 c(t) = 0.
-7, 2/7, 1
Let k be 1/1*1 + (-342)/(-342). Let -72/5 - 2/5*w**k - 24/5*w = 0. What is w?
-6
Let -226/7*f - 114/7 + 2/7*f**3 - 110/7*f**2 = 0. What is f?
-1, 57
Let d(o) = 2*o**4 + 2*o - 1. Let j(i) = -14*i**4 - 4*i**3 - 2*i**2 - 20*i + 10. Let l(c) = 10*d(c) + j(c). Factor l(n).
2*n**2*(n - 1)*(3*n + 1)
Let -20*z**4 - 940*z**4 - 256*z**5 + 2673*z**3 - 108*z - 3809*z**3 - 8 - 532*z**2 = 0. What is z?
-2, -1, -1/4
Let p(q) = q**3 - 4*q**2 - 2*q - 5. Let m be p(5). Let h = -8 + m. Determine u so that -2/3*u - 2/3*u**5 + 0 + 8/3*u**4 - 4*u**3 + 8/3*u**h = 0.
0, 1
Let p(h) be the first derivative of -12*h**5/5 + 75*h**4/4 - 50*h**3 + 105*h**2/2 - 18*h - 915. Suppose p(t) = 0. Calculate t.
1/4, 1, 2, 3
Let w be (3/(-2))/((-1)/2). Let s = w + -1. Factor -5 - 3 + 2*y**s + 0.
2*(y - 2)*(y + 2)
Suppose -5 = -3*x + 7. Let g(s) be the third derivative of 1/60*s**6 - 1/4*s**x + 0*s + 0*s**5 + 2/3*s**3 + 4*s**2 + 0. What is b in g(b) = 0?
-2, 1
Suppose 2*p + 56 = 16. Let k be (24/260)/((-3)/p). Determine a, given that k - 8/13*a + 2/13*a**2 = 0.
2
Let p(v) be the first derivative of -3*v**5/35 + 9*v**4/14 - 4*v**3/7 - 9*v**2/7 + 15*v/7 + 78. What is m in p(m) = 0?
-1, 1, 5
Let j be (2/(-5))/1 + 5049/85. What is k in -60 + 116 - j + 3*k**2 = 0?
-1, 1
Suppose 0*p = -4*p + 8, 0 = -c + p + 5. Let b = c + -12. Let k(f) = -3*f**2 - 3*f + 2. Let a(v) = -6*v**2 - 6*v + 5. Let w(o) = b*k(o) + 2*a(o). Factor w(h).
3*h*(h + 1)
Let l = -485 - -488. Let n(w) be the second derivative of -5*w + 1/24*w**4 + 1/2*w**2 - 1/4*w**l + 0. Factor n(z).
(z - 2)*(z - 1)/2
Let h(x) = -11*x**2 + 27*x - 48. Let b(c) = 31*c**2 - 82*c + 143. Let a(f) = -3*b(f) - 8*h(f). Solve a(w) = 0 for w.
3
Let t be (-20 - -18)*(-2 - 13/(-7)). Let s be (-3)/9 + 7/3. Solve 0 - t*o**3 + 0*o**s + 2/7*o = 0.
-1, 0, 1
Let p(j) = -j**3 - 19*j**2 - 15*j + 40. Let u be p(-18). Let d be 0/((-6)/(u/7)). Factor 0 + 1/4*n**3 + 0*n**2 + d*n - 3/4*n**4 + 1/2*n**5.
n**3*(n - 1)*(2*n - 1)/4
Let o(q) be the third derivative of 0 - 1/105*q**5 + 0*q + 0*q**3 - 1/42*q**4 + 9*q**2. Determine p so that o(p) = 0.
-1, 0
Let q be 2/(6/9)*1. Factor -10*t + 2*t + 12*t**q - 7*t + 6 - 6*t**2 + 3*t**3.
3*(t - 1)*(t + 1)*(5*t - 2)
Let p be (-129)/12 + 8 + 5. Find w such that 0*w - 3/2*w**2 - 3/4*w**4 - p*w**3 + 0 = 0.
-2, -1, 0
Suppose 2*p + 5*n = 5*p - 15, -2*n + 25 = 5*p. Let -15*h**3 - h**p - 570 - 7*h**4 - 9*h**2 + 570 = 0. Calculate h.
-3, -1, 0
Factor -f - 2*f + f**2 + 11 - 14*f + 5*f.
(f - 11)*(f - 1)
Let v(i) = i**3 + 510*i**2 + 17342*i + 196520. Let a(z) = 25*z**3 + 13770*z**2 + 468235*z + 5306040. Let u(y) = 2*a(y) - 55*v(y). Suppose u(c) = 0. What is c?
-34
Suppose 30*d**2 + 15*d**4 - 55*d**3 + 35*d - 40 - 10*d + 30*d + 5*d = 0. Calculate d.
