tor 1/2 + 9/4*d + m*d**2.
(d + 1)*(7*d + 2)/4
Determine r, given that -8/3*r**4 + 2/3*r**5 + 0*r**2 + 8/3*r**3 + 0*r + 0 = 0.
0, 2
Let z be -2 - (-3 - -2)*-1. Let s = z + 3. Solve s + 2/3*n - 2/3*n**2 = 0 for n.
0, 1
Factor 0 - 1/2*s**5 + 0*s**2 + 1/2*s**4 + 0*s + s**3.
-s**3*(s - 2)*(s + 1)/2
Suppose u - 15 = -2*v, -22 + 1 = -4*v + u. Find q, given that 6*q**4 - q - 16*q**2 - v*q**3 + q + 8*q + 12*q**4 = 0.
-1, 0, 2/3
Factor 49*i**2 + 4 + 0 + 5*i - 33*i.
(7*i - 2)**2
Let o(d) = -d**3 + 6*d**2 + d. Let h be o(6). Suppose 2*n + 2 = h. Factor -3*j - 1 + 3*j**2 + 5*j**3 + n - 3*j**3 - 3*j**3.
-(j - 1)**3
Let c(x) = -3*x - 9. Let o be c(-4). Factor -3*m + 3*m**3 - 9*m**3 + 6*m**2 + 0*m**3 + o*m**3.
-3*m*(m - 1)**2
Let c(t) be the third derivative of 0*t + 1/70*t**7 + 0*t**3 + 1/336*t**8 + 0*t**4 + 1/60*t**6 - 6*t**2 + 0*t**5 + 0. Factor c(a).
a**3*(a + 1)*(a + 2)
Suppose -20 + 0 = -4*y. Suppose 0 = -5*c + y*x + 5, -3*c + 3*x + 2 = x. Solve c*m - 2/5*m**2 + 2/5 = 0.
-1, 1
Let i = -1/293 + 591/1465. Let x = -258/5 - -52. Find t such that -x*t**2 + 2/5 - 2/5*t**3 + i*t = 0.
-1, 1
Let x(u) = -12*u**4 - 18*u**3 - 20*u**2 - 4*u. Let w = -6 + 7. Let o(c) = -c**4 - c**3 - c**2. Let q(b) = w*x(b) - 10*o(b). What is h in q(h) = 0?
-2, -1, 0
Let m(o) be the second derivative of 0 - 1/30*o**5 - o**2 - 1/12*o**4 - 2*o + 0*o**3. Let u(j) be the first derivative of m(j). Suppose u(r) = 0. What is r?
-1, 0
Suppose -9*g**2 - 7/2*g**3 - 4 - 1/2*g**4 - 10*g = 0. What is g?
-2, -1
Suppose -2*h = -2 - 4. Let k be -4 + (0 - (-21)/h). Factor -6/7*q + 2/7 - 2/7*q**k + 6/7*q**2.
-2*(q - 1)**3/7
Let l(m) = -m**5 + 5*m**4 - 4*m**3 - 6*m**2 + 6*m. Let n(d) = 5*d**4 - 5*d**3 - 5*d**2 + 5*d. Let u(j) = -5*l(j) + 6*n(j). Factor u(f).
5*f**3*(f - 1)*(f + 2)
Let r(z) = -10*z**2 + 1. Let q be r(1). Let k(l) = -4*l**3 + l**2 - 4*l. Let c(a) = a**3 + a. Let w(s) = q*c(s) - 2*k(s). Determine h so that w(h) = 0.
-1, 0
Let f(m) = -5*m**3 - 5*m**2 - 11*m - 3. Let s(o) = -5*o**2 - 2 - 7*o - o**3 + 0*o**2 - 2*o**3 + 2*o**2. Let y(j) = 5*f(j) - 8*s(j). Factor y(r).
-(r - 1)*(r + 1)**2
Let h be (-4 + 1 - -8) + -3. Solve 2 + 2*u**5 - 2*u**5 + 20*u**2 + 14*u - 4*u + 20*u**3 + 10*u**4 + h*u**5 = 0.
-1
Let 32/3*o - 256/3 - 1/3*o**2 = 0. What is o?
16
Let i(k) be the first derivative of 3*k**5/5 - 3*k**4/2 - k**3 + 3*k**2 + 16. Factor i(r).
3*r*(r - 2)*(r - 1)*(r + 1)
Suppose -2*n + 14 = 4*l, -26 = -4*n - 5*l + 2. Suppose 7 + 1 + 18*z**2 - 31*z + n*z = 0. Calculate z.
2/3
Let s(z) be the first derivative of -2/55*z**5 + 1 - 1/33*z**6 + 1/22*z**4 + 0*z**2 + 0*z + 2/33*z**3. Factor s(h).
-2*h**2*(h - 1)*(h + 1)**2/11
Let t(g) be the third derivative of 1/12*g**4 + 2*g**2 + 0*g**5 + 0*g - 1/180*g**6 + 1/2*g**3 + 0. Let q(z) be the first derivative of t(z). Factor q(n).
