 = 0. What is h?
0, 1, 2
Let k(l) = -74*l**2 + 1942*l + 318828. Let b(v) = 21*v**2 - 648*v - 106276. Let w(f) = -21*b(f) - 6*k(f). Solve w(d) = 0 for d.
-326
Determine x so that -9/7*x**2 - 5329/7 - 438/7*x = 0.
-73/3
Let w(o) = -16*o - 58. Let l be w(-7). Let r be 29/33 + l/(-99). Find z, given that -2/3*z**3 - 1/3*z**4 + r*z**2 + 2/3*z + 0 = 0.
-2, -1, 0, 1
Suppose -150 = 34*r - 84*r. Let g(a) be the first derivative of 2*a**2 + 6*a + 10 - 2/3*a**r. Find f such that g(f) = 0.
-1, 3
Let d(u) be the third derivative of 9*u**7/2 + 1089*u**6/4 + 1047*u**5 + 5165*u**4/3 + 1520*u**3 + 1006*u**2. Factor d(z).
5*(3*z + 2)**3*(7*z + 228)
Let n(q) be the third derivative of q**6/20 + 17*q**5/30 - 2*q**4/3 + 47*q**3/6 - 9*q**2 - 2*q. Let h(t) be the first derivative of n(t). Factor h(x).
2*(x + 4)*(9*x - 2)
Let d(b) = 19*b**2 - 140*b + 45. Let n(q) = 170*q**2 - 1260*q + 405. Suppose -2 = g - 37. Let x(s) = g*d(s) - 4*n(s). Factor x(k).
-5*(k - 9)*(3*k - 1)
Suppose -n - 62 = -5*v, 7*v - 3*v - 50 = n. Suppose 85*m - 101*m**2 - 7*m - 81*m**3 + v*m**4 + 85*m - 40*m**2 + 48 - m = 0. Calculate m.
-2, -1/4, 1, 8
Let v(g) be the third derivative of -g**6/420 - g**5/30 + 12*g**3/7 - 149*g**2 - 14. Find t, given that v(t) = 0.
-6, -3, 2
Let m = 42487 + -2549219/60. Let v(a) be the second derivative of 2/5*a**2 - m*a**4 + 41*a + 0 - 2/15*a**3 + 1/100*a**5. Factor v(f).
(f - 2)*(f - 1)*(f + 2)/5
Let p be 87/18 + 6/36. Let b(x) = -3*x**5 + 9*x**4 - 25*x**3 - 5*x**2. Let t(k) = -4*k**5 + 10*k**4 - 24*k**3 - 6*k**2. Let g(h) = p*t(h) - 6*b(h). Factor g(o).
-2*o**3*(o - 3)*(o + 5)
Factor -3508*y - 1197*y**2 - 900*y**2 - 120*y**3 + 3*y**4 - 219*y**3 - 6293*y - 9882 - 1116*y**2.
3*(y - 122)*(y + 3)**3
Let m(r) = 11*r + 7*r - 10*r - 5 + r**2. Let x be m(-10). Solve 219*c - 107*c - x*c**2 - 109*c = 0 for c.
0, 1/5
Find y, given that -515/2*y**4 + 41354280*y - 177447456 - 85555/2*y**3 - 1/2*y**5 - 4075425/2*y**2 = 0.
-177, 8
Let l = 1352/434775 - 1/527. Let w = 41/75 - l. Determine j so that w*j**2 + 384/11 - 96/11*j = 0.
8
Let j(y) be the second derivative of 0*y**2 - 9/100*y**5 - 7*y - 1/50*y**6 + 0*y**4 + 2 + 2/5*y**3. Suppose j(c) = 0. What is c?
-2, 0, 1
Let q = -640 - -416. Let y be -9 + (q/3)/(-8). Factor -4/3 - y*p**2 - 4/3*p.
-(p + 2)**2/3
Let o(j) be the first derivative of j**4/6 - 49*j + 17. Let f(c) be the first derivative of o(c). Suppose f(g) = 0. Calculate g.
0
Suppose -12*k = -14*k + 4. Factor -25*v**3 + 22*v**2 - 42*v - 14*v**3 - 18*v**3 + 11*v**k - 72 + 60*v**3.
3*(v - 2)*(v + 1)*(v + 12)
Let w = 50 + -52. Let m be (-4 + 1 + 1 + -10)/w. Factor 25*t**3 - m*t + 90*t**2 - 19*t - 125*t**4 - 27*t - 4 + 12.
-(t + 1)*(5*t - 2)**3
Let p(f) be the second derivative of -3*f**4/8 - 76*f**3 - 303*f**2/4 + 5236*f. Let p(q) = 0. What is q?
