 - 6*m**2 - 2*m**4 + 4*m + 13 - 13 + 6*m**3 = 0. What is m?
0, 1
Suppose b + 12 = -2*w + 6*w, -2*b + 3 = w. Suppose s - 8 = 4*s - 4*f, 2*f - 4 = b. Suppose s + 2/5*h**3 + 8/5*h + 8/5*h**2 = 0. What is h?
-2, 0
Let p(y) be the third derivative of y**5/105 - 2*y**4/21 + 2*y**3/7 + 29*y**2. Solve p(z) = 0.
1, 3
Let d(r) be the third derivative of -r**6/60 - 2*r**5/15 - 5*r**4/12 - 2*r**3/3 - 9*r**2. Factor d(w).
-2*(w + 1)**2*(w + 2)
Let y(o) = 0 + o + 0. Let x be y(0). Determine k, given that -6*k**3 + 4*k**3 + x*k**3 = 0.
0
Let a(d) = -d**2 - 5*d - 1. Let h be a(-4). Let f = h - 2. Suppose p**2 + f + 2*p**2 - 2*p**2 - 2*p = 0. What is p?
1
Suppose -3*b = -b. Let a(v) be the third derivative of 0*v**3 - 1/15*v**5 + 1/60*v**6 - v**2 + b*v**4 + 0*v + 0. Suppose a(s) = 0. Calculate s.
0, 2
Let h = 309/380 + -1/76. Let n = 1284 + -6418/5. Factor -n + h*t - 2/5*t**2.
-2*(t - 1)**2/5
Suppose 0 = -4*x + r - 1, 0 = -x + 2*x - 5*r + 5. Suppose x*m = 3*m - 4*n - 18, 5*m + n - 7 = 0. Factor m + 1 + 2*k**2 - 5.
2*(k - 1)*(k + 1)
Let d be (25 + -27)/(-9 + 1). Solve 0 + 1/4*t**2 + d*t - 1/4*t**3 - 1/4*t**4 = 0 for t.
-1, 0, 1
Suppose 3*m - 2 = -2*b, 4*m + b - 2 = 2*m. Let v be 2/(0 - (-6)/4). Determine l, given that v*l**m + l - 1/3 = 0.
-1, 1/4
Let q(u) = 10*u**3 - 10*u. Let h(b) = -b**3 + b. Let v(m) = -35*h(m) - 4*q(m). Factor v(j).
-5*j*(j - 1)*(j + 1)
Let c(l) be the third derivative of -l**8/40320 + l**7/3360 - l**6/720 + l**5/15 - 4*l**2. Let i(f) be the third derivative of c(f). Solve i(g) = 0.
1, 2
Suppose 0*o - 5*o + 5*f = 15, -5*o - 5*f - 45 = 0. Let z be (-1)/(-3) - o/9. Factor -3*p**2 - z + p - 2*p + p**3 + 4*p.
(p - 1)**3
Let s(o) = 6*o - 84. Let j be s(14). What is k in 1/4*k**2 - 1/4*k - 1/4*k**4 + j + 1/4*k**3 = 0?
-1, 0, 1
Let m = 6 + -4. Factor d + d**2 + m*d - 2*d.
d*(d + 1)
Determine i so that 44/3 + 2*i**3 - 106/3*i + 56/3*i**2 = 0.
-11, 2/3, 1
Let z(f) = 6*f**3 - 9*f**2 - 6*f + 6. Let h(o) = 11*o**3 - 17*o**2 - 11*o + 12. Let g(n) = 3*h(n) - 5*z(n). Factor g(v).
3*(v - 2)*(v - 1)*(v + 1)
Suppose 2*m**2 + 0*m**2 + 0*m - 2*m - 1 + m**2 = 0. Calculate m.
-1/3, 1
Suppose -4 + 0*n**3 + 3*n**2 - n**3 + 2*n**3 = 0. What is n?
-2, 1
Let g be (4/(-1))/((-4)/(-14)). Let i be 0 - (2 - (-32)/g). Factor 0 + 2/7*r**2 + 0*r - i*r**3.
-2*r**2*(r - 1)/7
Let s(v) be the first derivative of v**6/48 - v**5/4 + 25*v**4/32 + 5*v**3/6 - 5*v**2 - 8*v + 18. Factor s(z).
(z - 4)**3*(z + 1)**2/8
Factor 53*h - 25*h - 22*h + 16*h**2.
2*h*(8*h + 3)
Suppose -9 = 3*r - 6*r. Let z = 911/3213 + 1/459. Factor -z*o**r + 2/7*o**5 + 2/7*o**2 + 0*o - 2/7*o**4 + 0.
2*o**2*(o - 1)**2*(o + 1)/7
Let b(h) be the first derivative of -h**6/30 + h**5/20 + h**4/12 - h**3/6 - h + 6. Let m(k) be the first derivative of b(k). Factor m(s).
