2
Let l = 9 - 59/7. Suppose 0 = -5*m - 3*f + 3347 - 3337, 5*f = 5*m - 50. Factor l*o**3 + 0*o + 8/7*o**m + 0 + 12/7*o**4 + 0*o**2.
4*o**3*(o + 1)*(2*o + 1)/7
Let y(a) be the second derivative of a**4/24 + 113*a**3/12 - 655*a. Determine q, given that y(q) = 0.
-113, 0
Let t(a) be the first derivative of a**5/6 - 5*a**4/3 + 115*a**3/18 - 35*a**2/3 + 10*a - 3970. What is o in t(o) = 0?
1, 2, 3
Let m(d) be the first derivative of d**6/3 + 10154*d**5/35 + 918751*d**4/14 - 440198*d**3/7 - 263538*d**2/7 + 788. Let m(i) = 0. Calculate i.
-363, -2/7, 0, 1
Let l(x) be the third derivative of -x**5/210 - x**4/2 + 43*x**3/21 + 308*x**2 + 2*x. Factor l(r).
-2*(r - 1)*(r + 43)/7
Suppose -4 = -2*f + 4*i, 4*f - 2*i - 13 = i. Determine d so that -4*d**5 + 9 + 364*d + 536*d**2 + 344*d**3 + 78 + 5 + 76*d**f = 0.
-1, 23
Let z(l) = 14*l**3 + 2119*l**2 + 1048*l - 1061. Let w(u) = 2*u**3 + 2*u**2 - u - 3. Let y(o) = 2*w(o) - z(o). Suppose y(n) = 0. What is n?
-211, -1, 1/2
Let o(w) be the third derivative of w**6/780 + 7*w**5/390 + 2*w**4/39 - 16*w**3/39 - w**2 + 326. Suppose o(n) = 0. Calculate n.
-4, 1
Let v(t) be the first derivative of -27 + 125/3*t**3 + 0*t + 5/4*t**4 + 0*t**2. Factor v(y).
5*y**2*(y + 25)
Let -1006/5*f + 2/5*f**2 + 1004/5 = 0. What is f?
1, 502
Let s(i) be the third derivative of -1/180*i**6 - 11/90*i**5 + 0 + 0*i**3 - 43*i**2 - 2*i + 0*i**4. Suppose s(v) = 0. Calculate v.
-11, 0
Let q(s) = -s + 3. Let l(p) = p**2 + 738 - 1453 - 32*p + 736. Let o(w) = -2*l(w) - 10*q(w). What is a in o(a) = 0?
1, 36
Factor 496/7*g**2 + 31242/7*g + 60516/7 + 2/7*g**3.
2*(g + 2)*(g + 123)**2/7
Suppose -2*f - 4*q - 17 - 7 = 0, 0 = 2*f - 4*q. Let x be 6/(13 + -4 + f). Factor -18/5*t**3 + 33/5*t**x - 17/5*t + 2/5.
-(t - 1)*(3*t - 2)*(6*t - 1)/5
Let j(z) = 11*z**4 + 44*z**3 + 357*z**2 - 882*z - 2. Let s(i) = 93*i**4 + 354*i**3 + 2856*i**2 - 7056*i - 17. Let h(b) = 51*j(b) - 6*s(b). Factor h(o).
3*o*(o - 2)*(o + 21)**2
Suppose -l + g + 30 = 3*l, g = 3*l - 23. Suppose 8 = l*y - 13. Factor -12*h**3 - h**y + 5*h**3 - 15*h + 3*h**3 + 20*h**2.
-5*h*(h - 3)*(h - 1)
Let f(a) be the first derivative of -a**6/3 - 6*a**5/5 + 5*a**4 - 4*a**3/3 - 9*a**2 + 10*a + 3510. Factor f(l).
-2*(l - 1)**3*(l + 1)*(l + 5)
Let c(y) = -2*y + 62. Let a be c(29). Suppose -4*d + j + 13 = -4, -5*d + a*j + 35 = 0. Suppose -1/4*h**3 + d - 1/4*h**2 + 2*h = 0. Calculate h.
-2, 3
Factor 0*m - 2/13*m**5 + 0*m**3 - 16/13*m**4 + 0*m**2 + 0.
-2*m**4*(m + 8)/13
Let u(h) be the second derivative of h**4/27 + 50*h**3/27 + 32*h**2 + 13*h - 43. Factor u(f).
4*(f + 9)*(f + 16)/9
Factor -50/17*n**4 - 581042/17*n + 0 - 570262/17*n**2 + 10730/17*n**3.
-2*n*(n + 1)*(5*n - 539)**2/17
Let h(c) be the first derivative of -9/4*c**2 + 1/8*c**4 + 1/2*c**3 + 79 + 5/2*c. Find i, given that h(i) = 0.
