 0 for a.
-1, 0, 4
Let u be (-8)/4 - (1 + 2 + -142). Let w = u + -682/5. Factor 3/5*z**3 - w*z + 3/5*z**4 + 0 - 3/5*z**2.
3*z*(z - 1)*(z + 1)**2/5
Let u(z) be the second derivative of 0*z**4 + z**2 - 2*z + 1/15*z**5 - 8/3*z**3 + 0. Let y(i) be the first derivative of u(i). Find f such that y(f) = 0.
-2, 2
Factor -g**2 - 15*g**3 + 7*g**2 - 11*g**3 + g**3 + 15*g**3 + 18*g + 2*g**4.
2*g*(g - 3)**2*(g + 1)
Let s(o) be the third derivative of o**8/504 - 2*o**7/35 + 17*o**6/180 + 439*o**2. Factor s(w).
2*w**3*(w - 17)*(w - 1)/3
Let v(q) = -4*q - 44. Let t be v(-13). Suppose -a**2 - 11*a - a - 10*a**2 + t*a**2 - 12 = 0. What is a?
-2
Let w = -54 + 43. Let d be w/(-4) - 18/24. Factor 3/2*l**4 + 0 + 15/2*l**d + 6*l**3 + 3*l.
3*l*(l + 1)**2*(l + 2)/2
Let x = 20099 - 20097. Determine o, given that 8/7 - x*o + 4/7*o**2 + 2/7*o**3 = 0.
-4, 1
Suppose -3*h = -8 + 2. Factor -11*k**2 + 30*k**h - 12*k**2 - 11*k**2.
-4*k**2
Let j(o) = 2*o - 19. Let t be j(13). Let s = 15 + t. Find n, given that 8 - 8 + 24*n - 14*n**2 - s*n**2 - 3*n**4 + 18*n**3 = 0.
0, 2
Factor 2 + 5/2*o + 1/2*o**2.
(o + 1)*(o + 4)/2
Let m be 5 - (-2 - -2 - (1 - 3)). What is r in -780*r - 3*r**3 - 792 + 128 - r**m + 116*r**2 - 236 = 0?
-1, 15
Let v(l) = 29*l**3 - 40*l**2 - 14*l - 1. Let d(u) = -u**3 - u**2 + 1. Let r(p) = 5*d(p) + 5*v(p). Factor r(c).
5*c*(4*c - 7)*(7*c + 2)
Let y(z) be the first derivative of -8/7*z - 4/7*z**3 - 17 + 9/7*z**2 + 1/14*z**4. Determine m so that y(m) = 0.
1, 4
Suppose -6*d + 444 = -2*d. Let h = 335/3 - d. Solve -h*f**2 + 2/3*f**3 + 0*f + 0 = 0.
0, 1
Let 135*k**2 - 7*k**5 + 33*k**4 + 48*k**3 + 275 - 495*k**2 - 432*k + 10*k**5 + 1021 = 0. What is k?
-6, -3, 2
Let x(w) be the third derivative of -w**5/105 - 5*w**4/42 + 4*w**3/7 + 2*w**2 - 38*w. Solve x(s) = 0 for s.
-6, 1
Let s(l) = 3*l**2 + l. Let x(g) be the third derivative of 4*g**5/15 + g**4/6 - g**3/6 - 4*g**2. Let h(u) = -11*s(u) + 2*x(u). Let h(w) = 0. Calculate w.
-2, -1
Let n be 4 + 245/(-60) - (-110)/24. Factor -3/4*s**2 - 6 + n*s.
-3*(s - 4)*(s - 2)/4
Let a(s) = -2*s**2 - 253*s + 2443. Let w be a(9). Factor -f**w + 4/3*f**2 + 1/3*f**5 + 0 + 0*f**3 + 0*f.
f**2*(f - 2)**2*(f + 1)/3
Let k = -52588 - -52588. Factor -4*n**2 + k + 4/3*n**3 + 8/3*n.
4*n*(n - 2)*(n - 1)/3
Let v = 114 - 115. Let w be (12/162)/(v/(-3)). Let -2*s - w*s**3 + 0 - 4/3*s**2 = 0. Calculate s.
-3, 0
Suppose -2/7*s**3 - 4200*s + 60*s**2 + 98000 = 0. What is s?
70
Let r = 1/21877 + 7219403/153139. Let o = r - 324/7. Determine y so that o*y + 0 + 2/7*y**2 = 0.
-3, 0
Suppose 0 = -5*k - 5*f + 10, 123*f - 118*f = -4*k + 8. Let 0 + 8/5*a**3 - k*a**2 + 4/5*a - 2/5*a**4 = 0. What is a?
0, 1, 2
Solve 3*c**4 - 5*c**4 + 4911*c**5 - 10*c**3 - 4910*c**5 + 20*c**2 + 9*c - 18 = 0.
