2*(5*n - 2)/9
Let p = -2 + 6. Determine t, given that 2*t**3 - 2*t**p + 2*t**2 - 6 - 2*t**5 + 6 = 0.
-1, 0, 1
Let l(j) = -11*j**2 + 60*j - 64. Let m(w) = 5*w**2 - 30*w + 31. Let i(r) = 2*l(r) + 5*m(r). What is f in i(f) = 0?
1, 9
Let z(w) be the second derivative of 9*w**5/20 - 11*w**4/4 - 3*w**3 + 12*w**2 + w - 14. Let z(c) = 0. Calculate c.
-1, 2/3, 4
Suppose 3*c + 15 = -0*q + 5*q, 0 = -5*q - 4*c - 20. Suppose -g + 4 = -q*g. Factor -144*r**2 + 1 - 33*r - 4 - 411*r**4 - 312*r**3 - 144*r**5 + 75*r**g.
-3*(2*r + 1)**4*(3*r + 1)
Let p(n) = -8*n - 63. Let d be p(-8). Find z such that 15/2*z**4 + d + 39/2*z**2 + 41/2*z**3 + 15/2*z = 0.
-1, -2/5, -1/3
Let n be -3 - -1 - (-8 + 2). Suppose -2*z = -n*h - 7*z + 10, 0 = -4*h + 2*z - 4. Solve 2/9*m - 2/9*m**2 + h = 0 for m.
0, 1
Let r(v) be the second derivative of -3*v**5/40 + v**4/2 - v**3 + 4*v. Factor r(c).
-3*c*(c - 2)**2/2
Let s be ((-24)/9 + 3)/(4 - 3). What is i in s*i**2 + 1/3 - 2/3*i = 0?
1
Let v = -19 - -19. Suppose 0 = 3*g - v - 9. Factor 15/4*n**3 - g*n - 9/2*n**2 + 6 - 3/4*n**4.
-3*(n - 2)**3*(n + 1)/4
Let q be -1 - 1/(4/(-12)). Let v be -1*(4/q + -2). Determine z so that 3/4*z**3 + v + 0*z + 3/4*z**2 = 0.
-1, 0
Let l be 1/(-2)*(0 - -1)*-2. Find w, given that -2*w**2 + 9/2*w - l = 0.
1/4, 2
Let v(d) = -d**2 + 9*d - 6. Let y be (-1 - -7) + (-2 - -4). Let g be v(y). Suppose 2 - 2*k**2 + 0*k**g - 5*k + 5*k = 0. What is k?
-1, 1
Let s(m) be the second derivative of -3/4*m**2 + 1/24*m**4 + 1/6*m**3 - 4*m + 0. Factor s(g).
(g - 1)*(g + 3)/2
Let b(p) = p + 7. Let v be b(-5). Factor 3*m**3 + 32*m - 11*m**3 + 18 + 31 - v*m**4 - 17.
-2*(m - 2)*(m + 2)**3
Let r(j) = 5*j**2 - 4*j - 1. Let y(d) = -5*d**2 + 3*d + 2. Let m(i) = -3*r(i) - 4*y(i). Solve m(x) = 0.
-1, 1
Suppose -4*g + 5*s = 2, -2*s + 3*s + 4 = 3*g. Let h(a) be the first derivative of 1/5*a**5 + g + 0*a**2 + 0*a**4 + 0*a**3 - 1/6*a**6 + 0*a. Factor h(d).
-d**4*(d - 1)
Let z(s) be the first derivative of -s**4/4 + 2*s**3 + s**2 - 9*s - 3. Let m be z(6). Solve -m*i**4 - 3*i**5 + i**3 + 3*i**2 + 0*i**5 + 2*i**3 = 0.
-1, 0, 1
Let l be (-2 + 1)/((-5)/(-10)). Let x = 0 - l. Factor -2/9*b**x + 0*b + 2/9*b**5 - 2/9*b**3 + 2/9*b**4 + 0.
2*b**2*(b - 1)*(b + 1)**2/9
Let -5*u**2 + 53*u**4 + 3 - u**2 - 50*u**4 = 0. Calculate u.
-1, 1
Factor 14*a**4 - 11*a**4 - 2*a**5 + 0*a**5 + a**5.
-a**4*(a - 3)
Let r be (2 - 3)*(0 - -1). Let x = r + 1. Suppose 2/3 + x*t + 1/6*t**3 - 1/2*t**2 = 0. What is t?
-1, 2
Let g(o) be the third derivative of -1/210*o**5 - 2/21*o**4 + 2*o**2 + 0*o - 16/21*o**3 + 0. Factor g(z).
-2*(z + 4)**2/7
Let m(b) be the first derivative of 2/15*b**3 - 2/5*b**2 + 2 + 0*b. Factor m(d).