-5, 1
Let q(k) = -21*k + 237. Let c be q(11). Let c - 7 + 30*t + 2 - 2*t**2 - 26 - 3*t**2 = 0. What is t?
1, 5
Factor -2617*d**2 - 1320*d + 3*d**3 - 2785*d**2 + 5081*d**2 - 1332.
3*(d - 111)*(d + 2)**2
Solve -196/3*k - 614/9*k**3 + 2/9*k**5 - 10/9*k**4 + 0 - 1190/9*k**2 = 0.
-14, -1, 0, 21
Let q(j) be the third derivative of 27*j + 2*j**2 - 1/180*j**5 + 0 - 1/6*j**4 - 11/18*j**3. Factor q(n).
-(n + 1)*(n + 11)/3
Let s(i) = 15*i**2 - 222*i + 3. Let z(b) = -19*b**2 + 225*b - 4. Let w(t) = -4*s(t) - 3*z(t). Solve w(c) = 0 for c.
0, 71
Let p(y) be the third derivative of 5*y**8/336 - 4*y**7/3 + 37*y**6 - 728*y**5/3 + 1690*y**4/3 - 3*y**2 + 4*y + 56. Factor p(m).
5*m*(m - 26)**2*(m - 2)**2
Let a(v) = v**3 - 7*v**2 + 5*v + 8. Let m be a(6). Suppose 12*f + 205*f = 96*f. Suppose 1/3*g - 1/6*g**4 - 1/3*g**3 + 1/6 + f*g**m = 0. Calculate g.
-1, 1
Let n(p) be the second derivative of p**7/63 - 2*p**6/3 + 99*p**5/10 - 668*p**4/9 + 944*p**3/3 - 768*p**2 - 6088*p. Solve n(h) = 0.
3, 4, 16
Let f(x) = x**3 + 16*x**2 - 9*x - 130. Let u be f(-16). What is c in u*c - 5*c**2 - 91 + 25*c - 35 + 2*c**2 = 0?
6, 7
Let l(w) be the second derivative of -w**5/10 - 7*w**4/3 - 17*w**3 - 54*w**2 + 276*w. Factor l(g).
-2*(g + 2)*(g + 3)*(g + 9)
Let n(q) be the second derivative of 1/21*q**7 + 113*q - 7/3*q**4 - 3/10*q**5 - 8/3*q**3 + 4/15*q**6 + 2 + 0*q**2. Determine s, given that n(s) = 0.
-4, -1, 0, 2
Let o(u) be the second derivative of -u**6/1440 + u**5/240 - u**3/2 - 14*u**2 - 14*u + 2. Let p(y) be the second derivative of o(y). Find a such that p(a) = 0.
0, 2
Let 724/7*r + 488/7 - 12/7*r**2 + 4/7*r**4 - 244/7*r**3 = 0. What is r?
-1, 2, 61
Suppose 3*d = -2*j - 24, 5*j + 11*d = 7*d - 53. Let f be (1 - j) + (-480)/60. Find x, given that 1/3*x**f + 3 + 2*x = 0.
-3
Let p = 652 - 652. Factor 15*x - 127*x + x**2 - 2*x**2 - 3136 + p*x**2.
-(x + 56)**2
Suppose 87*k - 2*a - 30 = 85*k, 3*a + 33 = 0. Solve 0 - 32/3*u**2 + 0*u**k + 8*u**3 + 4*u - 4/3*u**5 = 0.
-3, 0, 1
Let d(o) be the first derivative of 3*o**5/5 + 11*o**4/3 - 4*o**3 - 16*o**2 + 212*o + 136. Let k(r) be the first derivative of d(r). Factor k(b).
4*(b - 1)*(b + 4)*(3*b + 2)
Factor 11*p**2 + 7/4 + 309/4*p.
(p + 7)*(44*p + 1)/4
Let x(m) be the second derivative of -3/16*m**5 + 3*m**2 - 3*m + 48 - 1/40*m**6 + 1/2*m**3 - 3/8*m**4. Factor x(g).
-3*(g - 1)*(g + 2)**3/4
Let r(c) be the first derivative of -5/2*c**4 + 4*c**2 + 1/3*c**6 + 2*c**5 + 40*c - 230 - 50/3*c**3. Find x such that r(x) = 0.
-5, -2, -1, 1, 2
Let d(c) be the first derivative of -c**3 - 129*c**2/2 - 126*c + 952. Determine o so that d(o) = 0.
-42, -1
Let d(p) be the first derivative of 0*p**2 + 112 + 2/39*p**3 - 8/13*p. Factor d(l).
2*(l - 2)*(l + 2)/13
Factor -164446*j + 7*j**3 + 7970882*j - 3*j**3 + 11176*j**2.
