. Factor j(a).
2*(a - 1)*(a + 1)*(a + 12)
Let c(z) = z**2. Let d(x) = 7*x**2 - x - 3. Let w(s) = 6*c(s) - d(s). Let l be w(0). Solve 3*u**l - 28*u**2 + 16*u**2 - u**3 + 10*u**2 = 0 for u.
0, 1
Let p be (-2 - (3 - 2)) + -7. Let s(g) = g**3 + 11*g**2 + 9*g - 8. Let d be s(p). Let 6*t + 4*t**d + 3 - 6*t**2 - 7*t**2 = 0. Calculate t.
-1/3, 1
Suppose 0 = 3*y + 3*t - 21, -9*y + 7*y + 5*t = 21. Factor -22 - 13*w**3 - 100*w**y + 8*w**3 + 22.
-5*w**2*(w + 20)
Let i = 50297/10 + -5023. Let x = i + 29/30. Solve x*l**3 + 7/3*l**4 - 5/3*l**5 + 0 - 2*l + 5/3*l**2 = 0.
-1, 0, 2/5, 3
Factor 49/4*f + 1/4*f**3 + 0 + 25/2*f**2.
f*(f + 1)*(f + 49)/4
Let n(d) be the third derivative of d**6/30 - 76*d**5/15 + 145*d**4/6 + 148*d**3 + 1416*d**2. Suppose n(t) = 0. What is t?
-1, 3, 74
Solve -53/5*l - 2/5*l**2 - 26/5 = 0 for l.
-26, -1/2
Let w(t) be the first derivative of -169*t + 251*t**3 + 107/4*t**4 - 222 + 4/5*t**5 + 481/2*t**2. Factor w(n).
(n + 1)*(n + 13)**2*(4*n - 1)
Find t such that -652082/5*t + 372338822/15 - 2/15*t**3 + 1142/5*t**2 = 0.
571
Factor -11445*o**3 - 10*o**4 - 14*o**4 + 60*o**2 + 3*o**5 + 11478*o**3.
3*o**2*(o - 5)*(o - 4)*(o + 1)
Let k(z) be the third derivative of -z**7/168 - z**6/360 - 35*z**3/6 - 3*z**2 - 2*z. Let y(n) be the first derivative of k(n). Let y(r) = 0. Calculate r.
-1/5, 0
Let u(m) be the first derivative of m**4/4 + 24*m**3 - 223*m**2/2 + 150*m - 924. Factor u(d).
(d - 2)*(d - 1)*(d + 75)
Let v = -12392 + 61962/5. Let y(c) be the first derivative of -v*c**5 - 9 + 13/2*c**3 - 5/2*c**2 + 0*c - 9/2*c**4. Determine z, given that y(z) = 0.
-10, 0, 1/2
Let t(n) be the second derivative of -15 + n - 23/5*n**3 - 1/20*n**4 - 1587/10*n**2. Factor t(z).
-3*(z + 23)**2/5
Let h(r) = -r**3 + 5*r**2 - 5*r + 4. Let u be h(4). Suppose u*b = b - 2. Let 12 - 3*x**3 + 2*x - 18*x**b + 10*x + 15*x**2 + 0*x**3 = 0. Calculate x.
-2, -1, 2
Let k be (-5)/(-1) + (-5 + -10)/5. Factor 12 + 69*t**2 - 71*t**2 + k*t + 8*t.
-2*(t - 6)*(t + 1)
Factor 400/9 - 20/3*s + 2/9*s**2.
2*(s - 20)*(s - 10)/9
Let k(z) = 13*z**2 - 141*z - 175. Let w be k(12). Let i(j) be the second derivative of w*j + 4*j**4 + 0 - 75/2*j**2 + 3/5*j**5 + 5/2*j**3. Solve i(p) = 0.
-5/2, 1
Let d(m) = -2*m**3 + 13*m**2 + 420*m - 2171. Let o be d(5). Factor -4*s**o + 0*s + 0*s**3 + 0 + 0*s**2 - 2/5*s**5.
-2*s**4*(s + 10)/5
Let l = -283/15 + 2071/105. Let -4/7*v**3 + 24/7*v**2 - l*v**4 + 2/7*v**5 - 16/7*v + 0 = 0. What is v?
-2, 0, 1, 2
Factor 51/2*b + 0 - 3/8*b**2.
-3*b*(b - 68)/8
Let t(s) = s**3 - 12*s**2 - 18*s - 3. Let r(f) = 4 + 3*f**3 - 36*f - 17 - 14*f**2 - 10*f**2 + 6. Let p(h) = 3*r(h) - 7*t(h). Suppose p(o) = 0. Calculate o.
-3, 0
Let o(t) be the third derivative of 0 + 1/9*t**3 - 13*t + 17/72*t**4 + 13/360*t**6 - 3*t**2 + 7/45*t**5. Find v such that o(v) = 0.
