 Let j(w) = -12*n(w) - 3*y(w). Solve j(r) = 0 for r.
-4, 1
Factor -684*z + 7*z**2 - 4*z**3 + 5*z**3 + 683*z - 7.
(z - 1)*(z + 1)*(z + 7)
Let l = 57 + -25. Suppose 0 = 2*f + 6*f - l. Factor 0*b - 1/4*b**f + 1/4*b**5 + 0 + 1/4*b**2 - 1/4*b**3.
b**2*(b - 1)**2*(b + 1)/4
Let o(x) be the second derivative of -5/2*x**3 - 3/8*x**4 + 0 + 1/8*x**6 + 27*x + 39/80*x**5 + 3*x**2. Suppose o(n) = 0. What is n?
-2, 2/5, 1
Let p(w) be the second derivative of -w**7/56 - 7*w**6/80 - 9*w**5/160 + w**4/4 + w**3/4 + 230*w. Suppose p(o) = 0. Calculate o.
-2, -1/2, 0, 1
Let q be (4/3)/(10/15). Suppose 4*k**q + 2*k**3 + 8/3*k + 1/3*k**4 + 0 = 0. What is k?
-2, 0
Factor -198 - 407 - 110*t + 342*t**3 + 5*t**4 - 232*t**3 + 600*t**2.
5*(t - 1)*(t + 1)*(t + 11)**2
Suppose -87/4 + 3/4*k**2 - 21*k = 0. Calculate k.
-1, 29
Let a(x) be the third derivative of x**5/15 - x**4/12 - x**3/3 - 27*x**2. Let k(g) = -g**2 + g + 19 - 19. Let c(w) = -a(w) - 6*k(w). Solve c(r) = 0 for r.
1
Let n(z) = 4*z**3 - z. Let i(d) = 3*d**3 - d**2 - 2*d. Let m(h) = 3*i(h) - 2*n(h). Suppose m(y) = 0. What is y?
-1, 0, 4
Let n(x) = 12*x**4 - 4*x**3 - 17*x**2 + 29*x + 5. Let z(t) = -5*t**4 + 2*t**3 + 9*t**2 - 14*t - 2. Let i(q) = 2*n(q) + 5*z(q). Factor i(v).
-v*(v - 4)*(v - 1)*(v + 3)
Determine o so that 15/2*o + 3/8*o**3 - 3*o**2 - 6 = 0.
2, 4
Let t be 12/(-21) - 64/(-14). Suppose m - 15 = -3*p - 0*p, t*p + 2*m - 22 = 0. Let 2*l**3 + 2*l**3 + 19*l**2 - 7*l**2 + p*l**2 + 12*l = 0. What is l?
-3, -1, 0
Suppose -9432*b**2 + 1 + 9370*b**2 - 1324*b + 363*b - b**3 - 1 = 0. Calculate b.
-31, 0
Let r(z) = 5*z + 2*z**2 - 2*z + z**3 + 2*z**2 - 2 + z**2. Let w be r(-4). Solve -p**w - 6*p - 3 - p + 11*p = 0 for p.
1, 3
Let f(s) be the third derivative of -1/10*s**5 + 0 + 0*s + 0*s**3 + 3/8*s**4 - 3*s**2 - 1/40*s**6. Let f(y) = 0. Calculate y.
-3, 0, 1
Let v be ((-16)/(-6))/(6/(-63)). Let w be (v/(-42))/((-1)/(-3)). Factor 3/5*p**3 + 0*p**w - 3/5*p**4 + 0 + 0*p.
-3*p**3*(p - 1)/5
Let r(o) = -22*o**2 + 178*o + 176. Let j(m) = -14*m**2 + 118*m + 117. Let u(z) = 8*j(z) - 5*r(z). Let u(g) = 0. What is g?
-1, 28
Let r(t) = -t**2 - t + 1. Let q be (2/5)/((-1)/5). Let f(y) = 4*y**2 - 4*y - 2. Let j(v) = q*f(v) - 4*r(v). Factor j(n).
-4*n*(n - 3)
Suppose -190*r + 210*r - 100 = 0. Let z(b) be the third derivative of 12*b**2 + 0*b - 1/6*b**4 + 1/15*b**6 - 1/15*b**r + 0 + 0*b**3. Let z(t) = 0. Calculate t.
-1/2, 0, 1
Factor -4144*s**5 - 75*s**3 + 4149*s**5 + 9*s**4 + s**4.
5*s**3*(s - 3)*(s + 5)
Factor 2*x**3 - 5/3*x**4 + 1 + 2/3*x**2 - 7/3*x + 1/3*x**5.
(x - 3)*(x - 1)**3*(x + 1)/3
Let o be -3*(-20)/24*-10. Let w = o - -33. Determine g, given that 6*g - 2*g**2 + w + 3 - 15 = 0.