2*d*(d - 2)/5
Let s(m) be the second derivative of -2*m + 1/12*m**4 + 2/3*m**2 - 1/12*m**5 + 0 + 2/3*m**3. Factor s(v).
-(v - 2)*(v + 1)*(5*v + 2)/3
Factor 2/13*b**3 + 2/13*b**2 - 2/13*b - 2/13.
2*(b - 1)*(b + 1)**2/13
Suppose -1 = 4*f - 5. Suppose 3*g = 5*y + 2, -g = -f - 3. Find d, given that -1/3*d**4 + 0*d + 1/3*d**y + 1/3*d**3 + 0 - 1/3*d**5 = 0.
-1, 0, 1
Let x(s) be the second derivative of 0*s**2 - s - 1/3*s**3 + 1/4*s**4 + 0. Suppose x(i) = 0. Calculate i.
0, 2/3
Factor 4/3*m + 2/9*m**2 - 2/9*m**3 + 0.
-2*m*(m - 3)*(m + 2)/9
Let d(a) be the first derivative of -a**6/360 + a**5/45 - a**4/18 + 5*a**2/2 + 3. Let z(l) be the second derivative of d(l). Factor z(u).
-u*(u - 2)**2/3
Let t(n) = n - 8. Let f be t(12). Suppose 5*x - 3 = -3*b, f*x + 0*x + 5 = 5*b. What is q in 1/2*q**2 - 1/2*q - b = 0?
-1, 2
Let r(b) be the third derivative of 0*b - 73/240*b**6 - 1/15*b**7 - 11/12*b**4 - 43/60*b**5 - 2*b**2 - 2/3*b**3 - 1/168*b**8 + 0. Suppose r(n) = 0. Calculate n.
-2, -1/2
Let q be -18 + 18 - 6/(-9). Factor 4/3*k + 2 - q*k**2.
-2*(k - 3)*(k + 1)/3
Let d(n) be the first derivative of 2*n**7/63 + n**6/15 - n**4/18 + 3*n + 1. Let m(o) be the first derivative of d(o). Let m(j) = 0. What is j?
-1, 0, 1/2
Let w(l) be the first derivative of -2*l**6/9 + l**5/15 + l**4/3 - l**3/9 - 6. What is b in w(b) = 0?
-1, 0, 1/4, 1
Let w(g) be the first derivative of -4*g**3 + 2*g**2 - 11. Let w(a) = 0. Calculate a.
0, 1/3
Factor 2/11*d**3 - 2/11*d - 2/11*d**4 + 2/11*d**2 + 0.
-2*d*(d - 1)**2*(d + 1)/11
Suppose -l + h - 1 = -3, 18 = 2*l + 5*h. Suppose -4*f**3 + 3*f**l - 2*f**4 + 6*f**5 + 8*f**4 + 7*f**3 = 0. Calculate f.
-1, -1/2, 0
Let n(d) = d**3 - d**2 + d. Let j(b) = -3*b**3 + 3*b**2 - b - 1. Let f(r) = -3*j(r) - 6*n(r). Solve f(i) = 0.
-1, 1
Let r be -3*(-1 - 0) - 3. Let 0*k + r - 7/4*k**3 + 7/4*k**5 + 1/2*k**4 - 1/2*k**2 = 0. Calculate k.
-1, -2/7, 0, 1
Let v(l) be the third derivative of -l**5/270 + l**4/36 - 2*l**3/27 - 8*l**2. Factor v(j).
-2*(j - 2)*(j - 1)/9
Let k(j) be the second derivative of -j**4/20 + 3*j**3/10 - 3*j**2/5 - 23*j. What is o in k(o) = 0?
1, 2
Let v = 310 + -310. Factor v*t - 1/5*t**2 + 0.
-t**2/5
Let c(q) be the first derivative of q**6/27 + 2*q**5/15 - q**4/18 - 14*q**3/27 + 8*q/9 + 6. Let c(p) = 0. Calculate p.
-2, -1, 1
Suppose -3*f + 7*f = 0. Let h be -2 - (f - (-15)/(-6)). Factor h*w - 1/2*w**3 + 0 + 0*w**2.
-w*(w - 1)*(w + 1)/2
Let r(v) = 5*v**5 + 2*v**4 - 9*v**3 + v**2 + 4*v. Let t(y) = -9*y**5 - 4*y**4 + 17*y**3 - y**2 - 8*y. Let z(h) = -5*r(h) - 3*t(h). Find o, given that z(o) = 0.
-2, -1, 0, 1
Let o = 13/32 - -3/32. Suppose 0 + 3/4*z**2 - 3/4*z**3 - o*z**4 + 1/2*z = 0. What is z?
-2, -1/2, 0, 1
Let b = -47 - -75. Factor 16*u**3 + 33*u**3 - u + 0*u + 5*u + b*u**2.
u*(7*u + 2)**2
Let m(y) be the third derivative of y**5/270 + y**4/54 + y**3/27 - y**2. Factor m(z).
