*a + 19*a = 3*z - 2, 0 = z + a - 2. Let v(i) be the second derivative of 0*i**2 - 1/11*i**3 + 4*i + 0 + 1/66*i**z. Factor v(n).
2*n*(n - 3)/11
Let m(g) be the second derivative of 5*g**4/12 + 6290*g**3/3 + 3956410*g**2 - 81*g + 12. Suppose m(j) = 0. What is j?
-1258
Let l(j) be the first derivative of 3/2*j**2 + 1/12*j**5 + 5/9*j**3 + 1/144*j**6 - 4 + 5/16*j**4 + 0*j. Let t(y) be the second derivative of l(y). Factor t(q).
5*(q + 1)**2*(q + 4)/6
Let u(g) be the third derivative of g**8/20160 + g**7/560 + g**6/90 + g**5/30 + 13*g**4/24 + 4*g**2 + 1. Let x(b) be the third derivative of u(b). Factor x(o).
(o + 1)*(o + 8)
Solve 18*f**2 + 0*f**3 + 60 + 22*f**2 - 260*f + 220 + 5*f**3 + 10*f**2 = 0.
-14, 2
Let b(w) be the second derivative of -w**4/3 + 20*w**3/3 + 238*w**2 + 3583*w. Factor b(c).
-4*(c - 17)*(c + 7)
Factor -8712/5 - 1718/5*r**2 + 56892/5*r + 13/5*r**3.
(r - 66)**2*(13*r - 2)/5
Let t(m) be the second derivative of 121/120*m**6 + 1/6*m**4 + 0*m**3 - 11/15*m**5 - 10*m + 6*m**2 + 0. Let d(h) be the first derivative of t(h). Factor d(g).
g*(11*g - 2)**2
Let j(l) = l. Let h = 20 - -2. Let k(u) = -50*u**2 - 26*u**3 + h*u**2 - 19*u**3 - 9*u. Let y(x) = -5*j(x) - k(x). Factor y(i).
i*(5*i + 2)*(9*i + 2)
Let w(g) = -g + 1. Let k(y) be the third derivative of 6*y**2 + 9/8*y**4 + 13/12*y**5 + 0 - 16/3*y**3 + 1/12*y**6 + 0*y. Let b(u) = -k(u) - 2*w(u). Factor b(h).
-5*(h + 1)*(h + 6)*(2*h - 1)
Let i(l) be the third derivative of -l**7/350 - 17*l**6/200 - 53*l**5/50 - 36*l**4/5 - 144*l**3/5 + 373*l**2. Determine s, given that i(s) = 0.
-6, -4, -3
Let f(y) = -67 + y + 67. Let z(o) = -2*o**3 - 12 + 4 + 2 - 1 + 5 - 7*o**2 - 9*o. Let x(c) = 10*f(c) + 5*z(c). Factor x(s).
-5*(s + 1)*(s + 2)*(2*s + 1)
Let c(w) = -w + 2 + 0 - 1. Suppose 0 = 35*v - 26*v - 45. Let j(l) = -5*l**2 + 55*l - 130. Let x(y) = v*c(y) + j(y). Suppose x(q) = 0. What is q?
5
Let p be (7/6)/(((-2394)/(-36))/19). Let x(u) be the first derivative of 0*u**2 + 0*u**3 + 2/15*u**5 - p*u**4 + 0*u + 9. Factor x(w).
2*w**3*(w - 2)/3
Let g be 1/4*(164 + 0). Let r(m) = 4*m**2 + 4*m. Let q be r(4). Factor 65*p**2 - q*p**3 - g*p**4 - 31*p**4 - 12*p - 3*p + 92*p**4.
5*p*(p - 3)*(2*p - 1)**2
Let b(t) be the first derivative of -6*t + 21 - 3/2*t**2 + 3/4*t**4 + 2*t**3. Suppose b(j) = 0. What is j?
-2, -1, 1
Let z(m) be the first derivative of m**4/4 + m**3 - 3*m**2 + 22*m + 112. Let f be z(-5). Solve -2/5*a**f + 2/5 + 0*a = 0 for a.
-1, 1
Let h = 372 - 354. Solve h*i**2 - 48*i**2 + 20*i**2 + 15*i + 15*i**2 + 5*i = 0 for i.
-4, 0
Let o = -8619 + 43291/5. Factor 56/5*w - 4/5*w**2 - o.
-4*(w - 7)**2/5
Let i(v) be the second derivative of -12/11*v**2 - 1/2*v**4 + 15*v - 24/11*v**3 - 1. Suppose i(a) = 0. What is a?
-2, -2/11
Let f(r) be the third derivative of -r**5/30 - 43*r**4/4 + 130*r**3/3 - 2*r**2 + 296. Factor f(x).
