-1, 1
Suppose 21*n - 1081 = -2*n. Factor -x**5 + 12*x**4 + 40*x - 43*x**4 + 21*x**3 - n*x**2 + 30*x**4 - 12.
-(x - 2)*(x - 1)**3*(x + 6)
Factor 1492*p**2 + 2 - 199*p + 82*p + 31*p - 295*p.
(4*p - 1)*(373*p - 2)
Solve -1/3*w**2 + 0 - 116/3*w = 0.
-116, 0
Let o = 98/37 - 290/333. Let r = o - 4/9. Find f such that r*f**3 + 52/9*f**2 + 64/9 + 1/9*f**4 + 32/3*f = 0.
-4, -2
Let d(w) = -14*w**2 - 155*w - 8. Let f be d(-11). Let a(b) be the second derivative of 0 + 10/3*b**3 + f*b - 25*b**2 - 1/6*b**4. Factor a(j).
-2*(j - 5)**2
Let r = 40 - 75/2. Suppose -68*a = -2*a. Factor -r*k**5 + 0*k + a*k**2 + 5*k**4 + 0 - 5/2*k**3.
-5*k**3*(k - 1)**2/2
Let i(b) be the first derivative of 5*b**4/4 - 145*b**3/3 + 345*b**2 - 1343. Let i(o) = 0. Calculate o.
0, 6, 23
Determine n so that 215697492/17*n - 80136*n**2 - 2/17*n**4 + 2860/17*n**3 + 217062666/17 = 0.
-1, 477
Factor 16*r**2 + 0 + 2/9*r**3 - 146/9*r.
2*r*(r - 1)*(r + 73)/9
Let b(z) be the first derivative of -2*z**3/39 + 90*z**2/13 + 14*z - 1095. Factor b(c).
-2*(c - 91)*(c + 1)/13
Let s(u) = 14*u**4 + 6*u**3 + 29*u**2 - 8*u + 33. Let m(n) = 13*n**4 + 7*n**3 + 28*n**2 - 8*n + 30. Let y(h) = 11*m(h) - 10*s(h). Suppose y(l) = 0. What is l?
-4, -2, 0, 1/3
Suppose l + 4*q = 2, -28*q + 33*q = -l + 2. Let b(p) be the second derivative of -1/2*p**3 + l*p - 1/4*p**4 + 9*p**2 + 0. What is v in b(v) = 0?
-3, 2
Solve -6/7*l**4 + 0*l**2 + 8/7*l - 2*l**3 + 0 = 0 for l.
-2, -1, 0, 2/3
Suppose 3312*c - 3201*c - 222 = 0. Factor -2/15*x**c - 16/15 + 6/5*x.
-2*(x - 8)*(x - 1)/15
Let s(l) be the third derivative of l**5/12 + 35*l**4/2 - 435*l**3/2 + 787*l**2. Suppose s(v) = 0. What is v?
-87, 3
Let w(n) = -122*n**3 + 2678*n**2 + 34980*n + 106272. Let b(s) = -17*s**3 + 383*s**2 + 4997*s + 15182. Let i(g) = -36*b(g) + 5*w(g). Factor i(h).
2*(h - 211)*(h + 6)**2
Let c(w) be the first derivative of -4*w**3/3 + 10*w**2 - 24*w - 982. Factor c(l).
-4*(l - 3)*(l - 2)
Let p(r) be the second derivative of 7/78*r**4 + 84*r + 0 + 110/39*r**3 - 32/13*r**2. What is t in p(t) = 0?
-16, 2/7
Let m(o) be the second derivative of -1/60*o**4 + 17/30*o**3 + 9/5*o**2 + 0 + 108*o. Factor m(b).
-(b - 18)*(b + 1)/5
Let j = 4493/53907 + -1/71876. Factor 19/12*u + j*u**2 - 5/3.
(u - 1)*(u + 20)/12
Let g be (3/3*-2)/(-2)*-2. Let y(z) = 5*z**4 + 8*z**3 - 7*z**2 + 15*z + 7. Let j(q) = -q**4 - 2*q**3 + q**2 - q - 1. Let d(w) = g*y(w) - 14*j(w). Factor d(r).
4*r*(r - 1)*(r + 2)**2
Let l(r) be the third derivative of -r**7/1785 + 961*r**6/510 - 307199*r**5/170 - 462241*r**4/51 - 925444*r**3/51 - 2*r**2 - r - 828. Factor l(y).
-2*(y - 962)**2*(y + 1)**2/17
Let l = 25 - 59. Let h be ((-17)/l)/(1 + 0)*22. Determine k so that 3*k**4 - 17*k**2 - 2*k - 2*k**4 + h*k**2 + 3*k**2 = 0.
