(h).
-3*(h + 2)*(h + 4)
Solve 37/2*l**2 + 0 - 6*l + 45/2*l**3 - 2*l**4 = 0 for l.
-1, 0, 1/4, 12
Let c(k) = -k**2 - 21*k - 78. Let g be c(-16). Let l(d) be the first derivative of -d**5 + 2*d + d**3 - 5 + 7/4*d**4 - 7/2*d**g. Factor l(u).
-(u - 1)**2*(u + 1)*(5*u - 2)
Factor 28/3 - 4/3*w**2 + 18*w.
-2*(w - 14)*(2*w + 1)/3
Suppose -95*r = 71*r. Solve r*u + 0*u**4 - 1/9*u**5 + 0 - 2/9*u**2 + 1/3*u**3 = 0.
-2, 0, 1
Let u be -2 - (2/2 + -23). Suppose -u*v = -16*v - 12. Factor 0 + 15/4*c**v + c**2 - c.
c*(3*c + 2)*(5*c - 2)/4
Let q(z) = -2*z**2 - 13*z - 14. Let o be q(-4). Factor o - 100*p + 15*p - 26 + 46*p**2 - 66*p**2.
-5*(p + 4)*(4*p + 1)
Let g(x) be the third derivative of -x**6/24 - 5*x**5/12 - 5*x**4/3 - 10*x**3/3 - 37*x**2 - 2. Factor g(o).
-5*(o + 1)*(o + 2)**2
Let k be (-4)/14 - (-2023)/49. Let -42*a**4 - 3*a**2 - k*a**4 - 3*a**3 - a + 82*a**4 = 0. What is a?
-1, 0
Let o be (-6)/(-10) + (-36)/(-90). Let h be (72/33)/4*o. Factor -h*l + 2/11*l**2 + 0.
2*l*(l - 3)/11
Let n(p) = -p**2 + 54*p + 174. Let v be (10 + -1)*(32/(-12) - -2). Let a(w) = 10*w**2 - 485*w - 1565. Let b(x) = v*a(x) - 55*n(x). Find d, given that b(d) = 0.
-6
Let y = 472/3 + -66079/420. Let s(u) be the third derivative of 0*u**4 - u**2 + 0*u**3 - y*u**6 - 1/105*u**5 + 0 + 0*u. Factor s(v).
-2*v**2*(v + 2)/7
Let x(a) be the third derivative of 0*a**3 - 1/12*a**5 + 0 + 0*a - 5/24*a**4 + 13*a**2 + 1/42*a**7 + 1/24*a**6. Solve x(y) = 0 for y.
-1, 0, 1
Let k(i) be the first derivative of -5*i**4/12 - 5*i**3/6 + 5*i**2 - 46*i + 13. Let b(s) be the first derivative of k(s). Suppose b(u) = 0. What is u?
-2, 1
Let t(y) = 31*y - 124. Let n be t(4). Let j(x) be the first derivative of -2*x**2 + 2*x**3 - 2 + n*x - 1/2*x**4. Determine h so that j(h) = 0.
0, 1, 2
Let z = 22498/3 - 7496. Suppose -z*f + 8/3*f**4 - 2/3 + 10/3*f**3 - 2*f**2 = 0. Calculate f.
-1, -1/4, 1
Find l such that 8*l - 33*l**3 + 36 + 2335*l**4 + 25*l - 39*l**2 - 2332*l**4 = 0.
-1, 1, 12
Factor -3*y**3 + 1/2*y**4 + 3*y + 4*y**2 - 9/2.
(y - 3)**2*(y - 1)*(y + 1)/2
Let a(d) be the third derivative of 0*d**3 + 1/270*d**5 + 0*d + 1/1080*d**6 + 1/216*d**4 + 0 - 7*d**2. Factor a(l).
l*(l + 1)**2/9
Factor 6/7*k**2 + 6/7*k - 36/7.
6*(k - 2)*(k + 3)/7
Let o(m) be the first derivative of -m**4/6 - 16*m**3/3 - 64*m**2 - m - 6. Let r(q) be the first derivative of o(q). Factor r(g).
-2*(g + 8)**2
Suppose 3*d - 12 = 2*z, -4*d + 3*z - 612 = -630. Factor -1/5*h**2 + 1/5*h**3 - 1/5*h + 1/5*h**4 + d.
h*(h - 1)*(h + 1)**2/5
Let o be (-5)/1 - (-239 + 235)*7/4. Find v such that 1/2*v**5 - 1/2*v**4 - v + 5/2*v**o - 3/2*v**3 + 0 = 0.
-2, 0, 1
Let h(i) be the first derivative of -i**4/26 - 14*i**3/39 - 14*i**2/13 - 16*i/13 - 29. Factor h(a).