4*j*(j + 1397)**2
Let 3*z**2 - 41*z - 82 - 15*z - 4*z**2 + 99*z = 0. Calculate z.
2, 41
Let g(f) = 1 - 5*f**2 + f - 3*f**2 + 9*f**2. Suppose -32 + 35 = -3*r. Let w(j) = -8*j**2 - 8*j - 14. Let k(q) = r*w(q) - 10*g(q). Factor k(o).
-2*(o - 1)*(o + 2)
Let u(i) be the second derivative of -i**4/24 + 9*i**3/4 + 45*i**2/2 - 681*i. What is q in u(q) = 0?
-3, 30
Let o(u) be the first derivative of -u**6/30 - 17*u**5/25 - 11*u**4/4 - 7*u**3/3 + 28*u**2/5 + 52*u/5 + 6206. Let o(x) = 0. Calculate x.
-13, -2, -1, 1
Let x(f) = 11*f**3 - 23*f**2 - 10*f. Let z(w) be the first derivative of -w**4/4 + w**3/3 + w**2/2 - 9. Let j(b) = 3*x(b) + 12*z(b). Solve j(i) = 0 for i.
-2/7, 0, 3
Let v(l) = -36*l**4 + 36*l**3 + 480*l**2 + 688*l - 16. Let s(x) = 7*x**4 - 7*x**3 - 96*x**2 - 138*x + 3. Let w(h) = 16*s(h) + 3*v(h). Let w(f) = 0. What is f?
-3, -2, 0, 6
Let s = 126 + -117. Factor s + 3 + 4*g**3 - 12 - 4*g.
4*g*(g - 1)*(g + 1)
Determine x so that -22464*x + 104*x**4 - 229*x**5 - 203*x**5 + 1164*x**3 + 24*x**4 + 20736 + 436*x**5 + 432*x**2 = 0.
-12, 1, 3
Let f(t) be the third derivative of t**7/210 - 17*t**6/60 - 37*t**5/15 - 19*t**4/3 + 217*t**2 - t. Factor f(a).
a*(a - 38)*(a + 2)**2
Let w(i) be the second derivative of -i**6/80 - 27*i**5/40 - 17*i**4/16 + 9*i**3/4 + 105*i**2/16 - 2*i + 110. Let w(x) = 0. Calculate x.
-35, -1, 1
Let n(i) = -i**2 + 12*i - 9. Let c be n(11). Solve 5*m**4 - 297*m**c + 58*m + m**5 - 24*m**4 + 112*m**3 + 5*m**3 + 212*m = 0 for m.
0, 3, 10
Factor 108/13 + 2/13*w**3 - 16/13*w**2 - 30/13*w.
2*(w - 9)*(w - 2)*(w + 3)/13
Let j be 300/(-30) + 47 + 76. Suppose -499/2*d**2 + 25*d**5 + 1/4*d**3 - j*d - 14 + 1405/4*d**4 = 0. What is d?
-14, -2/5, -1/4, 1
Let j(p) be the third derivative of p**6/24 + 211*p**5/12 + 520*p**4/3 + 690*p**3 + 525*p**2. Factor j(c).
5*(c + 2)**2*(c + 207)
Suppose 0 = 4*i - i - 2*b - 11, 4*b - 8 = -4*i. Let s be (6/3 - -1)/(i/2). Find a such that -375/4 - 3/4*a**3 - 45/4*a**s - 225/4*a = 0.
-5
Factor -1143/2*j - 3/2*j**2 - 570.
-3*(j + 1)*(j + 380)/2
Let f(n) be the second derivative of n**5/60 - 23*n**4/18 - 16*n**3/3 - 7711*n. Determine v, given that f(v) = 0.
-2, 0, 48
Suppose -2*s = 3*v - 0*s - 1, 0 = 4*v - 3*s - 24. Suppose v*n - 9 = f, 9*n = 4*n + 5*f + 25. Factor -18 - 6 + 18*o + 10*o + 12*o**n - 6*o**3 - 4*o**4 - 6*o**3.
-4*(o - 1)**2*(o + 2)*(o + 3)
Let w(c) = 42*c - 20. Let i be w(-5). Let g = i + 254. Factor 12*l**2 - g + 21/2*l**4 + 24*l**3 + 3/2*l**5 - 24*l.
3*(l - 1)*(l + 2)**4/2
Suppose 95*x - 98*x + 22 = -d, 3*d = 3*x. Factor -1/2*q**2 + d*q - 121/2.
-(q - 11)**2/2
Let p = -296 - -298. Factor 8*q**2 - 6*q**2 + 4*q**3 - 5*q**p - q**4 - 10 + 10.
-q**2*(q - 3)*(q - 1)
Let 0*w - 3/4*w**