/9*u**2 + 8/3 = 0.
-3, -1, 1, 2
Solve 26*p**2 - 376712 + 26*p**2 - 111*p**2 + 26*p**2 - 1736*p + 31*p**2 = 0.
-434
Suppose 118488*x = 118902*x - 1242. Factor 21*d + 18*d**2 - 3/2*d**4 + 15/2 + x*d**3.
-3*(d - 5)*(d + 1)**3/2
Let a(k) be the first derivative of 46 - 1/7*k**3 + 6*k - 39/14*k**2. What is b in a(b) = 0?
-14, 1
Solve 4*r**3 - 32/3*r**2 + 48 - 1/3*r**4 - 16*r = 0 for r.
-2, 2, 6
Let q be 152/40 - 2/(-10). Let y be (-3)/9 - q/(-12). Factor 0 + 0*h**2 + 0*h + y*h**4 - 2/21*h**3 + 2/21*h**5.
2*h**3*(h - 1)*(h + 1)/21
Let l(z) be the first derivative of 2*z**5/55 - 937*z**4/11 + 1759682*z**3/33 - 1754064*z**2/11 + 1752192*z/11 - 1875. Suppose l(d) = 0. What is d?
1, 936
Let s be (-21)/(-12)*((-6096)/(-144) + -33). Factor -4096/3 - 1/3*i**4 + 4864/3*i - 272*i**2 + s*i**3.
-(i - 16)**3*(i - 1)/3
Let d(s) be the second derivative of 25*s**2 - 6*s + 5/12*s**4 + 55/6*s**3 - 1. Factor d(u).
5*(u + 1)*(u + 10)
Let t = 113 - 106. Let x(m) = -m**2 + 5*m + 16. Let p be x(t). Factor -2/5*o**p + 0 + 0*o.
-2*o**2/5
Let p(u) = -u**3 + 5*u**2 - 5*u + 4. Let g be p(0). Suppose 65*q = 67*q - g. Find b such that 1/3*b + 1/6*b**q - 1/2 = 0.
-3, 1
Let n be -30*(-15)/(-135)*-12*(-13)/(-5). Factor n*b**2 + 74/3*b + 4/3.
2*(12*b + 1)*(13*b + 2)/3
Suppose a - 21 = -9. Suppose -a = b - 15. Factor 2 - m - 6*m + 4*m - 2*m**2 + 2*m**b + m.
2*(m - 1)**2*(m + 1)
Let s(y) = 33*y**3 - 18 - 11*y + 5*y**2 + 6*y**2 - 34*y**3. Let j be s(9). What is r in 57*r**3 + 48*r**4 + 17*r**3 + 6*r - 2*r**3 - j*r**2 = 0?
-2, 0, 1/4
Let i(d) be the third derivative of -d**7/2940 - 9*d**6/140 - 4*d**5 - 400*d**4/21 + 2*d**3 + 69*d**2. Let u(p) be the first derivative of i(p). Factor u(o).
-2*(o + 1)*(o + 40)**2/7
Let m(r) = 14*r + 0 - 3*r**2 - 3 - 31*r - r**2 - 3*r**2. Let s = -2 + 5. Let n(h) = -36*h**2 - 84*h - 16. Let y(v) = s*n(v) - 16*m(v). Let y(w) = 0. What is w?
-5, 0
Suppose -7*a + 59 - 38 = 0. Suppose 9 + 1 = u. Find s such that 4*s**2 + 18*s + 0*s**4 - 2*s**4 - 5*s**2 - 5*s**2 - u*s**a = 0.
-3, 0, 1
Let n(y) = y**2 + y - 7. Let p(z) = -12*z**2 + 2382*z + 98. Let v(u) = -14*n(u) - p(u). Suppose v(i) = 0. What is i?
-1198, 0
Let h = -1588355/108 - -14707. Let f(c) be the second derivative of 2/9*c**2 + 0 + h*c**4 - 5/54*c**3 + 25*c. Find n such that f(n) = 0.
1, 4
Let y(v) = -v**2 - v. Let a(r) = 9*r**2 + 17*r + 12. Let w(g) = -g**3 - g**2 - g - 4. Let s be w(-2). Let b(k) = s*a(k) + 14*y(k). Suppose b(c) = 0. What is c?
