7/630 + v**6/90 + v**5/36 + v**4/36 - 11*v**2. Let o(r) = 0. What is r?
-2, -1, 0
Let v = -163/4 + 41. Factor -1/4*w**3 + 0 + 0*w**2 + 0*w - v*w**4.
-w**3*(w + 1)/4
Let m(s) be the third derivative of s**7/252 - s**6/48 - 13*s**2. Find p such that m(p) = 0.
0, 3
Let z(w) be the third derivative of 5*w**8/336 - 5*w**7/42 + 7*w**6/24 + w**5/12 - 5*w**4/3 + 10*w**3/3 - 10*w**2. Find n such that z(n) = 0.
-1, 1, 2
Let w(d) = 2*d**3 - 2*d + 4. Let r(v) = -6*v**3 + 6*v - 11. Let p = 22 + -11. Let o(q) = p*w(q) + 4*r(q). Factor o(t).
-2*t*(t - 1)*(t + 1)
Let v(z) be the second derivative of 0 - 1/25*z**5 + 1/30*z**4 - 1/75*z**6 + 0*z**2 + 2/15*z**3 + 3*z. Find k, given that v(k) = 0.
-2, -1, 0, 1
Let b(w) be the first derivative of -1/15*w**3 - 1/5*w + 1/5*w**2 + 4. Factor b(t).
-(t - 1)**2/5
Let q be (-13)/39*(-103 - -1). Let j = 36 - q. Let -2*r**j + 0 - 2/3*r + 8/3*r**3 = 0. What is r?
-1/4, 0, 1
Let u(n) be the second derivative of -n**5/30 - n**4/9 - n**3/9 + 4*n. Let u(h) = 0. What is h?
-1, 0
Let t(p) be the first derivative of p**3 - 3*p**2 + 5*p + 3. Let x(b) = 13*b**2 - 25*b + 21. Let c(j) = -18*t(j) + 4*x(j). Solve c(r) = 0 for r.
1, 3
Let p(j) = 3*j**3 - j**2 - 5. Let c(n) be the third derivative of -n**6/40 + n**5/30 + 2*n**3/3 + 2*n**2. Let r(m) = -5*c(m) - 4*p(m). Factor r(h).
3*h**2*(h - 2)
Let n(r) be the second derivative of r**5/60 - r**4/12 - 10*r. Factor n(g).
g**2*(g - 3)/3
Let w(k) be the second derivative of -2*k**4/3 + 5*k**3/3 - k**2 + 11*k. Factor w(t).
-2*(t - 1)*(4*t - 1)
Let p(z) = -z**5 + 3*z**4 + 2*z**3 - z + 3. Let l(b) be the first derivative of -b**5/5 - b - 3. Let f(j) = 3*l(j) + p(j). Solve f(g) = 0.
-1, 0, 1
Factor -3/7*p**4 - 12/7*p + 0 + 12/7*p**3 + 3/7*p**2.
-3*p*(p - 4)*(p - 1)*(p + 1)/7
Determine s so that 7*s**2 + 44*s - 50*s + 20*s**2 + 40*s**3 - 7*s**3 = 0.
-1, 0, 2/11
Let c = 3/46 - -41/782. Factor c*n**2 + 0 - 2/17*n.
2*n*(n - 1)/17
Factor 2 + 8/3*r**2 + 13/3*r + 1/3*r**3.
(r + 1)**2*(r + 6)/3
Let w(u) = -7*u + 24. Let k(t) = -2*t + 6. Let v(s) = -22*k(s) + 6*w(s). Let l be v(-5). Find q such that 1/4*q**l - 1/2 - 1/4*q = 0.
-1, 2
Suppose -t = -2*t + 6. Let d be (-1)/t*12/(-8). Factor -3/2*f - d - 9/4*f**2.
-(3*f + 1)**2/4
Let i(x) be the second derivative of x**5/4 + 7*x**4/72 - 7*x**3/12 + x**2/6 - 7*x. Factor i(b).
(b + 1)*(3*b - 2)*(10*b - 1)/6
Suppose 10 + 20 = 15*q. Factor 0 + 2/9*b**4 + 2/9*b**q + 0*b + 4/9*b**3.
2*b**2*(b + 1)**2/9
Determine f so that 0 + 9/4*f + 3/2*f**2 - 3/4*f**3 = 0.
-1, 0, 3
Let d(o) be the second derivative of o - 1/4*o**2 - 1/40*o**6 + 5/48*o**4 + 1/24*o**3 + 0 - 1/80*o**5. Suppose d(g) = 0. What is g?
-1, 2/3, 1
Let b(s) = -8*s**4 - 4*s**3 + 4*s. Let h(o) = 23*o**4 + 12*o**3 - o**2 - 12*o. Let w(d) = -11*b(d) - 4*h(d). Factor w(x).
-4*x*(x - 1)*(x + 1)**2
Let u(t) be the third derivative of 4*t**7/21 + 19*t**6/30 + 11*t**5/15 + t**4/3 - 12*t**2. Suppose u(y) = 0. What is y?