-2*(n - 1)*(n + 1)
Let o(n) be the second derivative of n**5/40 - n**3/12 - 10*n. Factor o(w).
w*(w - 1)*(w + 1)/2
Let c(i) = 4*i - 6*i**2 + 7 - i**3 - 3*i - 4*i - i. Let l be c(-5). Factor -4*k - k**5 + 2*k**3 - 2*k**4 + 8*k**4 + 3*k**5 - 7*k**2 + k**l.
2*k*(k - 1)*(k + 1)**2*(k + 2)
What is k in -1/7*k**2 + 2/7 - 1/7*k = 0?
-2, 1
Let b(k) = -24*k**2 + 21*k - 139. Let i(n) = -2*n**2 - n - 1. Let r(z) = -2*b(z) + 22*i(z). Factor r(x).
4*(x - 8)**2
Let x = -1 + 3. Suppose 0 = 2*y + 3*i, 17 = x*y + y - 4*i. Factor y*b**2 + 1 - b**2 + 2 - 5.
2*(b - 1)*(b + 1)
Let d(f) be the third derivative of f**8/3528 - f**7/735 + f**6/420 - f**5/630 - 30*f**2. Factor d(b).
2*b**2*(b - 1)**3/21
Let b(a) be the third derivative of -a**7/840 + 7*a**6/480 - 3*a**5/40 + 5*a**4/24 - a**3/3 + 20*a**2. Factor b(o).
-(o - 2)**3*(o - 1)/4
Let -2/3*p**2 + 4/15*p**5 + 26/15*p**3 + 4/15 - 6/5*p**4 - 2/5*p = 0. Calculate p.
-1/2, 1, 2
Let m(k) = 1 - 2 + k**3 + 0 + 2. Let t be m(1). Let -2*a**4 + 0 - 2/3*a**5 - 2/3*a**t + 0*a - 2*a**3 = 0. What is a?
-1, 0
Suppose 6*g**2 - 92*g + 92*g + 9*g**3 = 0. Calculate g.
-2/3, 0
Factor 2*v**5 + 4*v**3 + 6*v**4 - 4*v**4 - 8*v**4 + 4*v**2 + 2 - 6*v.
2*(v - 1)**4*(v + 1)
Let m(f) be the first derivative of 4*f**3/3 + 10*f**2 + 16*f - 6. Factor m(a).
4*(a + 1)*(a + 4)
Let u(t) be the first derivative of -t**7/1050 + t**5/100 - t**4/60 + 3*t**2/2 + 10. Let h(q) be the second derivative of u(q). Let h(c) = 0. What is c?
-2, 0, 1
Let l(m) be the second derivative of 1/3*m**4 - 1/10*m**5 + 0 + 0*m**2 + 0*m**3 + 3*m. Factor l(a).
-2*a**2*(a - 2)
Find t, given that -2/15*t**2 + 2/15 - 2/15*t + 2/15*t**3 = 0.
-1, 1
Let n(b) be the third derivative of 0*b**3 + 0*b**4 + 1/30*b**6 + 5*b**2 + 0 + 0*b + 1/15*b**5. Factor n(z).
4*z**2*(z + 1)
Factor 93/2*p + 6*p**2 - 12.
3*(p + 8)*(4*p - 1)/2
Determine y, given that -1/5*y**2 + 0 + 1/5*y = 0.
0, 1
Suppose -5*j - c + 22 = 2*c, -24 = -4*j + 4*c. Suppose 3*a + 2*s - 7 - 6 = 0, j*s = -5. Solve 0 + 1/2*r - 1/4*r**2 + 1/4*r**4 - 3/4*r**3 + 1/4*r**a = 0.
-2, -1, 0, 1
Let z be 12/((-2 + 4)/(-2)). Let h = 18 + z. Solve 4*l**3 + 2 + 0*l + l**5 - h*l**4 + l**5 + 4*l**2 + l - 7*l = 0 for l.
-1, 1
Let v = -28 - -17. Let n(g) = 6*g**2 + 4 - 4 + 2*g + 2. Let t(c) = -c**3 + 31*c**2 + 11*c + 11. Let j(r) = v*n(r) + 2*t(r). Factor j(x).
-2*x**2*(x + 2)
Let g(v) = 57*v**3 + 36*v**2 - 36*v - 15. Let w(s) = 8*s**3 + 5*s**2 - 5*s - 2. Let z(q) = -2*g(q) + 15*w(q). Factor z(c).
3*c*(c + 1)*(2*c - 1)
Let a(t) be the first derivative of t**4/7 - 4*t**3/7 - 2*t**2/7 + 12*t/7 - 39. Factor a(d).
4*(d - 3)*(d - 1)*(d + 1)/7
Suppose -5*z = 10, -2*m + z = 3*m - 17. Let t(v) be the third derivative of 3*v**2 + 1/210*v**5 + 0*v**m + 0*v + 1/84*v**4 + 0. Find j, given that t(j) = 0.