-1, 0, 2
Factor -1/3*a**2 - 14/3*a - 13/3.
-(a + 1)*(a + 13)/3
Let g(d) = 346*d**2 + 5195*d + 77. Let s be g(-15). Let 188/5*l + 2/5*l**s + 4418/5 = 0. Calculate l.
-47
Let t(b) = 7*b**3 + 39*b**2 - 1. Let w(k) = -5*k**3 - k**2 + 1. Let g(u) = -t(u) - w(u). Factor g(m).
-2*m**2*(m + 19)
Let b(h) be the third derivative of -h**5/3 - 5*h**4/6 + 8*h**3/3 + 8*h**2 - 2*h. Let i(w) = -w**2 + w - 1. Let p(j) = b(j) - 24*i(j). Factor p(t).
4*(t - 10)*(t - 1)
Let h be (-12)/(-88)*(29 + -18). Let y be 0 + 2/(16/12). Let -y*x**3 - 1/2*x**2 - 1/2*x**5 - h*x**4 + 0 + 0*x = 0. What is x?
-1, 0
Let r(w) be the third derivative of w**7/2520 - w**6/6 + 30*w**5 + w**4/24 + 100*w**3/3 + 30*w**2 - 2*w. Let k(n) be the second derivative of r(n). Factor k(t).
(t - 60)**2
Let n = 219246 + -219246. Solve n - 1/6*z**2 - 7/3*z = 0.
-14, 0
Suppose 41*n + 192 = 17*n. Let l be ((-1)/(-12))/((-592)/(-72) + n). Solve 0 + 3/4*y**2 - 9/8*y + l*y**3 = 0 for y.
-3, 0, 1
Let c(p) be the first derivative of p**8/112 - p**7/21 + p**6/24 + p**5/12 - 77*p**3/3 + 23. Let n(k) be the third derivative of c(k). Factor n(d).
5*d*(d - 2)*(d - 1)*(3*d + 1)
Let c(m) be the third derivative of m**7/420 + 59*m**6/120 - 203*m**5/40 + 123*m**4/8 + 5347*m**2. Factor c(i).
i*(i - 3)*(i - 2)*(i + 123)/2
Let u(r) be the first derivative of -2/3*r**3 + 41 - 98*r - 14*r**2. Factor u(m).
-2*(m + 7)**2
Factor 184/3*c**4 - 1694/3*c**2 + 0 + 0*c + 3*c**5 + 781/3*c**3.
c**2*(c + 11)**2*(9*c - 14)/3
Let i(b) be the first derivative of -b**4/8 + b**3/4 - 109*b - 39. Let n(s) be the first derivative of i(s). Find a such that n(a) = 0.
0, 1
Let p be (1610/92 + (-1 - 16))/((-7)/(-6)). Find w such that 12/7 + 12/7*w - 6/7*w**3 - 9/7*w**2 + p*w**4 = 0.
-1, 2
Factor -1/2*c**4 + 198*c - 197/2*c**3 + 100*c**2 + 0.
-c*(c - 2)*(c + 1)*(c + 198)/2
Let b(f) be the third derivative of -f**8/2240 + f**7/420 - f**6/240 - 14*f**5/15 - 53*f**2. Let a(i) be the third derivative of b(i). Factor a(j).
-3*(j - 1)*(3*j - 1)
Factor 4311*x**4 - 4308*x**4 - 9*x**2 + 21*x**2 + 15*x**3.
3*x**2*(x + 1)*(x + 4)
Let l(c) be the first derivative of -c**6/6 + 4*c**5/5 - 5*c**4/4 + 2*c**3/3 + 2045. Factor l(o).
-o**2*(o - 2)*(o - 1)**2
Find p such that 6/7*p**4 + 0 + 96/7*p - 76/7*p**2 + 1/7*p**5 - 27/7*p**3 = 0.
-8, -3, 0, 1, 4
Let j(d) be the second derivative of -4*d - 7/24*d**4 - 6 + 7/60*d**6 + 1/21*d**7 - 3/20*d**5 + 0*d**2 + 1/6*d**3. Solve j(x) = 0 for x.
-2, -1, 0, 1/4, 1
Let c(j) be the second derivative of 20*j**6/27 - 29*j**5/9 + 79*j**4/27 + 56*j**3/27 - 8*j**2/3 - 468*j. Solve c(o) = 0.
-2/5, 3/10, 1, 2
Let k = 47483101/114 - 416523. Let s = k - -90/19. Factor -s*l**2 - 1/2 + 2/3*l.