-2*(x - 1)*(x + 130)
Solve -715*u**2 - 360*u + 220*u**3 - 14*u**4 - 570*u**3 + 4*u**4 + 15*u**4 = 0.
-1, 0, 72
Let u = -90 + 97. Factor 3*b**4 + 3*b**3 + 2 + 0 - 9*b + 2*b**3 + 15*b**2 - 9*b**3 - u*b**3.
(b - 1)**3*(3*b - 2)
Let s(i) = 13*i**2 + 10204*i + 6891. Let f(c) = 3*c**2 + 2548*c + 1723. Let p(j) = 22*f(j) - 6*s(j). Find k, given that p(k) = 0.
-430, -2/3
Find c, given that 20/3*c - 10/9*c**4 + 0 + 2/9*c**5 - 14/9*c**3 + 58/9*c**2 = 0.
-2, -1, 0, 3, 5
Let m be (-29)/435*75 + 5. Factor m + 2*p**2 + 3*p + 1/3*p**3.
p*(p + 3)**2/3
Let r(c) be the first derivative of 6*c**5/5 - 16*c**4/5 + 38*c**3/15 - 2*c**2/5 - 1712. Factor r(b).
2*b*(b - 1)**2*(15*b - 2)/5
Let q(p) = 10*p - 360. Let n be q(37). Suppose n*y + 55 = 85. Find m such that 12/11*m - 12/11*m**y - 6/11*m**4 + 6/11*m**2 + 0 = 0.
-2, -1, 0, 1
Let q be 7 - 6 - ((-1509)/132)/(-1). Let r = 123/11 + q. Suppose 0 + 1/2*w**2 + r*w - 1/4*w**3 = 0. Calculate w.
-1, 0, 3
Let v(q) be the first derivative of -q**4/20 - q**3/3 + q**2/5 + 24*q/5 + 842. Factor v(b).
-(b - 2)*(b + 3)*(b + 4)/5
Let l(s) be the second derivative of -24 - 3/20*s**5 + s + 0*s**2 + 1/10*s**6 + 0*s**3 - 1/2*s**4. Factor l(t).
3*t**2*(t - 2)*(t + 1)
Let a = -8465 + 50801/6. Let g(m) be the second derivative of -121/70*m**5 + 4/7*m**2 + 40/21*m**3 + 0 - 23*m + a*m**4. Factor g(n).
-2*(n - 1)*(11*n + 2)**2/7
Let m(s) be the third derivative of -s**7/15 - s**6/2 - s**5/30 + 5*s**4/2 + 8*s**3/3 + 88*s**2 + 22*s. Let m(t) = 0. What is t?
-4, -1, -2/7, 1
Let h(k) be the first derivative of k**3/9 + 43*k**2/3 - 4826. Suppose h(t) = 0. What is t?
-86, 0
Find g, given that -5/2*g**5 - 30 - 5/2*g**2 + 45/2*g**3 + 5/2*g**4 - 50*g = 0.
-2, -1, 2, 3
Let s(m) be the second derivative of 2*m**6/15 - 71*m**5/5 - 11772*m. Determine v, given that s(v) = 0.
0, 71
Let q be (-139 - -49)/(-360)*(0 - -4107). Find j such that -q*j**2 + 111/2*j - 3/4 = 0.
1/37
Let b be 32 + -30 + (49 - (-1 - 2)). Solve 27*d - 3*d**5 - 6*d**4 + 107*d**3 + b*d**2 - 69*d**3 - 14*d**3 = 0.
-3, -1, 0, 3
Let x(y) = -4*y**3 - 2*y + 2. Let z(m) = -m**5 - m**4 - 8*m**3 - 5*m + 5. Suppose 39*s - 15 = 42*s. Let u(h) = s*x(h) + 2*z(h). Factor u(b).
-2*b**3*(b - 1)*(b + 2)
Let k(u) be the second derivative of -2*u - 19/36*u**4 - 16 + 1/120*u**5 + 0*u**3 + 0*u**2. Let k(y) = 0. Calculate y.
0, 38
Suppose -2*l - 30 = -0*l. Let c(h) = 5*h**2 + 21*h + 4. Let x(v) = -35*v**2 - 145*v - 30. Let t(u) = l*c(u) - 2*x(u). Find g, given that t(g) = 0.
-5, 0
Let w(m) be the first derivative of -121*m**5 - 19305*m**4/2 - 612485*m**3/3 + 56160*m**2 - 5120*m + 1060. Solve w(i) = 0 for i.
-32, 1/11
Factor 0*s**2 + 113 - 223 + 21*s - s**2 + 42.
