+ 0*x**2 + 1/900*x**6 - 1/6*x**3 + 0. Let p(y) be the second derivative of r(y). Factor p(z).
2*(z + 1)*(z + 2)/5
Let g(v) be the second derivative of 2/21*v**4 - 2/7*v**2 + 0 - 2*v - 2/105*v**6 - 1/7*v**3 + 3/35*v**5 - 1/49*v**7. Let g(y) = 0. What is y?
-1, -2/3, 1
Suppose -p = -0*p - 2*o - 15, 5 = -o. Let t(w) be the second derivative of 0 + 7/150*w**6 - 3*w - 1/20*w**p + 0*w**3 - 1/30*w**4 + 0*w**2. Factor t(v).
v**2*(v - 1)*(7*v + 2)/5
Let o(y) = -y**2 - 10*y - 4. Let i be o(-9). Suppose b - i*b = 0. Factor 2*m**3 - m**4 - 8*m**5 - 5*m**4 + b*m**3.
-2*m**3*(m + 1)*(4*m - 1)
Let v(n) = 22*n - 35 - 32*n**2 + 12*n**3 + 36 - 3*n**3. Let g(o) = -4*o**3 + 16*o**2 - 11*o - 1. Let r(u) = -5*g(u) - 3*v(u). Factor r(q).
-(q - 1)**2*(7*q - 2)
Let q = 6 - 3. Let i(j) = j - 10. Let f be i(13). Solve -3*b**2 + b**3 - 3*b**3 + 2*b**2 + q*b**f = 0.
0, 1
Suppose 3*v + q + 6 = -9, 0 = -5*v - 3*q - 29. Let i be v/(-10) - 12/30. Let 0*s + 4/5*s**2 + i - 2/5*s**3 = 0. What is s?
0, 2
Suppose -2*j = 2*m, 5*m + 12 = 4*j + 30. Solve 0*h - m*h**2 - 2/3*h**3 + 8/3 = 0.
-2, 1
Let m(j) = j**4 - j**3 + j + 1. Let o(g) = 2*g**5 - g**4 + 3*g**3 - 3*g - 3. Let r(u) = 3*m(u) + o(u). Solve r(w) = 0.
-1, 0
Let j be (3/33)/(6 + (-192)/33). Factor 1/6*z**2 - 1/3*z - j.
(z - 3)*(z + 1)/6
Suppose -1/7*x**3 + 0 + 0*x + 2/7*x**4 + 3/7*x**5 + 0*x**2 = 0. What is x?
-1, 0, 1/3
Let p(a) be the first derivative of -1/8*a**4 - 1/5*a**5 + 0*a**2 + 1/3*a**3 + 1/12*a**6 + 4 + 0*a. Factor p(z).
z**2*(z - 2)*(z - 1)*(z + 1)/2
Let j(h) = 3*h**4 - 6*h**3 - 3*h**2 + 6*h. Let o(u) = -3*u**4 + 7*u**3 + 3*u**2 - 7*u. Let t(l) = -4*j(l) - 3*o(l). Find b, given that t(b) = 0.
-1, 0, 1
What is c in -16/9*c**4 + 20/9*c - 8/9 + 4/9*c**3 + 16/3*c**2 = 0?
-1, 1/4, 2
Let u be 3/(-6) - 2/(-4). Determine z so that z - z**3 + 4*z**3 + u*z**3 - 4*z + 9*z**2 - 9 = 0.
-3, -1, 1
Suppose -3*b - 12 = 0, 4*r + 5*b - 4 = -16. Determine u so that -3*u**2 - 2*u + 3*u**2 - 4 - 3*u**r + 5*u**2 = 0.
-1, 2
Let j(f) be the second derivative of -1/45*f**6 + 0*f**2 + 0 + 1/18*f**4 + 4*f - 1/9*f**3 + 1/30*f**5. Determine a so that j(a) = 0.
-1, 0, 1
Let g(x) be the second derivative of x**8/840 + x**7/525 - x**6/300 - x**5/150 + x**2/2 - 3*x. Let n(k) be the first derivative of g(k). Factor n(a).
2*a**2*(a - 1)*(a + 1)**2/5
Solve -64/7*z - 2/7*z**4 - 48/7*z**2 - 16/7*z**3 - 32/7 = 0 for z.
-2
Let x(a) = -a + 9. Let o be x(7). Factor -1/2*t + 1/2*t**o + 0.
t*(t - 1)/2
Let r(i) = -i**2 - 5*i - 1. Let b be r(-2). Suppose 2*t - 1 - b = 0. Factor -u**t - u**2 + u**2 + 0*u**2.
-u**3
Find d, given that 6*d + 0*d + d**2 - 7*d - 2*d**2 = 0.
-1, 0
Find h, given that -9/5*h**2 + 3/5*h**3 + 3/5*h**5 - 6/5*h + 0 + 9/5*h**4 = 0.