-1, 2/3, 2
Let a(i) = -i**3 + 7*i**2 - 6*i. Let s be a(6). Suppose m - 5 = -s. Factor 3*o**4 - 50*o - 3*o**m + 50*o.
-3*o**4*(o - 1)
Let t be 104/16 + -1 + -5. Let v(a) be the first derivative of 0*a**5 + t*a**4 - 5 + 0*a - 1/2*a**2 - 1/6*a**6 + 0*a**3. Solve v(l) = 0 for l.
-1, 0, 1
Suppose -5*x + 22 + 33 = 0. Suppose -18*j + 15*j + x = -b, -5*b = j - 9. Factor 1/5*q**j + 0 - 1/5*q**2 + 2/5*q**3 - 2/5*q.
q*(q - 1)*(q + 1)*(q + 2)/5
Let y(f) be the third derivative of 9*f**8/112 + 3*f**7/10 + 2*f**6/5 + f**5/5 + 5*f**2 + 15*f. Determine b, given that y(b) = 0.
-1, -2/3, 0
Let g be (8/(-6))/(1/(-3)). Find s, given that -15*s**2 - 3*s**3 + 18*s + 0*s**3 - 35*s + 8*s + 3*s**g = 0.
-1, 0, 3
Let w(k) be the third derivative of 3/50*k**5 - 7/60*k**4 + 2/15*k**3 + 0*k - 1/60*k**6 - 34*k**2 + 0 + 1/525*k**7. Let w(u) = 0. What is u?
1, 2
Let d(c) be the first derivative of -c**3/3 + 43*c**2/2 + 90*c - 166. Suppose d(j) = 0. What is j?
-2, 45
Let y = -2360 - -2364. Factor 3/2*a**2 + 5/6*a**3 + 1/6*a**y + 7/6*a + 1/3.
(a + 1)**3*(a + 2)/6
Let l(o) be the third derivative of o**8/84 + o**7/10 + 29*o**6/120 + o**5/10 - 378*o**2. Factor l(q).
q**2*(q + 2)*(q + 3)*(4*q + 1)
Find x such that 933/2*x**3 + 0 + 3/4*x**5 - 153/4*x**4 + 585*x**2 - 1014*x = 0.
-2, 0, 1, 26
Let h = 829/4862 + 5/442. Factor -h*k**5 + 4/11*k**2 + 0 + 2/11*k - 4/11*k**4 + 0*k**3.
-2*k*(k - 1)*(k + 1)**3/11
Let u(s) be the first derivative of -s**6/24 + s**5/20 + 3*s**4/16 - 5*s**3/12 + s**2/4 + 385. Factor u(g).
-g*(g - 1)**3*(g + 2)/4
Suppose -7 = 4*b - 0*b - x, 2*b + 9 = -5*x. Let k(c) = -2*c**3. Let d(h) = 4*h**3 + 26*h**2 + 22*h + 4. Let i(r) = b*k(r) + d(r). Determine w so that i(w) = 0.
-2, -1, -1/4
Let v(m) = m**2 - 3*m - 1. Let s be v(7). Let i = s - 24. Factor i*y**2 - 4*y**2 + 16*y - 12 - 3*y**2.
-4*(y - 3)*(y - 1)
Let z(k) be the third derivative of -k**9/3780 + k**8/840 - k**7/630 - k**4/24 - 23*k**2. Let v(h) be the second derivative of z(h). Factor v(x).
-4*x**2*(x - 1)**2
Let n(w) be the third derivative of 0*w**4 + 0*w - 6*w**2 + 1/30*w**5 + 0*w**3 + 1/40*w**6 + 0. Suppose n(u) = 0. What is u?
-2/3, 0
Let y = -33 + 3. Let u be (-2)/7 + y/(-7). Factor -6*j**3 + 3*j**3 - 3*j**4 + 0*j**u.
-3*j**3*(j + 1)
Let g = 79 - 127. Let c be (g/(-16))/((-3)/(-5)). Find n such that 8*n + c*n**2 - 5*n**4 - 20*n + 14*n - 2*n**3 = 0.
-1, -2/5, 0, 1
Let y = -70 + 74. Let d(j) be the second derivative of 0*j**2 - 1/10*j**6 - 1/14*j**7 + 0 - 4*j + 1/4*j**y + 0*j**3 + 3/20*j**5. Factor d(h).
-3*h**2*(h - 1)*(h + 1)**2
Let j be (-18 + 24)*4/8. Factor 0 + 0*n + 0*n**4 + 2/7*n**j - 2/7*n**5 + 0*n**2.
-2*n**3*(n - 1)*(n + 1)/7
Let w be 1236/15 - 44/110. Let t be 1/(-1) + 4 + -1. Suppose -v**3 + w - 82 + 2*v - v**t = 0. Calculate v.
-2, 0, 1
Let o(k) = 2*k**3 - 4*k**2 - k + 6. Let f be o(2). Suppose 4*i**2 - i**2 + 8 + 7*i**2 + 36*i - f*i - 50*i**3 = 0. What is i?