-1, 0
Factor 4/13*d**2 - 2/13*d**5 + 2/13*d + 0 - 4/13*d**4 + 0*d**3.
-2*d*(d - 1)*(d + 1)**3/13
Let l(u) be the second derivative of -u**8/840 + u**7/120 - u**6/40 + u**5/24 - u**4/24 + u**3/3 + 5*u. Let v(w) be the second derivative of l(w). Factor v(b).
-(b - 1)**3*(2*b - 1)
Let g(s) be the third derivative of s**8/252 + 4*s**7/315 + s**6/90 + 2*s**2. What is w in g(w) = 0?
-1, 0
Let s = 19 - 16. Suppose 18 = s*d + 4*z, -5*d - 3*z + 4*z = -7. What is u in 2/7*u**3 - 8/7*u**d + 10/7*u - 4/7 = 0?
1, 2
Let h = 51/13 - 240/91. Suppose 6/7*z**4 - 3/7*z**5 + 0 + h*z**3 - 12/7*z**2 - 12/7*z = 0. What is z?
-1, 0, 2
Let b(k) be the second derivative of -k**5/30 + k**4/9 - k**3/9 + 2*k + 7. Factor b(g).
-2*g*(g - 1)**2/3
Suppose -4*u - 10 = u. Let b be -6*u/(-6)*-1. Factor 3/5*t**3 - 3/5*t - 3/5*t**b + 3/5.
3*(t - 1)**2*(t + 1)/5
Factor 0*v + 1/3*v**3 + 0 - 1/3*v**2 - 1/3*v**5 + 1/3*v**4.
-v**2*(v - 1)**2*(v + 1)/3
Let n = 13/14 - -17/42. Let q(f) be the first derivative of -f**2 - 1 + 2*f - n*f**3. Find o, given that q(o) = 0.
-1, 1/2
Let z(g) be the second derivative of -3*g**5/20 - 5*g**4/4 - 4*g**3 - 6*g**2 - 4*g. Solve z(l) = 0 for l.
-2, -1
Let a(o) be the third derivative of -1/10*o**5 + 0*o**3 + 0 - 1/8*o**4 - 4*o**2 + 0*o - 1/40*o**6. Factor a(g).
-3*g*(g + 1)**2
Let l(d) = 3*d**2 + 6*d + 6. Let p(o) = 2*o**2 + 6*o + 5. Let r(g) = 5*l(g) - 6*p(g). Let r(t) = 0. What is t?
0, 2
Let g(t) be the third derivative of t**6/120 + 2*t**3/3 + t**2. Let z be g(0). Factor 4/9*u**3 - 4/9*u + 0*u**2 - 2/9 + 2/9*u**z.
2*(u - 1)*(u + 1)**3/9
Let v(f) be the third derivative of -1/360*f**6 + 0 + 1/180*f**5 + 0*f + 0*f**3 + 1/36*f**4 + 4*f**2. Solve v(n) = 0 for n.
-1, 0, 2
Let o(u) be the first derivative of -5*u**6/6 + u**5 + 5*u**4/2 - 10*u**3/3 - 5*u**2/2 + 5*u - 27. Factor o(v).
-5*(v - 1)**3*(v + 1)**2
Factor -1/2*s + 1/10*s**2 + 2/5.
(s - 4)*(s - 1)/10
Suppose 2*s + 2*s = 2*k + 4, 4*k - 4*s + 4 = 0. Let a(r) be the third derivative of 0*r**3 - 1/42*r**4 - 2*r**2 + 1/210*r**5 + 0 + k*r. Solve a(o) = 0.
0, 2
Let o be ((-6)/3 - -3) + -1. Let t be (-1 + 3)/(10 + -1). Factor -2/9 + o*b + t*b**2.
2*(b - 1)*(b + 1)/9
Let u = -282 - -288. Let o(h) = h + 7. Let m be o(-3). Factor 0*t**2 + 6*t**3 + 3/2*t**5 + 0*t - u*t**m + 0.
3*t**3*(t - 2)**2/2
Let s = -23 + 11. Let i = 15 + s. Factor 1/4*g**4 - 1/4*g**2 - 1/4*g**i + 1/4*g + 0.
g*(g - 1)**2*(g + 1)/4
Factor 0 + 3/2*b**4 + 3/2*b - 3/2*b**2 - 3/2*b**3.
3*b*(b - 1)**2*(b + 1)/2
Let k(o) = o**3 + 5*o**2. Let i be k(-5). Let v = 2/259 + 508/1295. What is m in -v*m**2 + 2/5*m + i = 0?
0, 1
Let m be (-1)/2 + (-1)/2. Let t be 12/(-8)*2/m. Solve -1/2*v**4 - v**t - 1/2*v**2 + 0*v + 0 = 0.
-1, 0
Determine x, given t