-3, -1, 1, 2, 3
Suppose 0 = -6*l + 2*l. Factor l*y**2 - y**2 - 2 + 4*y**2 - 3*y - 4*y**2.
-(y + 1)*(y + 2)
Let i(f) be the third derivative of 1/100*f**5 + 1/5*f**3 + 31*f**2 - 3/40*f**4 + 0*f + 0. Factor i(h).
3*(h - 2)*(h - 1)/5
Let i = 24155 - 24155. Factor 1/5*q**3 + 0 + 2/5*q**2 + i*q.
q**2*(q + 2)/5
Factor 0*w + 2/11*w**4 + 54/11*w**2 + 56/11*w**3 + 0.
2*w**2*(w + 1)*(w + 27)/11
Find h such that -1/2*h**2 - 1/4*h**3 + 0 + 0*h = 0.
-2, 0
Let f be (336/(-18))/8 + (-4)/(-3). Let k be f/(-1) + (-6 - (-119)/21). Solve -4/9*l**3 - k*l**2 + 4/9*l + 0 = 0.
-2, 0, 1/2
Let n(s) = s + 14. Let u be n(-6). Determine h so that -2*h**2 + h**2 - h**2 + h**2 + u*h - 16 = 0.
4
Factor 16 + 6*o + 54*o**2 + 44*o - 170*o**4 + 22*o**3 + 172*o**4.
2*(o + 1)**3*(o + 8)
Let b(n) be the third derivative of -75*n**6/32 - 155*n**5/16 - 35*n**4/24 + 5*n**3/6 - 19*n**2 + 3. Find c such that b(c) = 0.
-2, -2/15, 1/15
Let m(x) be the first derivative of 1/8*x**4 + 0*x**2 + 1/20*x**5 - 2 - 2*x + 1/12*x**3. Let n(v) be the first derivative of m(v). Factor n(s).
s*(s + 1)*(2*s + 1)/2
Suppose -2*q - 5*t + 17 = -1, -4*q + 4*t + 8 = 0. Let r be (2/q)/(6*4/120). Suppose -1/4 - 5/4*k**4 - 5/2*k**2 + 1/4*k**5 + 5/4*k + r*k**3 = 0. What is k?
1
Suppose 3*b - 5*y = -0*b + 115, -4*y - 110 = -3*b. Factor -96*q**3 + 97*q**3 - 6 + b - 20*q + 2*q**2.
(q - 2)**2*(q + 6)
Let x be ((-99)/(-12))/11*12 - 7. Factor -9/11*l - 1/11*l**3 + 6/11*l**x + 4/11.
-(l - 4)*(l - 1)**2/11
Let r = -4038 + 20194/5. Factor 0 + 8/5*x**3 + 0*x**4 - r*x + 0*x**2 - 4/5*x**5.
-4*x*(x - 1)**2*(x + 1)**2/5
Factor 2303/2*c - 95/2*c**2 + 1/2*c**3 - 2209/2.
(c - 47)**2*(c - 1)/2
Let j(l) = 20*l**3 + 5*l**2 - 15. Let g(i) = i**3 - 1. Let s = 20 - 19. Let k(u) = s*j(u) - 15*g(u). Factor k(r).
5*r**2*(r + 1)
Let m = 321/52 + -12/13. Let n be ((-11)/6 + 2)/((-122)/(-549)). Factor n - m*u**3 + 3/2*u**4 + 27/4*u**2 - 15/4*u.
3*(u - 1)**3*(2*u - 1)/4
Suppose 4*i + 22*f - 19*f = 29, 0 = -4*i + 3*f - 13. Let q = 4 - 4. Find m, given that q - 4/5*m**i + 2/5*m**5 - 6/5*m**3 + 0*m + 0*m**4 = 0.
-1, 0, 2
Let g = -119 - -126. Let u = -3 + 10. Solve 8*h + u*h**5 - 28*h**2 - 20*h**4 + g*h**3 + 29*h**3 - 3*h**5 = 0.
0, 1, 2
Let c(y) be the second derivative of y**6/630 + y**5/70 + y**4/21 + 3*y**3/2 + 16*y. Let k(v) be the second derivative of c(v). Factor k(n).
4*(n + 1)*(n + 2)/7
Let l(m) be the third derivative of m**8/84 - 13*m**7/105 + 2*m**6/5 - 17*m**5/30 + m**4/3 + 40*m**2. Solve l(z) = 0 for z.
0, 1/2, 1, 4
Let n(q) = q + 26. Let g be n(-16). Factor 0*z**4 + 10*z**4 - 9*z**2 - 6*z**2 + 5*z**3 + g*z**2.
5*z**2*(z + 1)*(2*z - 1)
Let v = 310 - 306. Let n(d) be the third derivative of 1/120*d**6 + 5/24*d**v - 1/3*d**3 + 0*d + 0 - 1/15*d**5 + 3*d**2. Suppose n(c) = 0. Calculate c.