-s*(s - 1)**2*(s + 1)
Let m(d) be the second derivative of d**8/4200 + d**7/1050 - d**3/6 - 2*d. Let c(u) be the second derivative of m(u). Factor c(z).
2*z**3*(z + 2)/5
Determine h, given that -2/3 + 4/3*h + 2*h**2 = 0.
-1, 1/3
Let u(p) be the third derivative of 3*p**2 + 1/630*p**7 + 0*p**3 - 1/360*p**6 + 1/72*p**4 + 0 + 0*p - 1/180*p**5. Factor u(k).
k*(k - 1)**2*(k + 1)/3
Let h be (1152/1680 - 2/7)/2. Factor -2/5*t + h - 4/5*t**3 - 7/5*t**2.
-(t + 1)**2*(4*t - 1)/5
Let i(b) be the second derivative of -b**7/6300 + b**6/450 - b**5/75 + b**4/6 - 4*b. Let n(p) be the third derivative of i(p). Factor n(o).
-2*(o - 2)**2/5
Suppose 2 = -3*a + 11. Factor -5*p - 1 + 0 - a*p**3 + p**3 + 7*p + p**4.
(p - 1)**3*(p + 1)
Let z(t) = 2*t**3 - 3*t**2 + t. Let v(s) = -4*s**3 + 5*s**2 - s. Let y(g) = -6*v(g) - 10*z(g). Factor y(n).
4*n*(n - 1)*(n + 1)
Let l be (-14)/(-30) + (-1)/(-5). Let j be 0 + 2/(-6) + 4 + -3. Factor j - l*h**2 + h**3 - h.
(h - 1)*(h + 1)*(3*h - 2)/3
Let q(f) = 5*f**2 + 5*f + 2. Let m(j) = 81*j**2 + 81*j + 33. Let a(k) = -2*m(k) + 33*q(k). What is t in a(t) = 0?
-1, 0
Suppose -5*i = -3*k - 0*k, -2*i - 3*k = -21. Let o(x) = x**2 - 3*x + 2. Let z be o(2). Factor g**3 - 4*g + z + 0 + i*g.
g*(g - 1)*(g + 1)
Let o be 8/196*14/(-6). Let w = o - -31/105. Solve 0*m - 1/5 + w*m**2 = 0.
-1, 1
Suppose 5*t - 7 - 33 = 0. Solve 5*l**2 - 12 - 6*l + 18*l - t*l**2 = 0 for l.
2
Let j(z) = -15*z - 90. Let n be j(-6). Find h such that n*h**2 + 3/2*h**4 + 0*h + 0 + 0*h**3 = 0.
0
Suppose -4*g = -3*l - 16, -3*l + g - 4 = -0. Let 0*v + l - 1/3*v**2 = 0. What is v?
0
Factor -10/9*a**3 + 0 + 2/3*a**2 + 4/9*a.
-2*a*(a - 1)*(5*a + 2)/9
Factor -1 - d**3 - 25/6*d**2 - 23/6*d.
-(d + 3)*(2*d + 1)*(3*d + 2)/6
Let p(q) be the first derivative of -q**3 - 9*q**2/2 + 12*q + 1. Factor p(r).
-3*(r - 1)*(r + 4)
Let x = -27 - -29. Let w(n) be the third derivative of -x*n**2 - 1/735*n**7 + 0*n**5 + 0*n + 0 + 1/21*n**4 + 0*n**3 - 1/140*n**6. Let w(p) = 0. Calculate p.
-2, 0, 1
Let p(z) = 2*z**3 + z**2 + z - 1. Let x be p(1). Factor -t**4 - 3*t**x + 5*t**3 - t**4.
-2*t**3*(t - 1)
Let k(y) be the third derivative of y**6/72 - y**5/36 - 5*y**4/18 + 10*y**3/9 - 9*y**2. Suppose k(f) = 0. Calculate f.
-2, 1, 2
Let s(r) = r**2 + r + 1. Let b(f) = f**2 + 12*f - 1. Let i(p) = -b(p) + 6*s(p). Let c(h) = -h**2 + h - 1. Let n(k) = -6*c(k) - i(k). Factor n(m).
(m - 1)*(m + 1)
Let z = 3/5 - -1/15. Find r, given that -z - 1/3*r - 2/3*r**4 - 1/3*r**5 + 4/3*r**2 + 2/3*r**3 = 0.
-2, -1, 1
Factor 25*n**2 + 20 + 12*n**2 - 2*n**3 + 18*n**2 + 60*n + 17*n**3.
5*(n + 1)*(n + 2)*(3*n + 2)
Let g(w) be the first derivative of w**6/20 + 9*w**5/40 + w**4/4 - 6*w - 8. Let q(z) be the first derivative of g(z). Solve q(m) = 0.
