*t - t**2.
-t*(t - 2)*(t + 1)
Suppose -6*v + 5*v - 218 = 4*l, 114 = -2*l - 3*v. Let n be ((-976)/80 + 11)*10/l. Find s, given that 14/9*s + 10/9*s**3 - n*s**4 - 4/9 - 2*s**2 = 0.
1, 2
Let q(r) = 15*r**3 - 54*r**2 + 405*r - 888. Let b(u) = -2*u**3 - u**2 - u + 1. Let z(f) = -6*b(f) - q(f). Determine o so that z(o) = 0.
6, 7
Let r(y) be the first derivative of 1/24*y**4 - 4/9*y**3 - 8/3*y + 61 + 5/3*y**2. Let r(w) = 0. What is w?
2, 4
Let v(n) be the first derivative of n**8/2520 + n**7/168 + n**6/45 - 2*n**5/45 - 25*n**3/3 + 23. Let h(x) be the third derivative of v(x). Factor h(p).
p*(p + 4)**2*(2*p - 1)/3
Let q be (74/148)/(1/6). Let z(k) be the second derivative of 0 + 1/315*k**7 + 0*k**q + 0*k**4 + 1/150*k**5 + 18*k + 2/225*k**6 + 0*k**2. Factor z(f).
2*f**3*(f + 1)**2/15
Suppose -s - 1510 = -280. Let i = s - -1232. Solve -2/5 - m - 3/5*m**i + 1/5*m**4 + 1/5*m**3 = 0 for m.
-1, 2
Let w(g) be the second derivative of -25*g**3/3 - 264*g**2 + 123*g + 3. Let c be w(-11). Factor -4*s - 2/11*s**2 - c.
-2*(s + 11)**2/11
Factor -2*c**3 - 869*c + 796*c + 3*c**3 - 72.
(c - 9)*(c + 1)*(c + 8)
Let g(u) = -u**2 + 13*u - 27. Let z be g(10). Let 16*d**5 - 4*d**5 + 28*d**4 + d**2 + 7*d**2 + 24*d**2 - 72*d**z = 0. What is d?
-4, 0, 2/3, 1
Factor -361/7*y + 341/7 + 1/7*y**3 + 19/7*y**2.
(y - 11)*(y - 1)*(y + 31)/7
Let z be 20/6*78/52. Let x(y) = 15*y**3 - 10*y - 15. Let h(q) = q**4 + 15*q**3 + q**2 - 11*q - 14. Let w(j) = z*h(j) - 4*x(j). Let w(a) = 0. Calculate a.
-2, -1, 1
Let k(r) = -7*r**3 + 2731*r**2 - 922077*r. Let q(j) = -11*j**3 + 4098*j**2 - 1383115*j. Let n(z) = -8*k(z) + 5*q(z). Factor n(p).
p*(p - 679)**2
Suppose 180*q = 168*q. Suppose -71*c + 75*c - 8 = q. Factor 2/5*g**c + 8/15*g - 2/15*g**3 + 0.
-2*g*(g - 4)*(g + 1)/15
Let k = 654158/2289357 - 8/327051. Factor 2/7*r + k*r**2 - 4/7.
2*(r - 1)*(r + 2)/7
Let k(d) = d**2 - 5*d + 6. Let g be k(7). Let x = -17 + g. Find l, given that x*l - l**3 - 305 + 305 - 2*l**2 = 0.
-3, 0, 1
Let f = -105 - -87. Let z(h) = -h - 16. Let k be z(f). Determine p so that 12*p + 15*p - 4*p**4 - 48*p**k + 5*p + 24*p**3 = 0.
0, 2
Factor -16 - 4*p**2 - 65*p**3 + 63*p**3 - 28*p - 10*p**2.
-2*(p + 1)*(p + 2)*(p + 4)
Let s(r) be the second derivative of r**6/150 + r**5/25 + r**4/30 - 2*r**3/15 - 3*r**2/10 + 6*r + 13. Suppose s(y) = 0. What is y?
-3, -1, 1
Let a(k) be the first derivative of -k**5 - 65*k**4/4 - 200*k**3/3 - 90*k**2 - 4988. Factor a(x).
-5*x*(x + 2)**2*(x + 9)
Let i(r) be the second derivative of 0*r**2 + 19/21*r**3 + 0 - 30*r - 1/42*r**4. Factor i(a).
-2*a*(a - 19)/7
Let b(n) be the second derivative of -n**4/120 + 39*n**3/20 - 29*n**2/5 - 1773*n. Solve b(r) = 0.
1, 116
Let p = -78565 - -78567. Let 4/3*m**p - 8/15*m**4 - 4/5 + 2/3*m - 2/3*m**3 = 0. Calculate m.