1, 2
Let x(h) be the third derivative of h**6/240 - 43*h**4/48 - 7*h**3/2 - 225*h**2. Solve x(l) = 0.
-6, -1, 7
Let j(t) be the second derivative of t**4/78 + 188*t**3/39 + 8836*t**2/13 + 326*t. Find k, given that j(k) = 0.
-94
Let c(j) = 3*j + 27. Let y be c(-7). Factor -8*w - w**2 + 18*w - 3 - y*w.
-(w - 3)*(w - 1)
Solve -102*m + 32*m - 5*m + m**2 = 0.
0, 75
Let b(j) be the third derivative of 0*j + 0 - 20*j**2 + 0*j**3 + 0*j**7 + 0*j**6 + 0*j**4 - 1/1344*j**8 + 0*j**5. Factor b(h).
-h**5/4
Let g(b) be the third derivative of -b**7/42 + b**6/3 - 2*b**5 + 20*b**4/3 - 40*b**3/3 - 169*b**2. Solve g(q) = 0.
2
Let j be (220/(-4))/((-6)/2 - -120). Let c = 9/13 + j. Factor -4/9*h - 2/9 - c*h**2.
-2*(h + 1)**2/9
Let i(d) = 2*d**2 + 4*d - 5. Let y be i(-4). Let p = -7 + y. Factor -n + 3*n**4 + 16*n**2 - 2*n**3 - 9*n**p - 7*n.
-2*n*(n - 1)*(n + 2)*(3*n - 2)
Suppose -3*x + 6*x + 1 = -4*m, x = -3. Suppose l = u + 4*u + 10, 5*l = 2*u + 27. Factor -d**3 - 3*d**2 - d**m + 2*d**2 - 4*d + 2 + l*d.
-(d - 1)*(d + 1)*(d + 2)
Let o(x) = 8*x**2 - 13. Let m(y) = -y**2 + y + 1. Let b(f) = -5*m(f) - o(f). Let i(g) = -65*g**2 - 110*g + 175. Let w(h) = 45*b(h) - 2*i(h). Solve w(j) = 0.
-2, 1
Find k such that -11/4*k**2 + 25/8*k**3 + 3/2*k**4 - 7/8*k**5 - 1 - 9/2*k = 0.
-1, -2/7, 2
What is d in 2/17*d**2 + 10/17*d + 12/17 = 0?
-3, -2
Let x(t) be the first derivative of t**5/360 + t**4/36 + t**3/12 + 7*t**2 + 11. Let q(i) be the second derivative of x(i). Factor q(d).
(d + 1)*(d + 3)/6
Suppose -2*s = z + 2*s - 18, -3*s = 5*z - 39. Suppose 2*o**2 - z + 6*o - 10 - 2*o = 0. What is o?
-4, 2
Let l(v) be the first derivative of 2*v**3/11 - 19*v**2/11 + 12*v/11 + 179. Factor l(u).
2*(u - 6)*(3*u - 1)/11
Let m(r) be the second derivative of 0 + 1/260*r**5 + 0*r**4 + 1/2340*r**6 + 2/3*r**3 + 4*r + 0*r**2. Let n(q) be the second derivative of m(q). Solve n(t) = 0.
-3, 0
Let i be (-17)/(2125/(-10))*(-270)/(-8). Let n(z) be the second derivative of 0 - i*z**2 - 1/20*z**4 - 9*z + 3/5*z**3. Suppose n(k) = 0. What is k?
3
Let z(q) = q**2 - q + 1. Let i(m) = -2*m**2 - 11*m - 37. Let j(g) = i(g) + z(g). Factor j(a).
-(a + 6)**2
Let x = 30 + -27. Factor -2*g**3 + 4 - 28*g**4 + 5*g + 27*g**4 + x*g + 3*g**2.
-(g - 2)*(g + 1)**2*(g + 2)
Factor 2/3 - 5/9*m + 1/9*m**2.
(m - 3)*(m - 2)/9
Let l(a) = a**3 + a**2 - 1. Let y(t) = 4*t**3 + t**2 - 2*t - 4. Let u(j) = 5*l(j) - y(j). Let m be u(-3). Factor 3 + v**m + 2*v - 5 - v.
(v - 1)*(v + 2)
Suppose 0*m = -2*m. Suppose -5*z + 0 + 15 = m. Factor 10 + 6*p + 7*p**2 - 10 - z*p**2.
2*p*(2*p + 3)
Factor 4/3 - 7/3*x**3 - 13/3*x + 5*x**2 + 1/3*x**4.
(x - 4)*(x - 1)**3/3
Factor -3/2*s**5 + 15/2*s**4 + 0 + 0*s**2 + 0*s - 9*s**3.
-3*s**3*(s - 3)*(s - 2)/2
Suppose t + 13 = 2*q, -8*t = -4*q - 5*t + 23. Let b be q/(-28) + 80/84. Let b*o**2 + 2/3*o**3 + 0 + 0*o = 0. What is o?