2*(z + 1)**2/9
Suppose i - 3 = -0. Let -3 + 2 + i*d**2 + 0 - 2 = 0. What is d?
-1, 1
Factor 0*v + 4/7*v**2 - 2*v**4 + 0 + 10/7*v**3.
-2*v**2*(v - 1)*(7*v + 2)/7
Let b(d) = 8*d**4 + 12*d**3 + 12*d**2 + 4. Let g(j) = 9*j**4 + 12*j**3 + 13*j**2 + 5. Let h(n) = 5*b(n) - 4*g(n). Suppose h(o) = 0. What is o?
-2, -1, 0
Let a(q) be the first derivative of -q**7/315 + q**5/90 - q**2/2 + 2. Let y(b) be the second derivative of a(b). Let y(i) = 0. What is i?
-1, 0, 1
Factor 3/2*x**4 - 3/2*x**2 + 3/2*x**3 - 3/2*x + 0.
3*x*(x - 1)*(x + 1)**2/2
Let a(n) be the second derivative of -1/30*n**4 + 0 - 9/5*n**2 - 2/5*n**3 - n. Factor a(p).
-2*(p + 3)**2/5
Let t(x) be the second derivative of 3*x**8/280 + x**7/140 - 2*x**6/45 - x**5/15 + x**3/6 - 3*x. Let k(n) be the second derivative of t(n). Factor k(v).
2*v*(v - 1)*(3*v + 2)**2
Let f(c) be the third derivative of c**8/20160 + c**7/1680 + c**6/360 - c**5/20 + c**2. Let d(t) be the third derivative of f(t). Factor d(x).
(x + 1)*(x + 2)
Let c(n) = -5*n**5 + 6*n**4 + 4*n**3 + 7. Let i(j) = -4*j**5 + 6*j**4 + 4*j**3 + 6. Let x(v) = 6*c(v) - 7*i(v). Factor x(h).
-2*h**3*(h + 1)*(h + 2)
Let i(b) = 5*b**4 - 6*b**3 - 3*b**2 + 4*b - 4. Let o(d) = 4*d + 5 + 7*d**3 + d - 6*d - 6*d**4 + 4*d**2 - 4*d. Let q(k) = 5*i(k) + 4*o(k). Factor q(n).
n**2*(n - 1)**2
Suppose 4*q - 3 = -5*t, 4*q - 39 = 5*t - 26. Factor 0 - 1/3*o**q + 0*o - 1/3*o**3.
-o**2*(o + 1)/3
Find c, given that 4/5*c**4 + 1/5*c + 9/5*c**3 + 6/5*c**2 + 0 = 0.
-1, -1/4, 0
Suppose -f - 3 = 3*q, -2*f - 3 = -f. Suppose b + b = q. Determine w, given that 0 + 0*w + b*w**3 - 1/2*w**4 + 1/2*w**2 = 0.
-1, 0, 1
Let z = 10 + -7. Factor 0*c**z + 26 - c**3 - 26 + c**4.
c**3*(c - 1)
Let w(s) be the first derivative of -8*s**5/55 - 15*s**4/22 - 32*s**3/33 - 3*s**2/11 + 4*s/11 + 11. Solve w(m) = 0 for m.
-2, -1, 1/4
Let g(s) be the first derivative of 0*s + 2 - 1/3*s**2 + 1/9*s**3. Suppose g(d) = 0. What is d?
0, 2
Let k(b) = -1. Let z(r) = r + 3. Let s(v) = 3*k(v) + z(v). Let p be s(2). Factor -j**p - j - 2*j + 2*j.
-j*(j + 1)
Let y(l) = l**3 + 3*l**2 + l. Let k(d) = -d - 12. Let c be k(-10). Let m be y(c). Find w, given that w**2 - m*w + w + 1 - 1 = 0.
0, 1
Let n(o) be the third derivative of o**5/270 + o**4/54 + o**3/27 + 4*o**2. Factor n(d).
2*(d + 1)**2/9
Let b(h) be the first derivative of -2*h**3/27 + 2*h**2/3 - 2*h + 9. Factor b(l).
-2*(l - 3)**2/9
Let y be ((-40)/5)/((-4)/2). Solve 2*g**2 - g**4 + 7*g**y + 2*g**5 + 0*g**5 + 6*g**3 = 0 for g.
-1, 0
Let y(l) be the first derivative of -l**5/90 + l**4/9 - 4*l**3/9 - l**2/2 - 3. Let b(h) be the second derivative of y(h). Solve b(a) = 0.
2
Let l = 104 - 104. Let n(m) be the second derivative of -1/54*m**4 + 0*m**2 + l - m + 0*m**3. Factor n(h).
-2*h**2/9
Let q