-2, -1, 0, 1
Let p(v) be the third derivative of 6*v**2 + 0*v - 1/390*v**5 + 0 - 2/39*v**3 - 1/52*v**4. Let p(r) = 0. What is r?
-2, -1
Let i(m) be the second derivative of m**6/20 - 3*m**4/8 - m**3/2 + 22*m. Factor i(y).
3*y*(y - 2)*(y + 1)**2/2
Let g = -228 + 230. Determine a so that -2/9*a**g - 8/9*a - 8/9 = 0.
-2
Let r(h) be the first derivative of -h**5 - 5*h**4 - 10*h**3 - 10*h**2 - 5*h + 5. Let r(j) = 0. What is j?
-1
Let w(f) be the third derivative of -f**7/420 + f**6/160 - f**5/240 + 26*f**2. Factor w(o).
-o**2*(o - 1)*(2*o - 1)/4
Let z = -247/30 + 42/5. Solve 2/3*j**3 - z*j**2 + 0 + 0*j - 1/2*j**4 = 0.
0, 1/3, 1
Let i(r) be the first derivative of -1 - 2/15*r**3 - 2/5*r - 2/5*r**2. Determine w, given that i(w) = 0.
-1
Let c = 116 - 116. Let n(s) be the first derivative of 4 + c*s**3 + 0*s - 1/4*s**4 + 0*s**2. Let n(x) = 0. What is x?
0
Let d(s) be the first derivative of 2*s**6 - 8*s**5/5 - 6*s**4 + 16*s**3/3 + 6*s**2 - 8*s - 1. Solve d(y) = 0 for y.
-1, 2/3, 1
Determine d, given that 0 + 1/7*d**4 + 0*d + 2/7*d**3 + 1/7*d**2 = 0.
-1, 0
Let d(v) be the third derivative of v**6/80 - 7*v**5/120 + 5*v**4/48 - v**3/12 - 6*v**2. Factor d(u).
(u - 1)**2*(3*u - 1)/2
Suppose -2*c + 3 + 7 = 4*j, j + 2 = c. Let l(v) be the first derivative of 2/9*v**2 + 0*v + 1/9*v**4 + 10/27*v**c - 1. Factor l(f).
2*f*(f + 2)*(2*f + 1)/9
Let f = 34 - 30. Suppose 5*x = 4*j - 6, -x + 3*j - 6 = f. Factor -2/9*d**3 + 0 + 4/3*d**x - 2*d.
-2*d*(d - 3)**2/9
Let z(g) be the third derivative of -g**6/480 + 7*g**5/240 - g**4/16 + 14*g**2. Suppose z(b) = 0. What is b?
0, 1, 6
Suppose -8/13 + 6/13*g**2 + 0*g - 2/13*g**3 = 0. What is g?
-1, 2
Let k(l) be the second derivative of 0*l**2 + 3/20*l**5 + 2*l - 1/2*l**4 + 0*l**3 + 0. Let k(h) = 0. What is h?
0, 2
Let v(l) = -4*l**2 - 11*l - 2. Let a be v(-2). Let s(k) be the third derivative of -1/120*k**5 - 1/12*k**3 + 0 - a*k**2 - 1/24*k**4 + 0*k. Factor s(m).
-(m + 1)**2/2
Let v(j) be the second derivative of 11*j**4/12 + 2*j**3/3 - 2*j. Let b(w) = -16*w**2 - 6*w. Let d(n) = 5*b(n) + 7*v(n). Factor d(q).
-q*(3*q + 2)
Let c(p) be the first derivative of p**4/22 + 10*p**3/33 + 7*p**2/11 + 6*p/11 - 5. Find j such that c(j) = 0.
-3, -1
Suppose -3*t + 4*b + 20 = 0, -t = b + 5 - 0. Suppose t = n + 1 - 3. What is r in 2*r + 2*r**n - 2*r**3 + 8 - 2*r**4 - 8 = 0?
-1, 0, 1
Let q(f) be the first derivative of -5*f**6/24 - 3*f**5/5 - 9*f**4/16 - f**3/6 + 8. Let q(d) = 0. Calculate d.
-1, -2/5, 0
Let p(r) be the second derivative of -1/60*r**5 - 2*r - 1/24*r**4 + 0*r**3 + 0 + 1/2*r**2. Let v(a) be the first derivative of p(a). What is k in v(k) = 0?
-1, 0
Suppose 3*q = 4*o - 10, -q = -2*q - o + 6. Let k(u) be the first derivative of 0*u + 1/10*u**2 + q + 1/15*u**3. Factor k(g).
g*(g + 1)/5
Suppose 0 = -3*d + d - 8. Let h(u) = 6*u**3 + 2*u**2 - 6*u + 6. Let r(q) = 6*q**3 + 3*q**2 - 6*q + 7. Let l(x) = d*r(x) + 5*h(x). Factor l(m).
