Let l(w) be the first derivative of 7 - 1/8*w**2 - 1/12*w**3 + s*w. Factor l(u).
-u*(u + 1)/4
Suppose -1828*b**2 - 3312/5 - 10*b**3 + 11022/5*b = 0. What is b?
-184, 3/5
Suppose 909 = 561*w - 258*w. What is i in 0*i - 27/5*i**w + 6/5*i**2 + 0 = 0?
0, 2/9
Let m(p) be the third derivative of -17*p**5/4 - 1765*p**4/24 + 70*p**3/3 - 50*p**2 + 4*p. Factor m(b).
-5*(b + 7)*(51*b - 4)
Let j(h) be the third derivative of h**6/30 + 19*h**5/15 + 83*h**4/6 + 130*h**3/3 - 7*h**2 + 2*h - 57. Determine a, given that j(a) = 0.
-13, -5, -1
Let v(l) = 11*l**3 + l**2 - 464*l - 454. Let s(g) = 3*g**3 + g**2 - 4*g - 2. Let b(p) = 3*s(p) - v(p). Factor b(c).
-2*(c - 16)*(c + 1)*(c + 14)
Let z = 111115/194047 - 33/27721. Find s such that 0*s + 2/7*s**3 + 6/7*s**2 + 0 - z*s**4 = 0.
-1, 0, 3/2
Suppose 63*w + 59 - 26 - 159 = 0. Solve -7/5*r + 1/5*r**w - 8/5 = 0.
-1, 8
Let d(w) be the third derivative of 3*w**6/140 + 2*w**5/105 - 19*w**4/84 - 2*w**3/3 - 166*w**2. Determine c so that d(c) = 0.
-1, 14/9
Let l(o) = -8*o**2 - 5985*o + 3018082. Let y(i) = i**2 - 3*i - 5. Let r(u) = l(u) + 11*y(u). Factor r(d).
3*(d - 1003)**2
Let 168/5*z - 3*z**3 + 0 + 2/5*z**2 + 1/5*z**4 = 0. What is z?
-3, 0, 4, 14
Suppose -2444*n + 2443*n = s + 19, 19 = -3*s - n. Solve s + 25/2*i**2 + 5/2*i**3 + 10*i = 0.
-4, -1, 0
Let j(a) be the second derivative of 2*a**6/15 + 36*a**5/5 + 89*a**4 + 1336*a**3/3 + 1080*a**2 + 4583*a. Factor j(s).
4*(s + 2)**2*(s + 5)*(s + 27)
Let k(p) be the second derivative of p**5/220 + 29*p**4/132 + 112*p**3/33 + 98*p**2/11 + 1574*p. Factor k(s).
(s + 1)*(s + 14)**2/11
Solve -2/7*i**2 - 384/7*i + 0 = 0 for i.
-192, 0
Let a(h) be the third derivative of 0*h**3 - 3*h**2 + 1/21*h**4 - 1/420*h**6 + 2/105*h**5 - 1/735*h**7 + 0*h + 25. Solve a(x) = 0.
-2, -1, 0, 2
Let g be 24/(-444) - (-7797)/2553. Solve -160/3*a - 1/6*a**4 - 10/3*a**g - 128/3 - 22*a**2 = 0 for a.
-8, -2
Let t = -261/1052 + 72825/13676. Solve -2/13*j**3 - 54/13 + t*j - 10/13*j**2 = 0.
-9, 1, 3
Let o(v) be the second derivative of -v**4/3 + 188*v**3/3 + 190*v**2 - 7*v + 66. Factor o(a).
-4*(a - 95)*(a + 1)
Suppose -42 - 13 = -p + 5*q, 5*q = 8*p - 160. Let h(l) be the third derivative of -1/630*l**5 + 0*l + 0 + 1/252*l**4 + 2/63*l**3 + p*l**2. Factor h(z).
-2*(z - 2)*(z + 1)/21
Let p(o) = -4040100*o**2 + 16054*o + 10. Let r(u) = 2020050*u**2 - 8028*u - 4. Let g(s) = -6*p(s) - 13*r(s). Suppose g(d) = 0. What is d?
2/1005
Let r(m) be the second derivative of -m**6/200 + m**5/20 - 7*m**4/40 + 3*m**3/10 + 18*m**2 - 12*m. Let o(z) be the first derivative of r(z). Factor o(v).
-3*(v - 3)*(v - 1)**2/5
Let c(b) be the second derivative of -b**5/5 + 32*b**4/3 - 38*b**3 - 180*b**2 - 1096*b. Factor c(f).
-4*(f - 30)*(f - 3)*(f + 1)
Let b = 9702 + -9699. Factor -2*q + 0 - 1/4*q**b - 3/2*q**2.
