i**2 + 2/3*i**5 = 0 for i.
0, 1, 2
Factor 15/2 + 8*g + 1/2*g**2.
(g + 1)*(g + 15)/2
Let l(s) = -s - 308*s**2 - 2 + 0 + 309*s**2. Let h(t) = -3*t**2 + 9*t + 12. Let m(f) = 3*h(f) + 12*l(f). What is a in m(a) = 0?
-4, -1
Suppose 1084*g - 67*g - 3316 = -589*g - 52*g. Factor -14/3*j**3 + 4 - 52/3*j**g - 26/3*j.
-2*(j + 1)*(j + 3)*(7*j - 2)/3
Let l(h) = -3*h**3 + 45*h**2 - 8*h + 24. Let a be l(15). Let o be (-16)/a - (-2)/(-12). Solve 2/7*s**4 + 0 + 3/7*s**3 + o*s - 1/7*s**5 + 0*s**2 = 0.
-1, 0, 3
Suppose 0 = 1570*p - 1559*p + 6 - 39. Let l(o) be the second derivative of 1/24*o**4 + 0 + 2/3*o**p - 9/4*o**2 - 22*o. Factor l(y).
(y - 1)*(y + 9)/2
Let d = -6839 + 33615. Factor d*f + 220*f**2 + 40*f**3 + 310*f**3 + 125*f**4 - 26736*f.
5*f*(f + 2)*(5*f + 2)**2
Suppose 530*i**2 - 245*i + 99*i**3 - 30 + 1685*i**4 - 1735*i**4 - 304*i**3 = 0. Calculate i.
-6, -1/10, 1
Let z(s) be the first derivative of -s**4/42 - 8*s**3/21 - 15*s**2/7 + 176*s - 154. Let t(w) be the first derivative of z(w). Determine g so that t(g) = 0.
-5, -3
Suppose -129*p = -406*p + 3147 + 177. Solve 6/7*a**4 - 69/7*a**3 - 192/7 + 48*a + 3/7*a**5 - p*a**2 = 0.
-4, 1, 4
Let t = 1844/7 + -263. Let w be 7/98*54 + -3. Factor t*z**4 + w + 3/7*z - 9/7*z**2 - 3/7*z**3.
3*(z - 2)*(z - 1)*(z + 1)**2/7
Let j(z) = 3*z**2 + 17*z - 3. Let b be j(-6). Suppose -r = 4*v - 4 - 0, 0 = v + b*r + 10. Factor q**v - 2 + 3 - 1.
q**2
Let a(t) = -3824*t**2 + 1812608*t - 1808808. Let x(i) = i**3 + 9*i**2 - i + 3. Let g(b) = -a(b) - 2*x(b). Factor g(w).
-2*(w - 951)**2*(w - 1)
Suppose 1295*d + 101*d - 123*d - 2546 = 0. Let -3 + 21/2*u - 3*u**d - 9/2*u**3 = 0. Calculate u.
-2, 1/3, 1
Let k be (17/408*27*2)/3. Let x(t) = -t**2 - 10*t - 11. Let o be x(-8). Solve -3/2*w**4 - 3/2 + 3*w**2 - 3/2*w**3 + 3/4*w + k*w**o = 0 for w.
-1, 1, 2
Let i = -1844/3 - -618. Let c(j) be the second derivative of -3*j + 1/3*j**4 + i*j**3 + 0 - 12*j**2. Factor c(g).
4*(g - 1)*(g + 6)
Suppose -22*b + 435 - 201 = 17*b. Let a(i) be the third derivative of -1/735*i**7 + 0*i**4 + 1/210*i**5 + 0*i + 0*i**3 + 0 + 7*i**2 + 0*i**b. Factor a(g).
-2*g**2*(g - 1)*(g + 1)/7
Suppose -3*m = 2*j - 3129, 4*m - 2*j + j = 4183. Suppose -m = -9*y + 4*y. Let -y*o - o**3 - 6*o**2 + 208*o + 4*o**2 = 0. What is o?
-1, 0
Let q = -10 - -12. Suppose r + 4*a - 3 = -0*a, -q*a = 2*r - 6. Let 9*t**r + 3*t**5 + 42*t**4 - 5*t**2 + 5*t**2 - 30*t**4 = 0. Calculate t.
-3, -1, 0
Let n(f) = -f**2 + f + 98. Let x be n(0). Let l be 1029/x + (1 - 1). Factor l*j**2 - 15/2*j**3 - 9/2*j + 0 + 3/2*j**4.
3*j*(j - 3)*(j - 1)**2/2
Let x(y) be the first derivative of -61 + 0*y + y**6 + 0*y**4 + 0*y**3 - 3/5*y**5 + 0*y**2. Factor x(c).