-1, 0
Let r(d) = d**2 - 2. Let g be r(2). Let x = 361/5 - 72. Determine h so that 2/5 - 1/5*h**g + x*h = 0.
-1, 2
Let w = -2573 - -2575. Suppose -9/2 + 73/4*t - t**w = 0. What is t?
1/4, 18
Let z(u) be the second derivative of u**4/42 - u**3/3 - 339*u. Let z(a) = 0. What is a?
0, 7
Let z(h) be the first derivative of -h**4/4 + h**3 + 14*h + 19. Let u(c) be the first derivative of z(c). Factor u(b).
-3*b*(b - 2)
Let n be 4 + 7/(-42) + 11/(-6). Factor -9/4 - 3/2*k - 1/4*k**n.
-(k + 3)**2/4
Let i(z) = 0*z**2 + 7*z**2 - z - 2*z**3 + 5 - z**3. Let t(w) = -5*w**3 + 13*w**2 - w + 9. Let a(p) = -7*i(p) + 4*t(p). Find x, given that a(x) = 0.
-1
Factor 136/9*j - 2/9*j**2 - 2312/9.
-2*(j - 34)**2/9
Let c(g) = -32*g - 219. Let z be c(-7). Let b(j) be the third derivative of 1/15*j**z - 5*j**2 - 2/3*j**3 + 0 + 0*j**4 + 0*j. Factor b(v).
4*(v - 1)*(v + 1)
Suppose s + q + 3 - 4 = 0, 5*s - 13 = 3*q. Let b = -104 - -108. Let -b*a**2 + 2*a**5 + 2 - 3*a**4 - 4*a**3 + 6*a**4 + s*a + 6*a**4 - 7*a**4 = 0. What is a?
-1, 1
Let z(m) = 3*m + 9. Let y be z(4). Suppose 0 = -5*b - y + 31. Let -4/5 - 8/5*c**3 - 24/5*c**b - 18/5*c = 0. What is c?
-2, -1/2
Find i, given that -578/3 + 68/3*i - 2/3*i**2 = 0.
17
Let r(m) = m**2 + 11*m - 14. Let z be r(-12). Let l be 1/z + (6/(-4) - -2). Determine j so that 0 + l*j - 1/4*j**3 - 5/2*j**4 - 2*j**5 + 1/4*j**2 = 0.
-1, -1/2, 0, 1/4
Suppose 3 - 13 = -2*w. Let i(r) = -r + 27. Let v be i(8). Let 0*f**2 + 84*f**4 - 114*f**3 - v*f - 24*f**5 - 1 + 4 + 75*f**2 - w*f = 0. Calculate f.
1/2, 1
Let c(s) = -5*s - 5. Let a be c(-5). Let -19*h**2 - 7*h**3 - 96*h - 8*h**5 - a*h**4 + 111*h**2 + 31*h**3 + 18 - 10*h**4 = 0. Calculate h.
-3, 1/4, 1
Factor 36*x + 0 + 66*x**2 + 3/2*x**5 + 27/2*x**4 + 45*x**3.
3*x*(x + 2)**3*(x + 3)/2
Let l be ((-4)/(-18))/(6 - 1032/216). Solve 6/11*h**2 + 0 - l*h**3 - 4/11*h = 0 for h.
0, 1, 2
Let t(z) = 2 + 4 - 5 + 0. Suppose -m + 1 = 2. Let n(u) = -u**2 - 2. Let s(c) = m*n(c) - 2*t(c). Factor s(j).
j**2
Let x(s) be the second derivative of -s**4/12 + 28*s**3/3 - 392*s**2 + s - 40. Suppose x(h) = 0. Calculate h.
28
Let q(m) be the third derivative of -1/1020*m**6 - 28*m**2 + 1/255*m**5 + 0*m**3 + 1/68*m**4 + 0 + 0*m. Factor q(u).
-2*u*(u - 3)*(u + 1)/17
Let s(t) be the first derivative of 0*t + 3/4*t**2 + 5 + 1/6*t**3. Factor s(a).
a*(a + 3)/2
Let w(q) be the third derivative of -q**7/9240 + q**6/1980 + q**5/1320 - q**4/132 + 13*q**3/6 + 18*q**2. Let v(y) be the first derivative of w(y). Factor v(z).
-(z - 2)*(z - 1)*(z + 1)/11
Let k(i) = -22*i**2 + 587*i. Let x(m) = 80*m**2 - 2054*m. Let g(z) = 18*k(z) + 5*x(z). Factor g(p).
4*p*(p + 74)
Let q(c) = c**2 + 1. Let z(p) = -p**2 - 5*p - 3. Let u be 0 + -3 + 2 + -3. Let h be z(u). Let l(t) = 5*t**2 - 2*t + 3. Let f(