-2, -1, 3/4, 1
Let a(k) be the first derivative of -k**4/14 - 120*k**3/7 - 177*k**2/7 + 716*k/7 - 3564. Factor a(l).
-2*(l - 1)*(l + 2)*(l + 179)/7
Suppose c - 4*c + 7 = 2*f, -5*c = f. Let a(j) be the first derivative of -2/25*j**f - 32/5*j + 0*j**4 - 1 + 0*j**2 + 16/15*j**3. Factor a(z).
-2*(z - 2)**2*(z + 2)**2/5
Let s = -77/8984 + 3037285/80856. Solve 0 - 52/9*x**2 + s*x + 2/9*x**3 = 0.
0, 13
Let o(z) be the first derivative of -32/5*z + 88/5*z**3 - 57 - 27/5*z**4 - 8*z**2. Find x such that o(x) = 0.
-2/9, 2/3, 2
Let q = 3992/9 - 3991/9. Let c(s) be the first derivative of -q*s**2 + 1/27*s**3 + 0*s - 13 - 1/45*s**5 + 1/18*s**4. Find y, given that c(y) = 0.
-1, 0, 1, 2
Let w(v) be the first derivative of 126 - 5/3*v - 11/4*v**2 + 7/18*v**3. Factor w(n).
(n - 5)*(7*n + 2)/6
Let w = -1050 + 2472. Suppose -q + 12 = 4. Find k, given that q*k - 4 + 4 - 1420*k**2 + w*k**2 = 0.
-4, 0
Let q(a) be the second derivative of 1/8*a**4 + 1/40*a**5 - 1/3*a**3 + 15 - 3*a**2 - 4*a. Factor q(w).
(w - 2)*(w + 2)*(w + 3)/2
Let p(o) be the first derivative of -o**4/12 + o**3/18 + 13*o**2/12 + o + 3782. Factor p(y).
-(y - 3)*(y + 2)*(2*y + 1)/6
Let s(m) be the first derivative of m**6/6 + 22*m**5/5 - 311*m**4/4 - 7760*m**3/3 + 11648*m**2 + 692224*m + 1. Factor s(y).
(y - 13)**2*(y + 16)**3
Let t be 0/3 - 0/1. Suppose -2*j - 10*g + 6*g + 26 = 0, -19 = 2*j - 5*g. Factor -2*x**j + 0*x**3 + t*x**3 + x + 3*x**5 - 2*x**5.
x*(x - 1)**2*(x + 1)**2
Let z = 451391/5 - 90277. Factor 66/5*h**4 - 39/5*h - 114/5*h**3 + z - 3*h**5 + 96/5*h**2.
-3*(h - 1)**4*(5*h - 2)/5
Factor 0 + 0*t + t**2 - 37/4*t**3.
-t**2*(37*t - 4)/4
Let n(w) be the second derivative of w**8/392 - w**7/105 + w**6/210 - 105*w**2/2 + 15*w - 5. Let i(b) be the first derivative of n(b). What is l in i(l) = 0?
0, 1/3, 2
Suppose -5*p - 2*i = -19209, 4*i - 7684 = -2*p + 3*i. Let p*j**3 + 34*j**2 - 52*j + 11*j**2 + 20 + j**4 - 3855*j**3 = 0. What is j?
1, 2, 10
Let j = -6206 + 6209. Suppose 0 = 2*k - 9 - 7. Factor -6*a**2 + k*a**2 - 10*a + 6*a**2 + 2*a**j.
2*a*(a - 1)*(a + 5)
Let u be (-4 - (-1755)/350) + (-69)/322. Suppose -8/5 + 1/5*m**3 - u*m - 4/5*m**4 + 1/5*m**5 + 2*m**2 = 0. What is m?
-1, 2
Let j(x) = x**2 - 7*x - 117. Let k be j(-8). Factor -11*p**3 + 4*p**3 - 12*p - 8*p**2 + 5*p**k + 6*p**3.
4*p*(p - 3)*(p + 1)
Suppose -6 - 5580*m**3 - 69 - 28529*m**4 + 25829*m**4 - 930*m - 3783*m**2 = 0. What is m?
-5/6, -1/5
Suppose 2*n + 1 = 3. Factor 980*f**2 + 224*f - n + 6 - 21.
4*(7*f + 2)*(35*f - 2)
Let s(o) be the third derivative of -o**7/630 + 521*o**6/180 - 271441*o**5/180 + 1399*o**2 - o. Let s(q) = 0. Calculate q.
0, 521
Let s be (300/(-45) - -6)/(-2 - 0). Let o(l) be the first derivative of -1/15*l**5 - 1/3*l**2 + 15 + 0*l - 5/9*l**3 - s*l**4. Factor o(u).