3*c**4*(2*c - 1)
Let k(p) = -5017*p - 747531. Let y be k(-149). Factor 46/9*c - 16/3 + 2/9*c**y.
2*(c - 1)*(c + 24)/9
Let x(a) be the first derivative of a**3/33 - 75*a**2/22 - 14*a - 3698. Factor x(v).
(v - 77)*(v + 2)/11
Let 622/7*y**2 + 64/7*y**3 + 248*y + 168 + 2/7*y**4 = 0. Calculate y.
-14, -3, -1
Let v(j) = 1866 + 80*j + 8*j**3 - 34*j**2 + 43*j - 13*j**2 - 1869. Let c(m) = -m**3 - m**2 - m + 1. Let k(r) = -3*c(r) - v(r). Factor k(t).
-5*t*(t - 6)*(t - 4)
Let p be (1 + 2118/(-28))*808/1515. Let i = p + 288/7. Let 0*c + 0 + i*c**2 - 1/3*c**3 = 0. What is c?
0, 4
Let -434*t**3 - 1182/11*t**2 + 8064/11*t**4 + 648/11*t**5 + 48*t + 104/11 = 0. Calculate t.
-13, -2/9, 1/2
Factor 2196/7 + 384/7*r + 3/7*r**2.
3*(r + 6)*(r + 122)/7
Let a(x) = -29*x**2 - 758*x - 70685. Let c(q) = -136*q**2 - 3788*q - 353426. Let y(j) = -28*a(j) + 6*c(j). Factor y(m).
-4*(m + 188)**2
Suppose -4*b - 4*k + 38 = -2*b, 0 = -4*b + k + 76. Suppose -3*t = -17 - b. Determine c so that 25*c + c + 2*c**3 + 109*c**2 - t - 125*c**2 = 0.
1, 6
Suppose -3003*o + 1095*o + 1620*o - 4624 + 1172*o + o**3 + 64*o**2 = 0. Calculate o.
-34, 4
Let q(x) = 8*x**2 + 44*x. Let u(z) be the third derivative of z**5/30 - z**4/12 + 122*z**2. Let r(v) = -q(v) + 6*u(v). Factor r(a).
4*a*(a - 14)
Let r be (1 - -298)/(35 - 34). Find l, given that l - r*l**3 + 298*l**3 - 5*l + 4*l**2 = 0.
0, 2
Let k(s) = 4*s**3 - s**2 + s + 6. Let g be k(2). Let f be (-100)/(-48) + (-27)/g. Factor f + 14/3*p**2 + 6*p.
2*(p + 1)*(7*p + 2)/3
Let m = 147681/5 + -29536. Factor -6/5 + j - m*j**2.
-(j - 3)*(j - 2)/5
Let o(w) be the second derivative of -5*w**4/12 - 2995*w**3/3 + 5995*w**2/2 + 2202*w + 2. Determine g so that o(g) = 0.
-1199, 1
Let a be 1/((-2)/(-4)*1). Suppose 6*p - 2*p - 2*r = 12, 2*p - 3*r - 10 = 0. Factor -165*z**4 + 163*z**4 + 2*z**3 + 2*z**3 - p*z**a.
-2*z**2*(z - 1)**2
Let s(u) = -12*u + 51. Let t be s(4). Solve -3*c**t - c**3 - 12*c + 4*c**3 - 9*c**2 + 3*c**3 = 0 for c.
-1, 0, 4
Let i(k) = -615*k - 214018. Let f be i(-348). What is p in 6/5*p**f - 36/5 - 6/5*p = 0?
-2, 3
Let j(n) = n**3 + 4*n**2 + 2*n + 8. Let q be j(-4). Suppose 5*y + 17 - 117 = q. Factor 3*l**3 - y*l + 20*l.
3*l**3
Let j(z) be the first derivative of z**3 + 1413*z**2 + 665523*z - 351. Factor j(y).
3*(y + 471)**2
Suppose -5*y = 2*r - 35, -y + 5*y - 10 = 2*r. Let d be 33/27 + (r - 6). Determine b so that 4/9*b + d*b**2 - 2/9*b**4 + 0 - 4/9*b**3 = 0.
-2, -1, 0, 1
Let k(h) be the first derivative of -96/5*h + 33/20*h**4 - 3/25*h**5 + 96/5*h**2 - 65 - 42/5*h**3. Determine w so that k(w) = 0.
1, 2, 4
Let p(n) = n**2 + 31*n - 21. Let a(g) = -2 - 2 + 96*g - 112*g - g**2 + 15. Let l(t) = -11*a(t) - 6*p(t). Determine b, given that l(b) = 0.
1
Let m(g) be the third derivative of -1/12*g**4 + 7/60*g**5 - 1/24*g**6 + 0*g**3 - 314*g**2 + 0 + 0*g. Suppose m(a) = 0. Calculate a.