-2*(a + 1)*(a + 2)*(a + 4)/13
Let r be 3 - (-1*1 + (4 - 3)). Factor -3*c**2 + 15 + 9*c**3 + r*c**4 + 6*c**2 - 9*c - 11 - 10.
3*(c - 1)*(c + 1)**2*(c + 2)
Let v(a) be the second derivative of -a**5/60 - a**4/4 - 3*a**3/2 + 2*a**2 + 3*a + 6. Let b(g) be the first derivative of v(g). Factor b(x).
-(x + 3)**2
Suppose 0 = q - 3. Let v be ((-6)/q - -5)*1. Factor 2*g + 4*g**2 - v*g**2 - 2*g**2.
-g*(g - 2)
Suppose 8/7 + 48/7*w + 18/7*w**3 + 58/7*w**2 = 0. What is w?
-2, -1, -2/9
Let v be 4/((-352)/(-106)) + -2 + 1. Let a = v + 359/396. Factor 0 - 8/9*y + 2/9*y**4 - a*y**3 + 16/9*y**2.
2*y*(y - 2)**2*(y - 1)/9
Let r(i) = -395*i**2 + 1 + 397*i**2 + 13 + 14*i. Let b be r(-6). Factor -3/7*q**3 + 0*q**b + 3/7*q + 0.
-3*q*(q - 1)*(q + 1)/7
Let p(t) be the first derivative of -t**4 + 220*t**3/3 - 1334*t**2 - 10092*t + 635. Factor p(f).
-4*(f - 29)**2*(f + 3)
Let t(q) = 2*q**2 - 2*q + 2. Let s be t(1). Let z be ((3 + -4)*2)/(-9). Factor z*b**s + 2/9*b + 0.
2*b*(b + 1)/9
Let j(f) be the third derivative of -f**6/2520 - f**5/840 - 11*f**3/2 + 44*f**2. Let k(r) be the first derivative of j(r). Find i such that k(i) = 0.
-1, 0
Let f be (-12)/(((-105)/40)/7). Factor -29 - u**2 - 6*u + 4*u**2 + f.
3*(u - 1)**2
Let m(u) be the second derivative of u**8/2240 + u**7/1120 - u**6/480 - u**5/160 - 3*u**3 - 12*u. Let x(z) be the second derivative of m(z). Factor x(t).
3*t*(t - 1)*(t + 1)**2/4
Suppose 9*d**3 - 1/2*d**4 + 189/4*d + 81/2*d**2 + 0 - 1/4*d**5 = 0. Calculate d.
-3, 0, 7
Factor 16*y**2 + 31*y + 54*y + 2*y**3 - 53*y.
2*y*(y + 4)**2
Let m = 1981/30 - 66. Let j(f) be the second derivative of 0*f**3 + 0 + 0*f**5 - 6*f + 0*f**2 + 1/12*f**4 - m*f**6. Solve j(b) = 0.
-1, 0, 1
Let y = 1/1718 - -6865/12026. Find z such that -2/7 + 12/7*z**2 + 6/7*z**5 - 2/7*z - 10/7*z**4 - y*z**3 = 0.
-1, -1/3, 1
Let o be 0/((8/(-3) + 2)*-3). Let y(v) be the second derivative of 0*v**2 + 9/85*v**6 + 27/170*v**5 + 3/34*v**4 - 4*v + 1/51*v**3 + o. Factor y(i).
2*i*(3*i + 1)**3/17
Factor 212 - 5*j**2 + 6*j**2 - 226 - 13*j.
(j - 14)*(j + 1)
Suppose 0 = -5*u - s - 22, -24 - 13 = 5*u - 4*s. Let a be (-5)/(0 - u) - -1. Suppose a + 1/4*y - 1/4*y**2 = 0. What is y?
0, 1
Let q(b) be the second derivative of -b**7/42 - 59*b**6/30 + b**5/20 + 59*b**4/12 - 317*b. Factor q(t).
-t**2*(t - 1)*(t + 1)*(t + 59)
Let p(y) be the third derivative of -y**7/210 + y**6/40 + y**5/60 - y**4/8 + 48*y**2 - 2. Solve p(f) = 0.
-1, 0, 1, 3
Let w(n) = n**2 - 7*n + 12. Let p be w(2). Determine o, given that -4/5*o + 1/5*o**p + 4/5 = 0.
2
Determine c, given that 4/5*c**3 + 0 - 8/5*c - 4/5*c**2 = 0.
-1, 0, 2
Let h(p) be the second derivative of 0*p**3 - 1/147*p**7 - 6*p - 1/35*p**6 + 0*p**2 - 1/35*p**5 + 0 + 0*p**4. Factor h(q).
-2*q**3*(q + 1)*(q + 2)/7
Factor 1/3*k**4 - 32/3 + 11*k**3 + 31/3*k**2 - 11*k.