-u*(u + 1)**2*(u + 2)/3
Let j be (-13)/624*-872 - 18. Let t(c) be the first derivative of -j*c**5 + 1 + 5/18*c**3 + 0*c**2 + 0*c**4 + 0*c. Suppose t(s) = 0. Calculate s.
-1, 0, 1
Let a be (410/656)/((-240)/(-256)). Solve -168*m**2 - a*m**3 - 395136 - 14112*m = 0.
-84
Let p(d) be the third derivative of -d**7/42 - d**6/12 + 13*d**5/12 - 25*d**4/12 - 639*d**2. Determine a so that p(a) = 0.
-5, 0, 1, 2
Let y(x) be the first derivative of -2*x**5/55 + 29*x**4/11 - 766*x**3/11 + 812*x**2 - 4312*x + 2853. Factor y(z).
-2*(z - 22)**2*(z - 7)**2/11
Let z(m) be the first derivative of 7*m**4/4 + 72*m**3 + 1755*m**2/2 + 1350*m - 1380. Factor z(s).
(s + 15)**2*(7*s + 6)
Let b = 179 - 177. Let v(o) = 245*o**3 + 558*o**2 + 322*o + 2. Let z(m) = -980*m**3 - 2231*m**2 - 1289*m - 9. Let r(k) = b*z(k) + 9*v(k). Solve r(w) = 0.
-8/7, 0
Let n(x) = -2*x**3 + x**2. Let u = -3 - -1. Let z be n(u). Find c, given that -4 - z*c - 4 - 4*c**3 - 16*c**2 + 19*c - 19*c = 0.
-2, -1
Let a(d) = -20*d**3 - 80*d**2 + 335*d - 256. Let g(k) = 11*k**3 + 41*k**2 - 167*k + 127. Let z(i) = 4*a(i) + 7*g(i). Solve z(x) = 0 for x.
-15, 1, 3
Suppose 286*v - 2417 - 2340 + 467 = 0. Factor 5/2*k**3 - 25/2*k**2 + v*k + 0.
5*k*(k - 3)*(k - 2)/2
Let g(z) be the first derivative of -112/3*z**3 - 29 - 20*z - 1/3*z**6 - 12/5*z**5 + 17*z**4 + 39*z**2. Determine l, given that g(l) = 0.
-10, 1
Let d(l) = 17*l**4 + 77*l**3 + 763*l**2 + 2078*l. Let s(k) = -7*k**4 - 38*k**3 - 382*k**2 - 1036*k. Let g(p) = -4*d(p) - 10*s(p). Factor g(w).
2*w*(w + 4)*(w + 16)**2
Let u = -919 + 11033/12. Let p(g) be the first derivative of g + 1/18*g**3 + 13 + u*g**2. Factor p(f).
(f + 2)*(f + 3)/6
Let g be (-84)/(-30)*2/7. Let l = 1/217 + 2599/1085. Suppose -g*b**2 - 8/5 + l*b = 0. What is b?
1, 2
Let o = -3319350/17 + 195256. Factor 88/17*k - 968/17 - o*k**2.
-2*(k - 22)**2/17
Let w(n) = 3*n**2 + 951*n + 12. Let a(d) = 18*d**2 + 5707*d + 76. Let m(s) = 3*a(s) - 19*w(s). Suppose m(f) = 0. What is f?
-316, 0
Let h(t) be the first derivative of 4*t**6 + 12*t**5 + 75*t**4/8 - 5*t**3/2 - 15*t**2/4 + 3*t/2 - 100. Suppose h(f) = 0. Calculate f.
-1, 1/4
Let d be 115/966*(4 - 595/150). Let n(a) be the second derivative of -1/180*a**6 - d*a**7 + 0*a**2 - 1/24*a**4 + 0*a**3 - 7*a + 0 + 1/24*a**5. Factor n(f).
-f**2*(f - 1)**2*(f + 3)/6
Let t be ((-4680)/10530)/((-2)/9). Factor -25/3*q - 5/3*q**5 - 25/3*q**4 - 5/3 - 50/3*q**3 - 50/3*q**t.
-5*(q + 1)**5/3
Let x = -2558/15 + 70469/195. Let j = 191 - x. Factor -j*p**3 + 4/13 - 4/13*p**2 + 2/13*p.
-2*(p - 1)*(p + 1)*(p + 2)/13
Let p = 4/541 - -63265/4328. Let j = p - 105/8. Factor 0*c + 0 + 12*c**3 - 6*c**2 + j*c**5 - 15/2*c**4.
3*c**2*(c - 2)**2*(c - 1)/2
Let b be 1/447*(7035 - -9)/(-12). Let i = 3/1