-2, -1, 0
Let f(z) = 33*z**3 + 21*z**2 - 57*z + 3. Let d(i) = 8*i**3 + 5*i**2 - 14*i + 1. Let y(a) = 21*d(a) - 5*f(a). Solve y(b) = 0.
-2, 1
Let v be (-27)/(-18)*(-4)/(-3). Let i be v/(-8)*(4 - 5). Factor -3/4*f + i*f**2 + 1/2.
(f - 2)*(f - 1)/4
Let x(y) be the second derivative of -y**5/120 - y**4/72 + y**3/36 + y**2/12 + 22*y. Solve x(w) = 0.
-1, 1
Let d(c) be the second derivative of -c**7/210 + c**6/30 - 7*c**5/100 - c**4/60 + 4*c**3/15 - 2*c**2/5 + 5*c. Find r such that d(r) = 0.
-1, 1, 2
Let s(v) = 2*v**3 + 4*v**2 + 8*v + 3. Let d(f) = -f**3 - f**2 - f. Let z(g) = 3*d(g) + s(g). Determine c so that z(c) = 0.
-1, 3
Let q(f) = f**2 + 4*f - 3. Let h(a) = -2*a**2 - 9*a + 6. Let t(l) = -2*h(l) - 5*q(l). Factor t(d).
-(d - 1)*(d + 3)
Suppose -2*n - 5*w - 38 = -9, 2*n = 4*w + 16. Let y be 3 - -1*(-3 - n). Solve k**3 + k - k + 2*k**2 - y*k**3 = 0.
0, 2
Determine v so that -4/5*v**4 - 12/5*v**2 + 0 + 12/5*v**3 + 4/5*v = 0.
0, 1
Let q(v) = -3*v - 2. Let s(j) = -5*j - 3. Let p(u) = 7*q(u) - 4*s(u). Let c be p(-6). Factor 2/3*h**3 + 0*h**2 - 1/3 + 1/3*h**c - 2/3*h.
(h - 1)*(h + 1)**3/3
Suppose 0 = -2*w + 14 + 2. Factor 2*v**2 + w*v - 2 + 6 + 4.
2*(v + 2)**2
Let c(v) be the third derivative of -v**7/945 + v**6/135 - v**5/90 + 60*v**2. Factor c(x).
-2*x**2*(x - 3)*(x - 1)/9
Let y(q) = -6*q**3 - 6*q**2 + 7*q - 7. Let a(l) = -l**3 - l**2 + l - 1. Let c(b) = 28*a(b) - 4*y(b). Find f, given that c(f) = 0.
-1, 0
Let p(i) = 3*i**3 + i**2 + i - 2. Let n be p(1). Let c(q) be the first derivative of -2/15*q**n + 0*q + 2 - 1/5*q**2. Factor c(w).
-2*w*(w + 1)/5
Let x(v) be the second derivative of v**7/3780 - v**4/4 + v. Let r(g) be the third derivative of x(g). Factor r(l).
2*l**2/3
Let b be 8/32 - (0 - 2/(-8)). Let g(m) be the first derivative of -2/3*m**3 + b*m**2 + 1/2*m**4 + 3 + 0*m. Determine h, given that g(h) = 0.
0, 1
Let c(h) = -h**2. Let s(m) = 2*m**2 + 20*m + 20. Let k(a) = 3*c(a) - s(a). Determine z, given that k(z) = 0.
-2
Let m be 357/85 + 9/(-3) + -1. Factor 2/5*p**4 + 0*p - m*p**5 + 0 - 1/5*p**3 + 0*p**2.
-p**3*(p - 1)**2/5
Let s(l) be the first derivative of -l**4/38 + 4*l**3/57 - l**2/19 - 9. Solve s(p) = 0 for p.
0, 1
Factor 0*s + 2*s + 0*s**2 - 6*s - s**2.
-s*(s + 4)
Let k(j) = -j**5 + j**4. Let o(d) = -2*d**5 + 3*d**3 + d**2 - 2*d. Let a(c) = 2*k(c) - 2*o(c). Suppose a(y) = 0. What is y?
-2, -1, 0, 1
Suppose 2*y = 4*y. Let h(c) = -c. Let u be h(y). Factor u*x + 1/2*x**2 + 0.
x**2/2
Let h(v) be the second derivative of -2*v**5/85 + 7*v**4/102 + 2*v**3/51 - 5*v. Let h(p) = 0. Calculate p.
-1/4, 0, 2
Let i(z) be the second derivative of 1/11*z**2 + 2/33*z**3 + 0 + 2*z + 1/66*z**4. Suppose i(h) = 0. Calculate h.
-1
Let q(m) be the third derivative of 0 - 7*m**2 + 1/3*m**3 + 1/18*m**5 + 1/180*