-2/5, 1
Let c(v) be the first derivative of 7 + 0*v - 1/14*v**4 + 0*v**2 + 0*v**3. Factor c(o).
-2*o**3/7
Suppose -5*f - 3*x = 12, -5*x = 4*f - 0*f + 20. Factor 14*q + f*q**2 - 5*q**2 + 13*q + 40 - 37*q.
-5*(q - 2)*(q + 4)
Suppose 20/9*a**2 + 0 + 0*a + 4/3*a**4 - 64/9*a**3 = 0. Calculate a.
0, 1/3, 5
Let k(z) = -3*z**2 + z + 2. Let x(h) = 12*h**2 - 114*h + 102. Let t(i) = 3*k(i) + x(i). Find m such that t(m) = 0.
1, 36
Factor 26*w**2 + w**3 - w - 26*w**2.
w*(w - 1)*(w + 1)
Let n be (3 - 6)/(9/(-6)). Determine i so that -i**n + 6*i**2 + i**2 + i**3 - 5*i**2 = 0.
-1, 0
Let w(q) = -10*q**4 - 60*q**3 + 200*q**2 - 205*q + 75. Let c(b) = -9*b**4 - 59*b**3 + 199*b**2 - 205*b + 74. Let z(h) = -5*c(h) + 4*w(h). Factor z(n).
5*(n - 1)**3*(n + 14)
Let i(d) = -d**4 - 89*d**3 + 591*d**2 - 1479*d + 1338. Let g(v) = 90*v**3 - 590*v**2 + 1480*v - 1340. Let j(a) = 6*g(a) + 5*i(a). Factor j(h).
-5*(h - 10)*(h - 3)**3
Let j = -2 + 12. Suppose 2 = -9*q + j*q. Factor -6*w + 12*w**2 - 6*w**q + 3*w**3 - 3*w**3 + 2 - 2*w**3.
-2*(w - 1)**3
Let c(m) = -m**2 - 10*m - 4. Let f be c(-9). Factor -55*n**3 + 380*n**4 + 60*n - 40 + 0*n**f - 5*n**5 - 350*n**4 + 10*n**2.
-5*(n - 2)**3*(n - 1)*(n + 1)
Suppose 13*j + 5*j = j. Let b(f) be the second derivative of j - 4/15*f**6 - 3*f + 0*f**5 + 2/3*f**4 + 0*f**2 + 2/21*f**7 - 2/3*f**3. Factor b(y).
4*y*(y - 1)**3*(y + 1)
Let 0 + c**5 + 3/2*c**4 + 1/2*c**2 + 3/2*c - 9/2*c**3 = 0. What is c?
-3, -1/2, 0, 1
Let v(s) = -s**4 - 8*s**3 + 10*s**2 - 10*s. Let c(l) = -l**4 - l**3 - l**2 - l. Let i(z) = -6*z + 42. Let o be i(8). Let x(j) = o*c(j) + 3*v(j). Factor x(a).
3*a*(a - 2)**3
Let i be 0/(3*(-4)/(-6)). Let q be -4 + ((-18)/(-3) - i). Suppose -1/3*p**3 - 4/3*p**q - p + 0 = 0. Calculate p.
-3, -1, 0
Suppose -4*k - 22 = -3*l, 3*k + 1 = -4*l - 3. Factor 35*u**l + 3 + 16 + 5 + 40*u**2 - 90*u.
3*(5*u - 4)*(5*u - 2)
Let k = 75 + -73. Let 0*f**2 + k + f - 4*f**2 + 3*f**2 = 0. Calculate f.
-1, 2
Factor -2/5 - 3/5*q + 4/5*q**3 + 2/5*q**2 + 0*q**4 - 1/5*q**5.
-(q - 2)*(q - 1)*(q + 1)**3/5
Suppose -m + 4*l + 1 = 15, 4*l - 12 = 2*m. What is t in -3*t**4 - 3*t**2 + t**2 - 3*t**3 + 3*t + 5*t**m = 0?
-1, 0, 1
Let f = 2366 + -2364. Solve 1/2*q + 3/2*q**f - 1/2*q**3 - 3/2 = 0 for q.
-1, 1, 3
Let -40 - 21*m + 53*m + 5*m**2 - 22*m = 0. Calculate m.
-4, 2
Let r(x) be the second derivative of -x**4/84 - 4*x**3/21 - 6*x**2/7 - 2*x - 23. Factor r(c).
-(c + 2)*(c + 6)/7
Let i = 714 + -2138/3. Let f(r) be the first derivative of 2*r**2 - 5/12*r**4 + 4 - i*r - 1/3*r**3. Determine z so that f(z) = 0.
-2, 2/5, 1
Let a(q) = -3*q**2 - 29*q + 13. Let t be a(-10). Factor -4*b**2 - t*