-1, -2/13
Let y(z) = -27*z**3 - z**2 - 1. Let r be y(1). Let u = r - -35. Suppose -10*v - 45*v**3 - 13*v**4 - 29*v**2 - 12*v**4 - u*v**2 - 5*v**5 = 0. Calculate v.
-2, -1, 0
Let z = 129013 + -129009. Factor 0 + 0*w**3 + 1/4*w**z + 0*w - 1/4*w**2.
w**2*(w - 1)*(w + 1)/4
Let f = 17164 + -17160. Let x(b) be the second derivative of 1/11*b**2 - 23*b - 3/220*b**5 - 1/66*b**f + 1/22*b**3 + 0. Factor x(z).
-(z - 1)*(z + 1)*(3*z + 2)/11
Let d(s) be the third derivative of -s**5/270 - 29*s**4/108 + 70*s**3/9 + s**2 - 86. Factor d(z).
-2*(z - 6)*(z + 35)/9
Let h be (-6)/(-39) - 3660/(-6630). Let j = h + -50/119. Suppose -32/7*c**2 + 16/7*c - j = 0. What is c?
1/4
Suppose 0 = -2*y + 10*y - 160. Let o be (3 - 55/y)*8. Find z such that -70*z - 2*z**o + 3 + 72*z + z**2 = 0.
-1, 3
Let a be (36/33)/(103365/7920 - 13). Solve 256/15 + 12/5*v**2 + 26/15*v**3 - a*v + 2/15*v**4 = 0 for v.
-8, 1, 2
Solve -1598/11 - 2/11*l**2 - 128/11*l = 0.
-47, -17
Let c = 59305 - 59303. Suppose 4*x = 5*y + 7, -4*x + 4 = -2*y - 6. Factor -7/2*d**c - 6 - 8*d - 1/2*d**x.
-(d + 2)**2*(d + 3)/2
Let v be 116/24 - ((-2)/6)/(17 - 15). Find q, given that 32/3*q**4 + 4*q**2 - 2*q**v + 22/3*q - 4 - 16*q**3 = 0.
-2/3, 1, 3
Suppose 0 = 5*v + 4*w - w - 1, -4*w = 2*v - 6. Let x be v + (-30)/(-12) + 5/(-4). Suppose -1/2*f + 0 - 1/4*f**2 + x*f**3 = 0. What is f?
-1, 0, 2
Let y be 9/2 - -6*13*28/(-546). Factor 10 - 1/2*i**2 - y*i.
-(i - 4)*(i + 5)/2
Let o be (-56 + (-5002)/(-82))*(-4)/(-25). Let u = 45817/15 - 3053. Factor -o + u*r + 2/15*r**3 - 4/5*r**2.
2*(r - 3)*(r - 2)*(r - 1)/15
Let y(z) = 68*z**2 + 9*z - 5. Let q be y(-3). Let k = 1163/2 - q. Find b such that 0 + 3/2*b**2 - k*b = 0.
0, 1
Let p(s) = -s**2 + s - 1. Let z(a) = 4*a**2 + 2*a + 4. Let q(r) = -3*p(r) - z(r). Let j be q(-4). Factor -2*v**j + 7*v**4 + 0*v**3 - 7*v**4 + v**4.
v**3*(v - 2)
Let g(w) be the second derivative of 5/6*w**2 - 21*w + 1/60*w**5 - 1/18*w**3 + 3 - 5/36*w**4. Factor g(r).
(r - 5)*(r - 1)*(r + 1)/3
Suppose 2 = q - 0*q, 3*r + 3*q + 3 = 0. Let v be (20 + -6)/(2/r*3). Let c(u) = u**2. Let t(g) = 3*g**2. Let l(m) = v*c(m) + 2*t(m). Factor l(f).
-f**2
Let p(y) be the second derivative of 17*y**5/20 - 35*y**4/12 + 19*y**3/6 - y**2/2 + 3531*y. Suppose p(u) = 0. What is u?
1/17, 1
Let p(o) = -2*o**2 - 14*o - 12. Let u(d) = 4 - 3*d - 11*d - 2*d**2 - 16. Let i = -7284 + 7280. Let t(q) = i*u(q) + 3*p(q). Solve t(r) = 0 for r.
-6, -1
Let h(r) be the first derivative of -r**5/15 - 5*r**4/2 - 92*r**3/9 + 52*r**2 + 799. Factor h(c).
-c*(c - 2)*(c + 6)*(c + 26)/3
Determine l, given that 5*l**2 + 7*l + 14*l + 15*l - 4*l**3 + 6*l**2 - 3*l**2 - 72 = 0.
-3, 2, 3
Let o be (-37)/((-5180)/(-50))*(-7)/2. Let 3/2 + o*z + 1/4*z**2 = 0. What is z?