-3, -2
Let o be (-186)/(-23560)*45 - 10/95. Factor -o*t**2 - 5/2*t + 0.
-t*(t + 10)/4
Let t be (-3)/(-1) + -12 + 18. Factor 1 + 18*y - 3*y - 5*y - t*y - 2*y**2.
-(y - 1)*(2*y + 1)
Suppose -4*j + 6*g + 6027 = 6105, -j - 72 = -4*g. What is f in 2*f - 2/3*f**2 + j = 0?
-3, 6
Let o(u) be the third derivative of u**3 + 3/10*u**5 - 7/8*u**4 - 1/35*u**7 + 0 - 45*u**2 + 1/40*u**6 + 0*u. Solve o(c) = 0 for c.
-2, 1/2, 1
Suppose 21*x**2 - 1/2*x**3 - 39/2*x - 41 = 0. Calculate x.
-1, 2, 41
Let m(c) = -2*c**2 + 2*c. Let d(x) = -9*x**2 - 162*x - 2040. Let a(i) = d(i) - 6*m(i). Factor a(q).
3*(q - 68)*(q + 10)
Factor -4/11*v - 8/11*v**3 + 2/11*v**4 + 10/11*v**2 + 0.
2*v*(v - 2)*(v - 1)**2/11
Determine d so that -39/2*d**2 + 87/2*d - 45/2 - 3/2*d**3 = 0.
-15, 1
Let 646*q**4 + 19033*q**3 + 176*q - 37997*q**3 + 18632*q**3 + 156*q**5 + 48 - 956*q**2 + 262*q**4 = 0. What is q?
-6, -1, -2/13, 1/3, 1
Let u(f) be the second derivative of 55/2*f**2 + 5/36*f**4 - 35/9*f**3 + 2 + 61*f. What is h in u(h) = 0?
3, 11
Let l be ((21696/18)/8)/((-8)/(-6)). Suppose -l*o - 48 = -274. Factor 0*g**4 + 0 - 6/13*g**3 + 4/13*g**o + 0*g + 2/13*g**5.
2*g**2*(g - 1)**2*(g + 2)/13
Let w(k) = -k**2 + k + 1. Let u(d) = 9*d**2 + 67*d + 29. Let b(m) = u(m) - 5*w(m). Factor b(c).
2*(c + 4)*(7*c + 3)
Let c(t) = -2906*t - 5809. Let y be c(-2). Factor -25/4*s**4 - 65/4*s**y + 5/4*s - 45/4*s**2 + 5/2.
-5*(s + 1)**3*(5*s - 2)/4
Let p(c) = -24*c**2 + 12*c + 32. Suppose -2*a - a + 4*h = -13, -3*a - h = -38. Let u(g) = -13*g**2 + 6*g + 16. Let d(s) = a*u(s) - 6*p(s). Factor d(y).
(y - 8)*(y + 2)
Let s = 198 - 223. Let c = s + 28. Factor -8/3*w**2 - 4/3*w**c + 0 - 4/3*w.
-4*w*(w + 1)**2/3
Let c(k) = 4*k - 16. Let f be c(5). Let s = 12 - f. Factor s*m**2 - m - 10*m**2 + 0*m - m.
-2*m*(m + 1)
Let k(d) be the third derivative of d**7/420 + 3*d**6/160 - 3*d**5/40 + d**4/96 + d**3/4 + 2*d**2 + 17. Solve k(m) = 0.
-6, -1/2, 1
Let n(t) be the second derivative of t**7/315 - 101*t**6/75 + 599*t**5/150 + 907*t**4/90 - 80*t**3/3 - 1204*t**2/15 + 6079*t. Find v, given that n(v) = 0.
-1, 2, 301
Let v(h) be the third derivative of 27*h**3 - 12*h**2 - 4/15*h**5 + 4 + 0*h + 15/8*h**4 + 1/120*h**6. Factor v(x).
(x - 9)**2*(x + 2)
Suppose -3*k - 42 = -9*k. Suppose 9 = n + k. Factor 10*j**n - 4*j**3 + 3*j**2 - j**2 + 0*j**2.