-(l - 3)*(l - 1)/6
Let d(g) be the second derivative of 5*g**4/12 - 55*g**3/3 - 115*g**2/2 + 1114*g. Let d(v) = 0. What is v?
-1, 23
Let a(c) be the third derivative of -c**6/40 - 31*c**5/20 - 319*c**4/8 - 1089*c**3/2 + 10*c**2 - 4. Factor a(w).
-3*(w + 9)*(w + 11)**2
Let x(s) = 11 + 7*s**4 + 282*s**3 - 6*s**2 + 4*s**4 - 41*s - 251*s**3. Let v(p) = -p - 1. Let j(f) = -3*v(f) - x(f). Factor j(o).
-(o - 1)*(o + 2)**2*(11*o - 2)
Let q(s) be the first derivative of -s**5/30 - 5*s**4/24 + 43*s**3/18 - 67*s**2/12 + 5*s + 1962. Let q(o) = 0. Calculate o.
-10, 1, 3
Let x = 38 - -1. Suppose 2*l - x = -11*l. Find d such that 5/3*d**l - 4/3*d - 4/3*d**2 + 0 + d**4 = 0.
-2, -2/3, 0, 1
Suppose 74*i + 2415 = 2859. Let y(g) be the third derivative of 0 + 3/20*g**4 + 0*g + 1/100*g**i - 1/5*g**3 - 7*g**2 - 3/50*g**5. Factor y(q).
6*(q - 1)**3/5
Solve -10/7*x**2 - 234/7*x - 92/7 = 0 for x.
-23, -2/5
Let l(r) be the first derivative of -r**5/20 + 9*r**4/8 - 33*r**3/4 + 101*r**2/4 - 30*r + 5848. Suppose l(h) = 0. Calculate h.
1, 3, 4, 10
Let k(l) be the third derivative of l**5/20 + 3*l**4/2 + 18*l**3 + 1289*l**2. Factor k(f).
3*(f + 6)**2
Factor 3427*q**2 + 92*q - 3365*q**2 + 48*q.
2*q*(31*q + 70)
Suppose 2*r + 4*c + 34 = 0, 2*r = -64*c + 67*c + 1. Let n be 3*r/(-84)*-3 - -1. Determine l, given that 1/2*l - n*l**2 - 1/4 = 0.
1
Determine d, given that -14/3*d**2 + 4/5*d - 194/15*d**4 - 226/15*d**3 + 0 - 10/3*d**5 = 0.
-2, -1, 0, 3/25
Let w(f) be the third derivative of f**5/180 - 25*f**4/72 + 11*f**3/3 - 637*f**2. Factor w(z).
(z - 22)*(z - 3)/3
Let -1/2*v**2 - 11858 + 154*v = 0. Calculate v.
154
Let p(b) = -33705*b - 33705. Let o be p(-1). Factor 6*t**3 + 2/9*t**5 + 6*t**2 + o*t + 2*t**4 + 0.
2*t**2*(t + 3)**3/9
Let u(z) be the second derivative of -7*z**6/60 + 2*z**5/5 + 71*z**4/8 + 67*z**3/6 - 14*z**2 + z - 2402. Suppose u(f) = 0. What is f?
-4, -1, 2/7, 7
Let g(h) be the first derivative of -1/4*h**4 + 9*h + 2*h**2 + 4 - 1/6*h**3. Let x(p) be the first derivative of g(p). Find q, given that x(q) = 0.
-4/3, 1
Let g(w) = 6*w - 35. Let l be g(6). Let o be (144/(-162))/(1/(-3)*l). Factor 4/3*r**3 - 4*r + o + 0*r**2.
4*(r - 1)**2*(r + 2)/3
Let f(i) be the first derivative of i**8/1120 - 3*i**7/280 + 19*i**3 - 55. Let l(r) be the third derivative of f(r). Let l(s) = 0. Calculate s.
0, 6
Factor -75*d**2 + 11984*d**3 - 11981*d**3 + 141*d - 54 - 15.
3*(d - 23)*(d - 1)**2
Let a be (74/(-18944))/(1/(-4)). Let y(o) be the third derivative of -a*o**4 + 1/560*o**7 - 1/160*o**5 + 0*o**3 + 0 + 0*o + 1/320*o**6 - 34*o**2. Factor y(p).
3*p*(p - 1)*(p + 1)**2/8
Let b(u) be the first derivative of u**8/10080 - u**6/1080 + u**4/144 - 18*u**3 - 58. Let i(q) be the third derivative of b(q). Find t such that i(t) = 0.
-1, 1
Let x = -239290/5509 - -6/787. Let v = x + 2806/63. Factor -v*g + 2/3*g**2 + 4/9.
2*(g - 1)*(3*g - 2)