-q*(q + 2)*(q + 4)/4
Suppose -4 + 1 = -u. Let j = 12 - 7. Suppose 6*h**j + 14*h**5 - 3*h**3 - h**u - h**3 = 0. What is h?
-1/2, 0, 1/2
Let q(v) be the first derivative of -v**7/336 + 59*v**6/360 + v**5/5 + v**3/3 - 3*v - 187. Let c(x) be the third derivative of q(x). Factor c(a).
-a*(a - 24)*(5*a + 2)/2
Let r(p) be the second derivative of -p**7/28 + 21*p**6/20 - 39*p**5/40 - 153*p**4/8 + 133*p**3/2 - 90*p**2 - 1929*p. Solve r(m) = 0 for m.
-3, 1, 2, 20
Factor 82/3*t**2 - 2/3*t**3 - 2688 - 160*t.
-2*(t - 24)**2*(t + 7)/3
Factor -65*l**2 + 18396*l - 499*l**2 + 81*l**3 + 106580 - 77*l**3.
4*(l - 73)**2*(l + 5)
Let v(j) be the first derivative of 3*j**4/4 - 94*j**3 + 276*j**2 - 53. Determine d so that v(d) = 0.
0, 2, 92
Let y(s) = s**3 - 8*s**2 + s + 6. Let o be y(6). Let r = 62 + o. Factor 6*c**2 - 9*c**2 + 3 + 6*c**r - 2*c**2 - 4*c.
(c - 3)*(c - 1)
Let t = -15559/5 + 15561/5. Suppose t*f**4 + 576/5*f + 192/5*f**2 + 0 - 44/5*f**3 = 0. What is f?
-2, 0, 12
Suppose 5*k = -a + 345, -2*k = 3*a + a - 1398. Let c be (-3)/(-7) - a/(-98). Suppose -2*i**5 - c*i**4 - 2*i + i + 3*i + 4*i**2 + 0*i = 0. What is i?
-1, 0, 1
Factor 580*n**2 - 3588*n - 21*n**3 + 508 + 321 + 3126 + 25*n**3 + 1481.
4*(n - 3)**2*(n + 151)
Let b be (-28 + 34 - 2)*(-1)/(-2). What is q in 3/7*q + 0 - 3/7*q**b = 0?
0, 1
Suppose 666 - 664 = y. Suppose -w + y = 9*z - 10*z, 0 = z. Suppose -4/5*l**w + 3/5*l + 1/5 = 0. What is l?
-1/4, 1
Factor 2/3*v**3 + 12 - 6*v - 4/3*v**2.
2*(v - 3)*(v - 2)*(v + 3)/3
Solve 10*w**5 - w**5 - 16*w**4 + 18*w**4 + 21*w**3 + 4*w**2 - 22*w**5 + 10*w**5 - 12*w = 0.
-2, -1, 0, 2/3, 3
Let w = 1006 + -1001. Let -2*h**2 + 61*h**5 + 0 + 300*h**4 + 105*h**3 + 0 + 64*h**w + 12*h**2 = 0. What is h?
-2, -1/5, 0
Let p(t) be the third derivative of -t**5/60 - 7*t**4/6 - 25*t**3/2 + 3796*t**2. Factor p(g).
-(g + 3)*(g + 25)
Let w(d) be the first derivative of d**7/315 + d**6/60 - d**4/9 - 18*d**2 + 12. Let g(i) be the second derivative of w(i). Let g(p) = 0. What is p?
-2, 0, 1
Let q(x) be the third derivative of 0 - 13/24*x**6 + 1/42*x**7 - 23/6*x**5 + 0*x**3 + 81*x - 20/3*x**4 - x**2. Factor q(r).
5*r*(r - 16)*(r + 1)*(r + 2)
Let t(h) be the first derivative of -15 + 69/4*h**2 - 21/2*h**3 - 3*h. Determine m so that t(m) = 0.
2/21, 1
Let m(l) = -2*l**3 + 15*l**2 + 6*l + 88. Let h be m(10). Let y = 1072/3 + h. Factor 2/3*u**4 + 16*u + y*u**3 + 44/3*u**2 + 6.
2*(u + 1)**2*(u + 3)**2/3
Let w be 1/2 + (-5)/(-2) + -3. Suppose 4*z + 11 - 23 = w. Factor 100*x**4 + 3*x**3 + z*x**2 + x - 99*x**4 + 0*x.
x*(x + 1)**3
Let s(a) be the third derivative of -a**7/525 - 37*a**6/150 - 479*a**5/50 - 198*a**4/5 + 1296*a**3/5 - 144*a**2 - 8. Determine j, given that s(j) = 0.