-(s - 17)*(s - 4)
Let y = -547 + 550. Let a be (77/22 - y) + 6/4. Factor -19/4*d + 1/2 + 57/4*d**a - 14*d**3 + 4*d**4.
(d - 2)*(d - 1)*(4*d - 1)**2/4
Let s(l) be the second derivative of 3*l**5/50 - l**4 - 52*l**3/5 - 168*l**2/5 + 36*l + 28. Let s(j) = 0. Calculate j.
-2, 14
Let b(i) be the first derivative of i**6/33 - 4*i**5/55 - 3*i**4/22 + 16*i**3/33 - 4*i**2/11 + 356. Find z such that b(z) = 0.
-2, 0, 1, 2
Suppose -74*u**3 - 38*u**2 + 10*u**5 + 2*u - 8*u**5 - 2*u + 122*u**4 - 156*u**4 = 0. Calculate u.
-1, 0, 19
Factor 2*c**2 - 9*c - 702 - 9*c - 98 + 78*c.
2*(c - 10)*(c + 40)
Let b(i) be the third derivative of -3*i**3 - 203*i**2 + 0*i - 43/8*i**4 + 27/40*i**6 - 33/10*i**5 + 0. Determine w, given that b(w) = 0.
-1/3, -2/9, 3
Let d(x) = 14*x + 25. Let c be d(-6). Let f = -57 - c. What is w in 0*w**4 - 5*w**4 - 160*w**2 + 185*w**f - 15*w - 5*w**3 = 0?
-3, 0, 1
Let f(w) be the second derivative of -w**4/54 - 230*w**3/27 + 543*w. Let f(c) = 0. What is c?
-230, 0
Let p be (3740/(-99))/(-10) - (-6)/27. Let d be ((-56)/40)/((-14)/p). Suppose d*w + 2/5*w**2 - 12/5 = 0. Calculate w.
-3, 2
Let v(n) = n**3 - 79*n**2 + 346*n - 406. Let d(k) = -k**3 + k**2 - k - 5. Let r(f) = 2*d(f) - v(f). Factor r(z).
-3*(z - 22)*(z - 3)*(z - 2)
Let h(s) = -s**3 + 2*s**2 - s. Suppose -42 - 3 = -15*f. Let m(a) = -4*a**3 + 37*a**2 + 190*a + 169. Let x(j) = f*m(j) - 15*h(j). Factor x(o).
3*(o + 1)*(o + 13)**2
Let h(z) be the third derivative of z**8/504 + 4*z**7/315 + z**6/90 - 2*z**5/45 - z**4/12 + 1594*z**2. Let h(k) = 0. What is k?
-3, -1, 0, 1
Let k(q) = q**3 + 2*q + 199. Let m be k(0). Factor 4*i**2 - 12*i - 199 + m.
4*i*(i - 3)
Let q(f) be the third derivative of -1/70*f**7 + 3/2*f**3 + 0 + 1/2*f**4 + 2*f + 30*f**2 - 1/10*f**5 - 1/10*f**6. Factor q(d).
-3*(d - 1)*(d + 1)**2*(d + 3)
Let w = 9230 - 19109/2. Let q = -320 - w. Determine l, given that -6*l - q - 3/2*l**2 = 0.
-3, -1
Suppose 0 = 218*q - 220*q. Suppose -10 = 3*m + 5*v - 6, -v = -m + 4. Solve 0*z + q*z**3 + 0 + 0*z**m + 2/5*z**4 = 0 for z.
0
Let u(a) be the second derivative of -a**6/30 - 253*a**5/20 - 251*a**4/12 + 253*a**3/6 + 126*a**2 + 112*a - 2. Factor u(h).
-(h - 1)*(h + 1)**2*(h + 252)
Suppose -19412 = -6*a - 17*a. Let y = 846 - a. Solve -y*h**2 + 2*h - 6/7*h**3 + 6/7 = 0 for h.
-3, -1/3, 1
What is d in -1/4*d**2 + 3/4*d + 1 = 0?
-1, 4
Let v(p) = 13*p**5 - 79*p**4 + 330*p**3 - 547*p**2 + 399*p - 105. Let x(h) = h**5 - h**4 + 2*h**3 - h**2 - h + 1. Let a(g) = -2*v(g) + 22*x(g). Factor a(c).
-4*(c - 29)*(c - 2)*(c - 1)**3
Let i be 2/(-4) + 82/(-4). Let c = i - -25. Factor 3*s**c - 21 - 3*s**3 - s**2 + 21 + 3*s**5 - 2*s**2.
3*s**2*(s - 1)*(s + 1)**2
Let b be -1*(-5 + (28/21 - -3)). Let m(l) be the second derivative of 1/30*l**5 + 15*l + 5/9*l**3