-101, -1/3
Let x(n) = n**3 + 13*n**2 + 23*n - 13. Let k be x(-11). Let v be 9 - 23/((-92)/k). Suppose 33/2*o + 9/2 + 21*o**2 + 9*o**v - 3/2*o**5 - 3/2*o**4 = 0. What is o?
-1, 3
Let p(x) be the third derivative of x**6/40 + 97*x**5/10 + 1137*x**4/8 + 846*x**3 + 5881*x**2. Factor p(y).
3*(y + 3)**2*(y + 188)
Suppose 271 - 289 = -3*o. Factor -5*w**5 + 2*w**5 + 5*w**2 + 21*w**3 - 17*w**2 + o*w**4 - 12*w**4.
-3*w**2*(w - 1)**2*(w + 4)
Let k(o) = -o**2 + 4*o + 1. Let z be k(3). Suppose 3*u + z = 46. Solve 5*y**2 + 20*y + 2 - 41 + u = 0 for y.
-5, 1
Let h(y) be the third derivative of -19*y**2 + 2*y**5 + 0*y - 1/24*y**6 - 40*y**4 + 1280/3*y**3 + 0. Solve h(v) = 0.
8
Let s(v) = v**2 + 352*v + 8177. Let z be s(-25). Factor 2/25*j**5 + 0 + 4/25*j**4 - 2/5*j + 28/25*j**z - 24/25*j**3.
2*j*(j - 1)**3*(j + 5)/25
Let t(o) be the third derivative of -o**7/2205 - 3*o**6/70 - 781*o**5/630 - 39*o**4/7 - 676*o**3/63 + 84*o**2 - 1. Factor t(s).
-2*(s + 1)**2*(s + 26)**2/21
Let l = -47/660 + 45869/4620. Solve -l*x**2 + 0 + 18/7*x + 78/7*x**3 - 3*x**4 - 6/7*x**5 = 0.
-6, 0, 1/2, 1
Let p(o) = -o + 3. Let j be p(4). Let i(d) = -5*d - 3. Let c be i(j). Factor 16 - 6*z**c - 2*z**3 + 22 - 30.
-2*(z - 1)*(z + 2)**2
Let o(s) = 120*s**3 - 1170*s**2 + 10240*s - 22130. Let b(j) = 11*j**3 - 106*j**2 + 931*j - 2012. Let t(m) = 65*b(m) - 6*o(m). Factor t(l).
-5*(l - 16)*(l - 5)**2
Suppose -5*h + 4*x + x - 5 = 0, 4*x = -4*h + 28. Let v(b) = 1112*b**2 - 13342*b - 20. Let k be v(12). Factor 18/7 + 48/7*j + 16/7*j**h + 2/7*j**k + 44/7*j**2.
2*(j + 1)**2*(j + 3)**2/7
Factor 434*l - 65*l**3 + 1460 - 1825*l**2 + 5*l**4 - 1460 - 2189*l.
5*l*(l - 27)*(l + 1)*(l + 13)
Let 0*r - 4/7*r**5 - 28*r**3 + 96/7*r**2 + 104/7*r**4 + 0 = 0. What is r?
0, 1, 24
Let p(c) be the second derivative of c**4/3 + 836*c**3/3 + 87362*c**2 + 75*c + 1. Factor p(t).
4*(t + 209)**2
Let c be 3/2*(-618)/515*(-20)/18. Let v(m) be the second derivative of 5/2*m**3 - 16*m + 5*m**c + 5/12*m**4 + 0. Factor v(k).
5*(k + 1)*(k + 2)
Let h(o) be the third derivative of -o**5/20 - 277*o**4/2 - 153458*o**3 - 98*o**2 + 27*o. Suppose h(b) = 0. Calculate b.
-554
Let p(f) = f**3 + 5*f**2 - f - 12. Let w be p(-2). Solve 10*h**5 + 6*h**w + 10*h + 8*h**2 - 5*h**5 - 5*h**4 - 9*h**2 - 15*h**3 = 0 for h.
-1, 0, 1, 2
Let l(o) be the third derivative of 1/20*o**7 + 1/448*o**8 + 16*o**3 + 159*o**2 + 8*o**4 + 0*o + 5/2*o**5 + 0 + 19/40*o**6. Factor l(h).
3*(h + 2)**3*(h + 4)**2/4
Factor -128/19*g + 382/19*g**2 + 122/19*g**4 + 0 + 2/19*g**5 - 378/19*g**3.
2*g*(g - 1)**3*(g + 64)/19
Suppose 0 = -26*c + 69 + 61. Suppose 568*d**2 - 61*d**2 - 42135*d + 288*d**2 - c*d**3 + 172287 + 572098 = 0. What is d?