-36, -3, 1
Suppose 5*n - 3*q = 42, 2*n - 4*q + 0 = 14. Let o(m) be the first derivative of -5/9*m**3 - 1/2*m**2 + 2/3*m - n. Factor o(v).
-(v + 1)*(5*v - 2)/3
Determine d so that -3396*d**3 - 428*d**4 - 18*d**5 + 113 - 4265*d**2 + 414 - 4986*d + 726 + 367 - 5327*d**2 = 0.
-9, -5, -1, 2/9
Let p(g) be the first derivative of -g**4 + 8*g**3 - 10*g**2 - 1439. Let p(x) = 0. Calculate x.
0, 1, 5
Let a = 7776 - 7776. Let p(t) be the second derivative of 0 - 1/40*t**6 + 3/40*t**5 + a*t**2 - t**3 + 3*t + 1/4*t**4. Factor p(r).
-3*r*(r - 2)**2*(r + 2)/4
Suppose 10*k - 13*k - 216 = -5*o, -4*o = 5*k + 360. Let x be 1/6 + (-978)/k. Solve -x*t - 15/4*t**2 - 15/2 = 0 for t.
-3, -2/3
Let -9*z**2 + 73*z + 141*z + 765 + 5*z**2 + 62*z + 403 = 0. What is z?
-4, 73
Let v = 23 + 20. Suppose v = 3*c + 43. Let c*i**3 - 14*i**3 - 15*i**5 + 35*i**4 + 15*i**4 - 6*i**3 - 40*i**2 = 0. What is i?
-2/3, 0, 2
Let -11*q**5 - 10 - 4593*q**4 - 25*q**3 - 6*q**2 + 35*q - 19*q**2 + 4628*q**4 + q**5 = 0. What is q?
-1, 1/2, 1, 2
Suppose 990 = 419*o - 254*o. Let f(g) be the third derivative of 0 - 16/9*g**4 - 1/180*g**o + 0*g - 26*g**2 + 0*g**3 + 8/45*g**5. Factor f(h).
-2*h*(h - 8)**2/3
Let m(z) be the second derivative of z**6/10 + 9*z**5/20 - 11*z**4/2 - 12*z**3 + 4724*z. Find k, given that m(k) = 0.
-6, -1, 0, 4
Let p(l) be the second derivative of 0*l**2 + 8/15*l**4 + 12 + 12/25*l**5 + l + 2/105*l**7 + 0*l**3 + 4/25*l**6. Factor p(y).
4*y**2*(y + 2)**3/5
Solve -5*z**2 + 424*z + 275*z + 11*z = 0.
0, 142
Let r(w) = w**4 - w**3 + 4*w. Let s(i) = -2*i**4 + 122*i**3 - 242*i**2 + 106*i. Let h(t) = 4*r(t) + s(t). Factor h(c).
2*c*(c - 1)**2*(c + 61)
Factor -4070*h + 331 - 59 - 28*h**2 + 2025*h + 2001*h.
-4*(h + 4)*(7*h - 17)
Let y(a) be the second derivative of a**7/168 - a**6/24 - a**5/6 + 32*a**3/3 + 55*a. Let l(v) be the second derivative of y(v). Factor l(r).
5*r*(r - 4)*(r + 1)
Let c be (3*6/(-30))/(4/(-20)). Factor -8*g**5 - 230*g**c + 377*g**3 - 92*g**4 - 191*g**3.
-4*g**3*(g + 11)*(2*g + 1)
Let m(w) = 12*w - 282. Let j be m(25). Let t be ((-644)/1449)/((-4)/j). Suppose 5/2*g**5 + 0 + 0*g**t + 7/2*g**4 + g**3 + 0*g = 0. What is g?
-1, -2/5, 0
Find h such that 47*h**4 - 34*h + 24 + 95/2*h**3 + 15/2*h**5 - 92*h**2 = 0.
-4, -3, -2/3, 2/5, 1
Suppose 0 = -151*p - 111*p + 290*p - 28. Suppose -1/2*l + p + 1/2*l**3 - l**2 = 0. What is l?
-1, 1, 2
Let l(m) be the first derivative of -119 + 0*m + 2/27*m**3 - 5/9*m**2. Suppose l(r) = 0. Calculate r.
0, 5
Factor 1/3*j**3 + 0*j + 0 + 205/3*j**2.
j**2*(j + 205)/3
Let t(i) be the second derivative of 0*i**2 + 1/140*i**5 + 0*i**3 - 13*i - 2/7*i**4 + 0. Find f, given that t(f) = 0.
0, 24
Let s be 2*((-625)/(-10))/25. Let a(i) be the third derivative of 0 - 1/15*i**s - i**2 + 0*i**3 + 1/12*i**4 + 1/60*i**6