(k - 1)*(k + 1)**2*(k + 32)/3
Suppose 5*g = -2*o + 14, -2*o = 3*g - 4*g - 2. Let -6*c**2 - 10 + 18 + g*c**3 - 10 + 6*c = 0. Calculate c.
1
Factor -4*a**3 + 72*a**3 + 6*a**3 + 6300*a**2 + 231*a**3 + 40000 + 5*a**4 + 46000*a.
5*(a + 1)*(a + 20)**3
Let t be 12/4 + (4 - 1 - 51). Let h be 0/(22/(-18) - 10/t). Factor h*c**2 - 2/3*c**4 + 0 - 2/3*c**3 + 0*c.
-2*c**3*(c + 1)/3
Let o(i) = 5*i**3 - 6*i**2 - 25*i + 22. Let c(u) = 30*u**3 - 35*u**2 - 150*u + 130. Let h(p) = -4*c(p) + 25*o(p). Factor h(x).
5*(x - 3)*(x - 1)*(x + 2)
Find q, given that -12/11*q - 2/11*q**5 + 2/11*q**4 + 0 - 2/11*q**2 + 14/11*q**3 = 0.
-2, -1, 0, 1, 3
Let w(f) be the second derivative of f**4/48 - 23*f**3/24 - 27*f**2/2 - 14*f + 2. Solve w(a) = 0.
-4, 27
Let m = 780 - 780. Suppose -4/7 + 0*k**3 - 4/7*k**4 + 8/7*k**2 + m*k = 0. What is k?
-1, 1
Let b = 7018 + -7015. Factor 0*d + 2/17*d**b + 0 + 4/17*d**2.
2*d**2*(d + 2)/17
Let d(l) be the third derivative of l**6/120 + l**5/80 - l**4/24 - l**3/8 - 2*l**2 - 3*l. Factor d(r).
(r - 1)*(r + 1)*(4*r + 3)/4
Let b(l) = -l**2 + 4*l**2 + 0*l**2 - 2*l**2 - 1. Let r(s) = 6*s**2 - 12*s - 3. Let z(g) = b(g) + r(g). Factor z(p).
(p - 2)*(7*p + 2)
Let h(r) be the second derivative of -r**5/12 - 5*r**4/6 - 10*r**3/3 + r**2/2 - 23*r. Let x(j) be the first derivative of h(j). Factor x(t).
-5*(t + 2)**2
Let o(q) be the second derivative of 0*q**2 - 1/9*q**4 + 9*q - 2/15*q**5 + 0*q**3 + 0. Factor o(j).
-4*j**2*(2*j + 1)/3
Let s(a) be the third derivative of -a**8/448 - 19*a**7/840 - a**6/15 + a**5/10 - 19*a**4/24 - 26*a**2. Let g(c) be the second derivative of s(c). Factor g(f).
-3*(f + 2)**2*(5*f - 1)
Let y(g) be the first derivative of -3*g**5/25 - 3*g**4/4 - 8*g**3/5 - 6*g**2/5 + 109. Factor y(u).
-3*u*(u + 1)*(u + 2)**2/5
Let t(w) be the first derivative of -w**6/12 + 39*w**5/10 - 233*w**4/4 + 281*w**3 - 2125*w**2/4 + 867*w/2 + 205. What is l in t(l) = 0?
1, 3, 17
Let i = 72 - 36. Factor -41*l**4 - 10*l**3 + i*l**4 + 0*l - 5*l**2 + 0*l.
-5*l**2*(l + 1)**2
Factor -1058/13 + 92/13*b - 2/13*b**2.
-2*(b - 23)**2/13
Let k = -7/219 - -599/5037. What is j in k*j**3 + 2/23*j + 0 + 4/23*j**2 = 0?
-1, 0
Let s = 10669/11 + -969. What is h in 6/11*h + 4/11 - 4*h**3 - s*h**5 - 16/11*h**2 - 36/11*h**4 = 0?
-1, 2/5
Let q(h) be the first derivative of h**6/8 + 27*h**5/20 + 39*h**4/8 + 9*h**3/2 - 81*h**2/8 - 81*h/4 - 17. Let q(t) = 0. What is t?
-3, -1, 1
Let m be (1/(-6))/((-1)/64). Let d(j) = -857*j - 4283. Let n be d(-5). Factor -20/3*u**3 + 28/3*u**n + m*u - 16/3.
-4*(u - 2)*(u + 1)*(5*u - 2)/3
Let y = 1955 + -1952. Solve 0*q + 0 + 0*q**4 - 1/2*q**y + 0*q**2 + 1/2*q**5 = 0 for q.
-1, 0, 1
Solve 5/8 + 1/8*t**3 + 7/8*t**2 + 11/8*t = 0.
-5, -1
Let r(x) = -x - 9. Let s be r(-11). Let i(p) = 5*