53
Let o(l) = -12*l**3 + 10*l**2 + 2*l - 2. Let j(r) be the third derivative of -r**7/210 + r**4/24 - r**3/6 + r**2 + 63*r. Let k(m) = -2*j(m) + o(m). Factor k(v).
2*v**2*(v - 5)*(v - 1)
Let u(z) be the third derivative of z**8/84 - 22*z**7/105 - 13*z**6/30 + 11*z**5/15 + 2*z**4 - 1539*z**2. Let u(v) = 0. What is v?
-1, 0, 1, 12
Let z be (26/78)/(285/35 - 16/2). Factor 0 - 2*j - 1/3*j**3 + z*j**2.
-j*(j - 6)*(j - 1)/3
Suppose p - 1 = 4*n - 2*n, 4*n - p + 3 = 0. Let d(o) = -o**2 + o - 1. Let h(c) = 20*c**2 - 60*c + 85. Let q(y) = n*h(y) - 15*d(y). What is v in q(v) = 0?
2, 7
Let r(j) be the first derivative of -2*j**3/3 + 120*j**2 - 7200*j + 12554. Factor r(u).
-2*(u - 60)**2
Let u(r) be the first derivative of r**7/210 - r**6/50 + r**4/15 + 45*r - 76. Let t(g) be the first derivative of u(g). Factor t(c).
c**2*(c - 2)**2*(c + 1)/5
Let t = 74 + -69. Find u, given that -6 + 1 - t*u**2 - 5 + 15*u + 0 = 0.
1, 2
Let f(m) be the third derivative of m**7/105 - 26*m**6/15 + 34*m**5/5 + 139*m**2. Factor f(k).
2*k**2*(k - 102)*(k - 2)
Find u such that -645*u - 27*u**2 + 22*u**2 + 2*u**2 + 1310 - 2*u**2 = 0.
-131, 2
Let g(m) be the third derivative of 49/60*m**6 + 0*m + 5/4*m**4 - 39*m**2 + 1/3*m**3 + 21/10*m**5 - 2. Solve g(h) = 0.
-1, -1/7
Suppose 39601/6 + 1/6*v**2 + 199/3*v = 0. What is v?
-199
Let q(w) be the first derivative of -4/3*w**3 - 7/2*w**4 + 16*w + 28*w**2 + 78. Factor q(p).
-2*(p - 2)*(p + 2)*(7*p + 2)
Let b = 302485 + -302485. Let i be 1/(-2)*8*-1. Factor -1/6*p**5 + 0 + b*p**2 + 0*p**3 + 1/6*p**i + 0*p.
-p**4*(p - 1)/6
Let j = -27559 + 193013/7. Factor -4/7*k**3 - 60/7*k - 36/7*k**2 + j.
-4*(k - 1)*(k + 5)**2/7
Let z(r) = r**2 - 18*r + 83. Let t be z(10). Factor 4*v**3 + v**4 + v**2 - v**2 + 0*v**2 + t*v**2.
v**2*(v + 1)*(v + 3)
Let 578/3*v**2 + 486 - 612*v = 0. What is v?
27/17
Let o(a) be the third derivative of 37*a**8/448 - 4*a**7/5 + 493*a**6/160 - 47*a**5/8 + 43*a**4/8 - a**3 + 268*a**2 + 6*a. Suppose o(p) = 0. What is p?
2/37, 1, 2
Factor 158*t**2 - 3*t**4 + 165*t**3 + 8*t**4 - 54 + 577*t**2 + 995*t - 90 + 564.
5*(t + 1)**2*(t + 3)*(t + 28)
Let b be (-160)/(5 + -13)*8/40. Let k(d) be the first derivative of -1/2*d**2 - 1/6*d**6 + 0*d**3 + 0*d + 16 + 0*d**5 + 1/2*d**b. Find s, given that k(s) = 0.
-1, 0, 1
Let f = 153 - 289. Let v be f/(-340) + (2/(-5) - 0). Determine d, given that 1/2*d**5 - 1/2*d**3 + v*d + d**2 - d**4 + 0 = 0.
-1, 0, 1, 2
Let m(q) = -q**2 + q + 2. Let k(p) = 5*p**2 - 21*p + 10. Let i = -213 + 214. Let v(o) = i*k(o) + 3*m(o). Factor v(a).
2*(a - 8)*(a - 1)
Factor 27/5*x**3 - 3/5*x**4 + 0*x + 6*x**2 + 0.
-3*x**2*(x - 10)*(x + 1)/5
Let j(v) = 2*v - 5. Let n be j(5). Determine t so that 5*t**4 - 1115*t**2 + 2*t**n + 5*t**4 + 14*t**3 + 1121*t**2 = 0.
-3, -1, 0
Let v be -2 - ((-72)/6 - -10). Let t be 