-3, -2
Factor -108*x**2 + 495616/13 + 244992/13*x + 2/13*x**3.
2*(x - 352)**2*(x + 2)/13
Factor 7*p**2 - 47*p + 563*p + 15*p**2 + 2*p**3 + 432 + 64*p**2.
2*(p + 1)*(p + 6)*(p + 36)
Let u(y) be the third derivative of -y**5/15 - 253*y**4/6 + 508*y**3/3 + 150*y**2. Factor u(z).
-4*(z - 1)*(z + 254)
Suppose 3*i + 2*i + 25 = -4*f, -3*f - 20 = 5*i. Let z(s) = 0*s**2 + 102*s - 118*s + 12 - 12*s**2. Let g(o) = o - 1. Let a(m) = i*z(m) - 8*g(m). Factor a(h).
4*(h + 1)*(3*h - 1)
Let h(x) be the third derivative of -x**6/30 + 98*x**4/3 + 142*x**2 + 2*x - 2. Factor h(d).
-4*d*(d - 14)*(d + 14)
Let k(z) = -19063*z - 247817. Let i be k(-13). Factor 30*a**i - 10*a - 40 + 5/2*a**4 + 35/2*a**3.
5*(a - 1)*(a + 2)**2*(a + 4)/2
Suppose 1022 = -15*q + 272. Let y be q/(-175) + (-46)/(-35). Suppose 2*w + 4/5 + y*w**2 + 2/5*w**3 = 0. What is w?
-2, -1
Let g(f) = -f**2 + 5*f - 1. Let z be g(4). Let x(t) be the first derivative of 4*t**z - 18*t**2 + 9*t**2 + 18 + 27*t - 2 - 9*t**2. Factor x(i).
3*(2*i - 3)**2
Factor -3*z**2 + 1 + 7/6*z + 5/6*z**3.
(z - 3)*(z - 1)*(5*z + 2)/6
Suppose -477 - 405 = -1214*o + 332. Factor -1/4*b**4 - 15/4*b**2 - 7/4*b**3 - 13/4*b - o.
-(b + 1)**3*(b + 4)/4
Let i(f) be the third derivative of -3/16*f**4 - 1/8*f**3 - 13/80*f**5 + 0*f - 1/70*f**7 + 0 - 3/40*f**6 + 70*f**2. Determine s, given that i(s) = 0.
-1, -1/2
Let f = -293279/80 + 3666. Let t(d) be the second derivative of 0*d**2 - f*d**5 + 8*d + 1/16*d**4 + 0 - 1/12*d**3. Suppose t(n) = 0. What is n?
0, 1, 2
Determine z so that -738/5*z**2 - 54*z**3 + 0 - 168/5*z - 24/5*z**4 = 0.
-7, -4, -1/4, 0
Let b = -1114 - -1100. Let s be (-10)/15 + b/(-3). Let -5/9*m**5 - 1/3*m**s + 7/9*m**3 + 0 - 2/9*m + 1/3*m**2 = 0. What is m?
-1, 0, 2/5, 1
Factor 80/3*d - 2/3*d**2 + 56.
-2*(d - 42)*(d + 2)/3
Let t = 232224/5 + -46444. Factor t*f**2 + 0 - 4/5*f.
4*f*(f - 1)/5
Let s(j) be the second derivative of -j**7/630 - j**6/45 - j**5/10 - 15*j**4/4 - 34*j. Let y(n) be the third derivative of s(n). Suppose y(u) = 0. Calculate u.
-3, -1
Suppose -401 = 8*x - 561. Let b be 7 + 90/x - 11. Suppose k - 1/2 - b*k**2 = 0. Calculate k.
1
Let f(x) = -3*x**4 + 58*x**3 - 128*x**2 + 24. Let q(m) = -2*m**4 + 57*m**3 - 127*m**2 + 21. Let z(d) = 7*f(d) - 8*q(d). Factor z(n).
-5*n**2*(n - 2)*(n + 12)
Let p be (-2*12/(-28))/(9/14). Let q(m) be the first derivative of -13 - 4/5*m**5 + 2/3*m**6 - 5*m**4 + 16*m**2 + p*m**3 + 16*m. Factor q(c).
4*(c - 2)**2*(c + 1)**3
Suppose 0 = 3*x + m - 10, -2*x + 5*m = 2*x + 12. Suppose -5*w - 5 = 0, -2 = -o + 4*w + x. Suppose -1/2*b**3 - 3/2*b**2 - b + o = 0. What is b?
-2, -1, 0
Let l = -3117/4 - -10591/12. Let v = 104 - l. Let 0 + 2/3*s + v*s**2 = 0. What is s?
-1, 0
Let p = -33287 + 66575/2. Solve p*b**2 - 5*b + 2 + 13/4*b