2*(m - 1)*(m + 1)*(3*m - 1)
Suppose -4*v + 24 = 4. Suppose -8*z = -v*z. Factor -1/4*n**3 + 1/4*n + 0 + z*n**2.
-n*(n - 1)*(n + 1)/4
Let 3/7*n + 36/7*n**2 - 81/7*n**3 - 2/7 = 0. What is n?
-2/9, 1/3
Let z be (1 - -3)*(2 + -3). Let y(i) = 2*i**3 - 2*i**2 - 4*i. Let l(m) = 3 - 3 + 2*m**2 + 3*m - m**3. Let n(k) = z*l(k) - 3*y(k). Factor n(d).
-2*d**2*(d + 1)
Let g(z) be the first derivative of z**3/3 - 8*z**2 + 19*z - 6. Let o be g(15). Factor 0*a**3 - 2/5*a**o + 6/5*a**2 + 4/5*a + 0.
-2*a*(a - 2)*(a + 1)**2/5
Let b = 83 - 31. Factor -70*h**3 - h + 31*h**4 - 80*h**4 + b*h**2 - 7*h.
-h*(h + 2)*(7*h - 2)**2
Let m = 238/3 - 79. Let r(b) be the first derivative of -4 + 4/3*b**3 - 6/5*b**5 + 3*b**2 - b**4 + 2*b - m*b**6. Factor r(z).
-2*(z - 1)*(z + 1)**4
Let v(o) be the second derivative of -9*o**5/100 + 7*o**4/20 - 6*o**2/5 - 2*o. Let v(g) = 0. Calculate g.
-2/3, 1, 2
Let m(a) be the second derivative of 2/9*a**4 - 1/6*a**2 - 7/90*a**6 - 1/30*a**5 + 2/63*a**7 + 0 - 2*a - 1/9*a**3. Determine p so that m(p) = 0.
-1, -1/4, 1
Factor 0*a - 2/5*a**5 - 18/5*a**4 + 0 - 54/5*a**2 - 54/5*a**3.
-2*a**2*(a + 3)**3/5
Solve k**3 - 2 + k**2 - k**2 - 4*k**2 + 5*k = 0 for k.
1, 2
Let o(u) = 5*u - 218. Let a be o(44). Factor v + 1/3*v**a + 2/3.
(v + 1)*(v + 2)/3
Let y = 215/9 - 71/3. Let g(j) be the first derivative of 0*j + 1/3*j**2 - y*j**3 - 1/6*j**4 + 2/15*j**5 - 1. Let g(m) = 0. Calculate m.
-1, 0, 1
Let o = -5 + 12. Let h = 10 - o. Solve 4*f**2 - 13*f**h + 3*f**3 - f + f = 0.
0, 2/5
Let y = -4 + 8. Suppose i - y*i + 6 = 0. Factor 6*t**i - 5*t**2 + t**2 - 2*t.
2*t*(t - 1)
Factor -2*g**2 - 5/2 - 1/4*g**3 + 19/4*g.
-(g - 1)**2*(g + 10)/4
Let o be (-68)/(-18) + 2/9. Suppose 4*l - o = -0*l. Solve 3*k**2 + 0*k**2 - l - k**2 - 1 = 0.
-1, 1
Let t(g) = -g + 5. Let w be t(3). Find x, given that 3*x**w - 3 - 1 + 1 = 0.
-1, 1
Factor 4*a**3 + 11*a - 8*a**2 + 24 - 7*a - 8*a**2.
4*(a - 3)*(a - 2)*(a + 1)
Let w(x) be the first derivative of 0*x + 3/2*x**2 + 0*x**3 + 1/72*x**4 + 1/180*x**5 - 2. Let l(c) be the second derivative of w(c). Factor l(q).
q*(q + 1)/3
Let z(q) be the first derivative of q**3 + 9*q**2/2 + 5. Factor z(v).
3*v*(v + 3)
Let r(p) be the second derivative of -2/3*p**2 - 1/126*p**7 - 11/36*p**4 + 1/60*p**5 + 1/30*p**6 - 8*p + 2/3*p**3 + 0. Solve r(x) = 0.
-2, 1, 2
Suppose -4*c = -2*c + 5*j - 5, c + 1 = j. Factor -3*o**4 + 2*o - o**4 + 4*o**2 + c*o**5 - 2*o**5.
-2*o*(o - 1)*(o + 1)**3
Factor -j + 7*j**2 + 10*j**2 - 18*j**2.
-j*(j + 1)
Find q such that -9/4*q**3 - 7/4*q**2 - 1/4*q**5 + 0 - 5/4*q**4 - 1/2*q = 0.
-2, -1, 0
Let a(w) = 3*w**2 - 6*w**4 + 3*w + 6*w**2 - 3*w**2. Let q(j) = -7*j**4 + 5