at is u in 30*u + 0*u**4 + u**3 - 16*u**3 + 14*u**2 - 21*u**4 - 12*u**3 - 3*u**5 + 7*u**2 = 0?
-5, -2, -1, 0, 1
Let w(g) be the first derivative of -43 + 20/3*g**3 + 6*g**2 - 36*g + g**4. Solve w(k) = 0 for k.
-3, 1
Let x(y) = 10*y + 12. Suppose -5*g - 10 + 32 = 3*s, -21 = -4*s - 5*g. Let m be x(s). Let 8/5*o - m + 2/5*o**2 = 0. What is o?
-5, 1
Let g(u) = -19*u**3 + 2104*u**2 - 16*u - 2097. Let w(d) = 8*d**3 - 1051*d**2 + 7*d + 1048. Let x(q) = 3*g(q) + 7*w(q). Factor x(m).
-(m - 1)*(m + 1)*(m + 1045)
Factor 1/3*i**3 - 7*i**2 + 24*i - 68/3.
(i - 17)*(i - 2)**2/3
Let u(v) be the first derivative of 2*v**6/3 + 90*v**5 + 12315*v**4/4 - 38305*v**3/6 + 4845*v**2 - 3249*v/2 + 7522. Determine r so that u(r) = 0.
-57, 1/2
Let i(r) be the third derivative of r**5/180 + 457*r**4/12 + 208849*r**3/2 - 6*r**2 + 230*r + 2. Factor i(v).
(v + 1371)**2/3
Factor -42/5*m**2 + 0 + 2/5*m**4 - 8*m + 0*m**3.
2*m*(m - 5)*(m + 1)*(m + 4)/5
Let v(k) = -k**3 - 5*k - 6. Let a be v(-1). Let x(l) be the first derivative of 2/5*l**3 - 3/5*l**5 + 0*l + a*l**2 + 41 + 9/20*l**4. What is b in x(b) = 0?
-2/5, 0, 1
Solve -1/7*l**2 - 260/7*l + 0 = 0 for l.
-260, 0
Let l be 66/(-297) + -14*(-46)/(-18). Let k be 2*(-138)/l + 3. Find b such that -128/9 - k*b - 2/9*b**3 - 8/3*b**2 = 0.
-4
Suppose m = v + 5, -m - 3 = -5*v - 28. Suppose -4*y = -2*l - 9 - 3, 4*l + 8 = m. Factor -1/2*r + 1 + 1/2*r**3 - r**y.
(r - 2)*(r - 1)*(r + 1)/2
Suppose -5 = 2*d - 5*v, 3*v + 5 = 2*d - 0*v. Suppose 2*f - 23 - 17 = 2*m, 4*m + 5 = -f. Factor 34*z**4 + 0*z**2 - 14*z**4 - 15*z**2 + d*z - f*z**4.
5*z*(z - 1)**2*(z + 2)
Let w(t) = 5*t**2 + 41*t + 11. Let i be w(-8). Suppose 3*j - 16 = -j. Factor 3*h**2 + 0*h**j - h**4 + 2*h**3 + 10*h - 7 - 6*h**i - 1.
-(h - 1)**2*(h + 2)*(h + 4)
Suppose q = u - 6, -7*q + 10*q + 28 = 5*u. Let i be (-8)/(-10 - -14)*u/(-2). Determine d so that 0*d**3 - 8/11*d**4 + 32/11*d**2 + 2/11*d**i + 0 - 32/11*d = 0.
-2, 0, 2
Suppose -272/3*l**2 - 136*l**3 + 404/3*l - 64/3*l**4 + 112 + 4/3*l**5 = 0. What is l?
-4, -1, 1, 21
Let n be 479/(-119) - 702/5967 - (1 - 6). Find m such that -6/7*m**2 + n*m**3 + 3/7 + 3/7*m**4 - 3/7*m - 3/7*m**5 = 0.
-1, 1
Find z such that -2203 - 2681*z**2 + 2358*z + 2684*z**2 - 158 = 0.
-787, 1
Let w be (14/(-4))/(3/30). Let c be ((-2)/7 - 220/w) + -2. Solve 13*y**3 - 6*y + 10*y**3 - 21*y**3 - c*y**2 = 0.
-1, 0, 3
Suppose 0 = -15*l + 14*l + 2. Let -244*z**3 + l*z - 655*z**4 + 122*z + 174*z**2 + 16 + 585*z**4 = 0. Calculate z.
-4, -2/7, -1/5, 1
Find s, given that 1125/2*s - 5*s**3 - 375/4*s**2 + 0 + s**4 = 0.
-10, 0, 15/2
Let l(w) be the third derivative of -w**9/105840 - w**8/17640 - 19*w**5/15 - 85*w**2. Let m(k) be the third derivative of l(k). Solve m(j) = 0.