-4*j**2*(j - 3)
Let b be 15 + 23/34*3124/(-142). Factor 16/17 + 12/17*p + b*p**2.
2*(p + 2)*(p + 4)/17
Let p = 6423/10 + -608. Let h(s) be the third derivative of 1/200*s**6 + p*s**3 + 0 + 0*s + 21/100*s**5 - 17*s**2 + 147/40*s**4. Find v such that h(v) = 0.
-7
Let n(w) be the third derivative of 226*w**2 + 0 + 1/8*w**4 + 0*w + 13/24*w**3 - 1/240*w**5. Let n(g) = 0. Calculate g.
-1, 13
Let f(d) be the second derivative of 3*d**5/10 + 13*d**4/8 + 3*d**3/4 - 1109*d. Find a such that f(a) = 0.
-3, -1/4, 0
Let i(l) = 5*l + 29. Let n be i(-13). Let t = n + 39. Factor 7*f**2 - 57*f - 10*f**3 + 25*f**2 + 3*f**t + 2*f**3 + 18.
-(f - 3)**2*(5*f - 2)
Let w(f) be the first derivative of 5/4*f**4 - 5/2*f**2 + 116 + 0*f + 0*f**3. Factor w(m).
5*m*(m - 1)*(m + 1)
Let t(a) = -20*a**4 + 60*a**3 - 70*a**2 - 60*a + 15. Let r(o) = 5*o**4 - 15*o**3 + 17*o**2 + 15*o - 4. Let u(n) = -25*r(n) - 6*t(n). Factor u(k).
-5*(k - 2)*(k - 1)**2*(k + 1)
Let r(i) = 27*i**4 + 241*i**3 + 398*i**2 + 69*i - 33. Let q(n) = -n**3 - n**2 + 9*n - 1. Let c(o) = -5*q(o) + r(o). Let c(g) = 0. Calculate g.
-7, -2, -1/3, 2/9
Let f(d) be the first derivative of -d**6/12 - 2*d**5/5 + 5*d**4/8 + 3682. Factor f(w).
-w**3*(w - 1)*(w + 5)/2
Let l(d) be the third derivative of d**5/480 - 189*d**4/32 + 107163*d**3/16 + 145*d**2 + 6. Factor l(v).
(v - 567)**2/8
Suppose -3*c - 4 = 4*m - 111, -4*c - 3*m + 131 = 0. Factor 7327 - c*s**2 + 33*s**2 + 496*s + 2616 + 5433.
4*(s + 62)**2
Suppose -2/3*w**3 + 32/3*w**2 + 24*w + 0 = 0. Calculate w.
-2, 0, 18
Let r(f) be the second derivative of f**6/30 + 3*f**5/10 - 41*f**4/12 - f**3 + 20*f**2 - 26*f - 26. Find q such that r(q) = 0.
-10, -1, 1, 4
Let j(o) be the first derivative of -o**8/2520 + o**7/420 + o**6/135 - o**3/3 + 6*o**2 + 195. Let x(t) be the third derivative of j(t). Factor x(i).
-2*i**2*(i - 4)*(i + 1)/3
Let d(f) = -1. Let z = 19 - 22. Let l(n) = -5*n**2 + 30*n - 42. Let m(k) = z*d(k) - l(k). Factor m(v).
5*(v - 3)**2
Let d = 536 - 532. Factor -2*b**4 + 6*b**2 + 8 + 20*b - 25*b - 11*b + d*b**3.
-2*(b - 2)*(b - 1)**2*(b + 2)
Suppose -34*f + 25*f + 648 = 0. Factor -23*l**3 - 21*l**3 - f + 84*l + 4*l**4 - 22*l**3 + 4*l**2 + 46*l**3.
4*(l - 3)**2*(l - 1)*(l + 2)
Find n such that -5/8*n**2 + 13*n + 0 - 1/8*n**3 = 0.
-13, 0, 8
Factor -3 + 135/4*y**2 + 66*y.
3*(y + 2)*(45*y - 2)/4
Let g(o) be the second derivative of 0*o