1, 2
Let a(z) be the third derivative of 11881*z**6/360 - 12317*z**5/180 + 55*z**4/9 - 2*z**3/9 + 217*z**2. Let a(y) = 0. What is y?
2/109, 1
Let b(u) be the third derivative of -u**6/100 + u**5/60 - 130*u**2. Factor b(m).
-m**2*(6*m - 5)/5
Find o such that -3/7*o**2 + 0 + 0*o - 69/7*o**3 - 429/7*o**4 - 363/7*o**5 = 0.
-1, -1/11, 0
Suppose 28 = 3*r - 2*m - 20, 4*r + m = 75. Let g be (-189)/r*3/(-42). Find o, given that 1/4*o**2 + 0 + 0*o**4 + o**5 - g*o**3 + 0*o = 0.
-1, 0, 1/2
Suppose -6*r - 4*r - 17 - 3 + 8*r**2 - 2*r = 0. Calculate r.
-1, 5/2
Let s be ((-45)/60)/(3/4 - 1). Find i such that 8*i**4 - 10*i**2 + 4*i + 3*i**3 + 6*i**3 - 10*i**4 - i**s = 0.
0, 1, 2
Let j be (-72)/(-10) + 5/(-25). Suppose 0 = b - y, -5*b - 4*y + j*y + 6 = 0. Determine w, given that 0*w + 0 + 2/7*w**b - 6/7*w**2 = 0.
0, 3
What is j in -70*j**3 + 915*j**4 - 930*j**4 + 249*j**2 + 180*j + 16*j**3 - 108 = 0?
-6, -1, 2/5, 3
Let g(p) = -5*p**4 - 35*p**3 - 75*p**2 - 49*p. Let a(t) = -20*t**4 - 140*t**3 - 300*t**2 - 195*t. Let c(n) = -4*a(n) + 15*g(n). Solve c(j) = 0.
-3, -1, 0
Let i(z) be the third derivative of z**8/280 + 17*z**7/525 + 19*z**6/900 - 59*z**5/450 - 4*z**4/45 + 4*z**3/9 + 5*z**2 + 8*z. Determine g so that i(g) = 0.
-5, -1, 2/3
Find l such that -2*l**3 + 344*l - 3*l**3 - 148*l**2 + l**3 - 23*l**2 + 7*l**2 = 0.
-43, 0, 2
Suppose f - 14 = 3*u + 6, -f = 4*u - 6. Suppose 19*j - f*j - 15 = 0. Determine d, given that 5/4*d**4 - 1/2*d - 5/4*d**2 + 0 + 1/2*d**j = 0.
-1, -2/5, 0, 1
Factor 3/5*r**5 + 12*r**3 + 48/5*r**2 + 0 + 24/5*r**4 + 0*r.
3*r**2*(r + 2)**2*(r + 4)/5
Let u(h) be the second derivative of -h**5/90 - h**4/9 + 2*h - 186. Determine i so that u(i) = 0.
-6, 0
Let r = -9/143 - -146/2145. Let t(c) be the third derivative of -1/780*c**6 + 2*c**2 + 0*c**3 + r*c**5 + 0 + 0*c - 1/156*c**4. Factor t(i).
-2*i*(i - 1)**2/13
Let k(y) be the first derivative of y**5/60 - y**4/6 + y**3/2 - 3*y**2/2 - 6. Let d(h) be the second derivative of k(h). Suppose d(x) = 0. Calculate x.
1, 3
Suppose -5*s - 3*g = -s - 8, 2*s = g + 14. Factor -5*r**3 + 3*r**3 + s*r - r**3 - 2*r**3.
-5*r*(r - 1)*(r + 1)
Let s(w) be the third derivative of w**8/336 + 26*w**7/105 - 27*w**6/20 + 41*w**5/15 - 55*w**4/24 - 8*w**2 - 10*w. Factor s(o).
o*(o - 1)**3*(o + 55)
Let s = -17511 + 35023/2. Factor -s*n**2 + 0 + 1/2*n.
-n*(n - 1)/2
Let z be 1 + 10 + 162/(-18). Find j, given that 27/7*j**3 + 24/7*j**5 - 66/7*j**4 - 6/7*j + 3*j**z + 0 = 0.
-1/2, 0, 1/4, 1, 2
Let r(n) = -n**2 + 2*n + 6. Let y be r(0). Find k, given that y*k**5 - 10*k**3 - 25*k**4 - k**5 + 0*k**3 - 25 + 5*k + 43*k**2 + 7*k**2 = 0.
-1, 1, 5
Suppose -5*t + 10*t - 18 = -4*c, -c - 8 = -5*t. Let m be 33/(-27) + 1 - (-31)/18. Factor 1/2*n**2 + m - t*n.
(n - 3)*(n - 1)/2
Let p be