-2, 0
Let x(n) = 38*n**4 + 122*n**3 - 1186*n**2 - 7250*n - 10012. Let d(o) = -12*o**4 - 38*o**3 + 395*o**2 + 2417*o + 3337. Let z(g) = -16*d(g) - 5*x(g). Factor z(i).
2*(i - 17)*(i + 2)*(i + 7)**2
Suppose 0 = 2*a - 3*r - 3980, -7*a - 4*r - 5972 = -10*a. Let i = a + -13960/7. Find c, given that -i*c**2 + 20/7*c - 8/7 = 0.
2/3, 1
Let n(s) be the third derivative of s**5/120 - 65*s**4/48 + 21*s**3/2 - s**2 + 20*s + 25. Factor n(c).
(c - 63)*(c - 2)/2
Let g(n) = 20*n**2 - 144*n + 196. Suppose -189 - 3 = -8*k. Let h(o) = -o**2 - 2. Let t(i) = k*h(i) + g(i). What is f in t(f) = 0?
-37, 1
Let s(x) be the third derivative of x**6/540 + 4*x**5/45 - 79*x**4/108 + 2*x**3 - 16*x**2 + 82*x. Factor s(q).
2*(q - 2)*(q - 1)*(q + 27)/9
Let i(l) = -5*l**3 + 5*l**2 + 334*l - 332. Let z be i(1). Factor k + 1/2*k**3 - 3/2*k**z + 0.
k*(k - 2)*(k - 1)/2
Let r(h) be the second derivative of -h**4/54 + 20*h**3/27 + 23*h**2/3 + 22*h + 14. Factor r(o).
-2*(o - 23)*(o + 3)/9
Let o(q) = -q**2 - q. Let x(u) = -2*u**2 - 9*u - 1. Let h(t) = -3*o(t) + x(t). Let b(y) = -y. Let r(v) = 6*b(v) - h(v). Factor r(a).
-(a - 1)*(a + 1)
Let d(i) be the first derivative of 2*i**5/5 + 210*i**4 + 836*i**3 + 1252*i**2 + 834*i + 8274. Factor d(q).
2*(q + 1)**3*(q + 417)
Suppose -5*m - 102 = 8. Let k(d) = -d**2 - d - 1. Let i(j) = 3*j**3 - 18*j**2 - 11*j - 7. Suppose -9*x - 18 = -36. Let s(r) = m*k(r) + x*i(r). Factor s(v).
2*(v - 2)*(v - 1)*(3*v + 2)
Factor -86*l**2 + 175 - 30*l + 31*l**2 + 25*l**2 - 155*l.
-5*(l + 7)*(6*l - 5)
Let a(v) be the second derivative of -v**6/10 + 269*v**5/20 - 535*v**4/36 + 89*v**3/18 - 7*v + 20. Solve a(d) = 0 for d.
0, 1/3, 89
Let w(k) be the third derivative of 23*k**6/72 + 557*k**5/180 - 91*k**4/72 - 5*k**3/18 - 2*k**2 - 4554. Factor w(m).
(m + 5)*(5*m - 1)*(23*m + 1)/3
Solve 4/3*f**2 - 11/3*f - 10 + 1/3*f**3 = 0.
-5, -2, 3
Let s = -36 - -42. Suppose 0 = a - s*m + 3*m, -4 = -2*a + 2*m. Let 5*l**a + 150*l - 10*l**4 + 5*l**5 - 150*l = 0. What is l?
0, 1
Suppose 24*i - 38*i = 17906. Let j = i - -1282. Factor -1/5*m**j + 3/5*m**2 + 4/5*m + 0.
-m*(m - 4)*(m + 1)/5
Factor 3/2*r**2 - 594*r + 58806.
3*(r - 198)**2/2
Let k(b) be the second derivative of 2/15*b**4 + 3 - 4/15*b**3 + 0*b**2 - 1/50*b**5 + 10*b. Solve k(j) = 0 for j.
0, 2
Factor 1124/5*p**2 - 2232/5*p - 32/5.
4*(p - 2)*(281*p + 4)/5
Suppose 54*b - 18*b = 14*b + 17*b. Let m(l) be the second derivative of 10/9*l**4 + 0*l**2 - 1/12*l**5 - 19*l + b*l**3 + 0. Factor m(o).
-5*o**2*(o - 8)/3
Let h = -54862 - -54865. Determine l, given that -3/5 + 7/5*l**2 + 2/5*l**h + 2/5*l = 0.
-3, -1, 1/2
Solve -60 + 34*g**4 + 1165*g**3 + 14*g - 1192*g**3 + 13*g - 31*g**4 + 57*g**2 = 0.
-1, 1, 4, 5
Let n = 285 - 1985/7. Find b, given that 0 - n*b - 2/7*b**2 = 0.