0, 2/5, 1
Suppose -3*g - 80 = -5*i, g + 3*i = -27 - 9. Let a be 40/g*21/(-154). Factor -4/11*x - 2/11*x**4 + a + 4/11*x**3 + 0*x**2.
-2*(x - 1)**3*(x + 1)/11
Let v be (3 - 3)/(-1)*(9 - 4)/(-20). Factor 2/9*p**4 + v*p + 0 - 2/9*p**2 + 0*p**3.
2*p**2*(p - 1)*(p + 1)/9
Let j(a) be the third derivative of -32/3*a**3 + 0 + 0*a - 1/15*a**5 - 5/3*a**4 - 13*a**2. Solve j(w) = 0 for w.
-8, -2
Suppose 0 = -22*o + 2673 + 1045. Let s be (-26)/o + (-2)/(-13). Determine f, given that 0 + s*f + 2/3*f**2 = 0.
0
Let s(r) be the first derivative of 5*r**6/3 - 366*r**5/5 - 269*r**4/2 + 214*r**3/3 + 264*r**2 + 152*r - 682. Find b such that s(b) = 0.
-1, -2/5, 1, 38
Let c(v) be the first derivative of -3*v**4/14 + 120*v**3/7 - 177*v**2/7 + 4028. Let c(r) = 0. Calculate r.
0, 1, 59
Factor 26*u**2 + 6*u**2 + 11*u**2 - 45*u**2 + 397*u + 639*u.
-2*u*(u - 518)
Suppose 2156*t - 206*t**2 + 65*t**2 + 71*t**2 - 1162084 + 69*t**2 = 0. What is t?
1078
Let t(z) be the first derivative of z**3/6 - 521*z**2/2 + 271441*z/2 - 1205. Factor t(o).
(o - 521)**2/2
Let b(n) = 0 - 62*n + 63*n + 1. Let z(d) = -3*d**2 - 30*d - 27. Let g(c) = 3*b(c) + z(c). Factor g(u).
-3*(u + 1)*(u + 8)
Let t(u) = -u**3 - 65*u**2 - 737*u + 653. Let s be t(-50). Let 0*k + 1/3*k**2 - 4/9 - 1/9*k**s = 0. What is k?
-1, 2
Let t be (-12)/(-2)*3/6. Suppose -4*o + 8 = -3*y - y, 3*y + t*o - 18 = 0. Factor 2*u**2 - 8*u**2 + 6*u + 3*u**y + 0*u**2.
-3*u*(u - 2)
Suppose -4 = -4*t + 2*m, -m - 2 = 25*t - 24*t. Find n, given that 9/8*n**2 + t - 3/4*n - 9/8*n**4 + 3/8*n**5 + 3/8*n**3 = 0.
-1, 0, 1, 2
Determine x so that -110/9*x + 0 - 2/9*x**2 = 0.
-55, 0
Let f(g) = 2*g**3 - 52*g**2 - 246*g + 4. Let k(a) = -a**3 + 2*a**2 + a - 1. Suppose -39 = 8*y - 7. Let c(d) = y*k(d) - f(d). Suppose c(v) = 0. Calculate v.
-11, 0
Let d = 235356 - 235354. Factor -22/3 - 3*y + 1/3*y**d.
(y - 11)*(y + 2)/3
Let a be ((-60368)/(-2304))/7 + 6/(-32). Solve -a*k + 0 + 8/9*k**2 + 4/9*k**3 = 0 for k.
-4, 0, 2
Let 4/7*a**5 - 204/7*a**2 + 0 - 52/7*a**3 - 144/7*a + 12/7*a**4 = 0. What is a?
-3, -1, 0, 4
Let m(w) be the first derivative of 20*w - 2/3*w**3 - 5/3*w**4 - 12 + 1/5*w**5 + 10*w**2. Let g(k) be the first derivative of m(k). Factor g(s).
4*(s - 5)*(s - 1)*(s + 1)
Let k(w) be the third derivative of w**5/420 - 449*w**4/168 - 451*w**3/21 - 1006*w**2. Solve k(f) = 0 for f.
-2, 451
Let f(g) be the third derivative of -g**7/210 + 11*g**6/60 + 23*g**5/60 - 303*g**2 - 2. Factor f(q).
-q**2*(q - 23)*(q + 1)
Determine x so that 52/3*x + 2/3*x**3 + 112/3 - 58/3*x**2 = 0.
-1, 2, 28
Let u(t) be the second derivative of -2*t**6/105 - t**5/5 - 2*t**4/7 - 1899*t. Factor u(q).
-4*q**2*(q + 1)*(q + 6)/7
Let h(v) be the second derivative of v**6/105 + v**5/14 + 2*v**4/21 - 2033*v. Factor h(i).