-5, 0
Let t be (3 + -295)/(3*(-4)/66). Determine l so that 8*l**2 + 10*l**3 + t*l + 2*l**4 - 1606*l = 0.
-4, -1, 0
Let f(w) be the first derivative of -5*w**6/6 - 13*w**5 - 115*w**4/4 - 55*w**3/3 + 1826. Let f(y) = 0. Calculate y.
-11, -1, 0
Let d = -417 - -423. Let r(u) be the second derivative of 36/5*u**3 + 0 - 2*u**5 - 27/5*u**2 - 3*u**4 + 5/3*u**d - 19*u. Factor r(a).
2*(a + 1)*(5*a - 3)**3/5
Find g such that -4*g**4 - 12/5*g**3 + 56 + 748/5*g**2 - 996/5*g = 0.
-7, 2/5, 1, 5
Let b(p) = -p**3 + 5*p**2 - p - 9. Let q be b(4). Suppose -228*u + 15*u**5 - 26*u**5 + 553*u**2 + 348*u**4 - 61*u**5 + 36 - 638*u**q = 0. What is u?
1/2, 2/3, 3/2
Find l such that -92/7*l**2 + 24 + 3860/7*l = 0.
-1/23, 42
Let w(o) = 20*o**2 - 8*o + 36. Let p be -2 + ((-112)/12)/((-4)/6). Let l(i) = 8*i**2 - 3*i + 15. Let k(x) = p*l(x) - 5*w(x). Factor k(h).
-4*h*(h - 1)
Let j(r) = 30*r - 104. Let p be j(4). Suppose -177*v**3 + 86*v**3 - p*v**2 + 24*v + 93*v**3 = 0. Calculate v.
0, 2, 6
Let s(i) = 82*i**2 - 40*i**2 - 43*i**2 + 2 + 11*i - 24. Let v(m) = -12*m + 21. Let w(n) = -3*s(n) - 4*v(n). Factor w(q).
3*(q - 1)*(q + 6)
Suppose -12*p - 15 = 21. Let v(i) = 2*i**3 - 43*i**2 + 3*i + 3. Let d(w) = 6*w**3 - 130*w**2 + 8*w + 8. Let f(l) = p*d(l) + 8*v(l). Factor f(g).
-2*g**2*(g - 23)
Suppose 5*o + u + 0*u = -29, 5*o + 2*u = -33. Let b be 9/(-78)*o*(-32)/(-120). Find d such that -b + 2/13*d**2 + 0*d = 0.
-1, 1
Determine b so that 0 + 21*b**4 + 3/2*b**5 + 729/2*b - 405*b**2 + 18*b**3 = 0.
-9, 0, 1, 3
Let -4374/7 - 3/7*b**3 - 1215/7*b - 108/7*b**2 = 0. What is b?
-18, -9
Factor -58*b + 160302*b**3 - 160284*b**3 - 2*b**4 + 45 + 6*b**2 - 9.
-2*(b - 9)*(b - 1)**2*(b + 2)
Factor -2/3*p**3 + 0 - 10*p**2 - 24*p.
-2*p*(p + 3)*(p + 12)/3
Let m = 427269 + -2990867/7. Solve 0 - m*i**2 + 8/7*i**3 + 4/7*i**4 + 0*i - 2/7*i**5 = 0 for i.
-2, 0, 2
Let p = 1/78 - -71/546. Let c be ((7/2 - 2)/(378/72))/(85/255). Let -v**2 + p - c*v = 0. What is v?
-1, 1/7
Let o(c) be the second derivative of c**6/300 + 7*c**5/40 + 19*c**4/5 + 656*c**3/15 + 1408*c**2/5 + 2324*c. Factor o(u).
(u + 8)**3*(u + 11)/10
Let g be (-1739)/(-423) + 130/(-117). Find o, given that 25/6 - 25/6*o - 1/6*o**2 + 1/6*o**g = 0.
-5, 1, 5
Suppose 36/5*z - 3*z**2 + 27/5 = 0. Calculate z.
-3/5, 3
Let k(j) be the third derivative of -j**5/120 + 73*j**4/48 + 37*j**3/6 - 4*j**2 + 159*j. Suppose k(l) = 0. Calculate l.
-1, 74
Suppose -13*u + 3*v + 30 = -9*u, -8 = 4*v. Let p be 6/u*6/(1 + 2). Let 2/13 - 4/13*q + 2/13*q**p = 0. Calculate q.
1
Let t(g) = 5*g**2 - 16*g. Let s(u) = -32*u**2 + 82*u + 120. Let j(l) = -s(l) - 6*t(l). Factor j(q).
2*(q - 5)*(q + 12)
Let z be (-415)/7553*(-2352)/140. Find a, given that z*a - 112/13*a**3 + 0 + 10/13*a**2 = 0.
-2/7, 0, 3/8
Let u(g) be the second derivative of g**8/84 + 2*g**7/3