-1, -1/2, -2/5, 0
Let f(d) = -3*d + 10. Let h be f(9). Let w = h + 29. Find j, given that -3*j**5 - 2*j**4 - j**5 + 2*j**5 - 10*j**3 + 2*j**2 + w*j**3 = 0.
-1, 0, 1
What is n in 2/13*n**5 + 0*n + 2/13*n**2 + 0 - 2/13*n**4 - 2/13*n**3 = 0?
-1, 0, 1
Let l(i) = 9*i**3 - 4*i**2 - 5*i - 5. Let v(b) = 5*b**3 - 2*b**2 - 3*b - 3. Let q(d) = 3*l(d) - 5*v(d). Find h, given that q(h) = 0.
0, 1
Let m(i) = -7*i**2 - i - 3. Let h(p) = -41*p**2 - 6*p - 17. Let t(z) = 6*h(z) - 34*m(z). Let t(r) = 0. What is r?
-1/4, 0
Let l(t) be the third derivative of -t**8/336 - t**7/105 - t**6/120 + 8*t**2. Find x, given that l(x) = 0.
-1, 0
Suppose -4*s = 3*s + 14*s. Let s*w**2 - 4/13*w**4 + 6/13*w**5 - 2/13*w**3 + 0*w + 0 = 0. Calculate w.
-1/3, 0, 1
Factor 37/5*h + 58/5*h**2 + 9/5 + 42/5*h**3 + 1/5*h**5 + 13/5*h**4.
(h + 1)**4*(h + 9)/5
Let p(v) be the first derivative of -v**7/3780 + v**6/324 - 2*v**5/135 + v**4/27 + v**3/3 - 1. Let k(b) be the third derivative of p(b). Factor k(f).
-2*(f - 2)**2*(f - 1)/9
Let v(d) be the third derivative of 0*d + 0*d**3 - 1/135*d**5 - 7*d**2 - 1/108*d**6 + 0 + 0*d**4. Factor v(o).
-2*o**2*(5*o + 2)/9
Let v be 12/(-10)*10/(-18). Factor -2/3*x - v*x**2 + 0.
-2*x*(x + 1)/3
Let a = -5 + 11. Suppose -v - 10 = -a*v. Factor 2*b + 5*b**3 - 2*b**v - 11*b**3 + 4*b**3 + 2*b**4.
2*b*(b - 1)**2*(b + 1)
Suppose -t + q = 4*t - 23, 0 = 4*t + 2*q - 24. Let d(h) be the first derivative of 1/8*h**4 - 2 - 1/10*h**t + 0*h**2 + 0*h**3 + 0*h. Factor d(x).
-x**3*(x - 1)/2
Let o be (-2)/5 + (-1058)/(-345). Find l such that -2/3*l**2 - 8/3 - o*l = 0.
-2
Let f(j) be the first derivative of -2 - 5/3*j**3 + 0*j - 7/4*j**4 + j**2. Factor f(a).
-a*(a + 1)*(7*a - 2)
Determine p so that -6*p**2 + 4*p**2 - p - p**2 + 3*p + p**3 = 0.
0, 1, 2
Let p(a) = -a**3 + a**2 + 2*a + 1. Let n be p(-1). Let k be 0 + n + (-9)/(-3). Determine h, given that 3 - 4*h**2 + 1 - 5 + k*h = 0.
1/2
Let m(o) = o**2 + 131*o - 360. Let v(b) = 26*b - 72. Let t(r) = -2*m(r) + 11*v(r). What is s in t(s) = 0?
6
Factor -2*y**3 - 9*y**2 - 54 + 3*y**2 - 12*y**2 - 54*y.
-2*(y + 3)**3
Suppose 2*l = -3*j - 2*l - 7, -j + 19 = -4*l. Let r(o) be the second derivative of 0*o**2 + 0 + 0*o**j - 1/18*o**4 - 1/20*o**5 + o + 1/18*o**6. Factor r(x).
x**2*(x - 1)*(5*x + 2)/3
Let c = 123 + -123. Let a(m) be the first derivative of 1/16*m**4 - 1/12*m**3 + 0*m**2 - 2 + c*m. Solve a(h) = 0.
0, 1
Let x(t) be the second derivative of t**6/1080 - t**5/360 + t**3/6 + 2*t. Let l(w) be the second derivative of x(w). Solve l(u) = 0 for u.
0, 1
Let d(j) = 4*j**4 - 27*j**3 + 91*j**2 - 128*j + 64. Let l(h) = -4*h**4 + 26*h**3 - 90*h**2 + 128*h - 64. Let t(v) = 6*d(v) + 5*l(v). Solve t(p) = 0.
2
Let o(n) be the second derivative of 0 - 3/20*n**5 + 5*n + 3*n**2 + n**4 - 5/2*n**3. Factor o(x).
-3*(x - 2)*(x - 1)**2
Let i(m) = -4*m - 4. Let w(g) = -g**4 - g**3 + g**2 + 12*g + 11. Let y(o) = -11*i(o) - 4*w(o). Solve y(a) = 0.
-1, 0, 1
Let n(k) = k**4 - k**3 + 6*k**2 - k + 4. Let f(d) = d**4 - 2*d**3 + 6*d**2 - 2*d + 3. Suppose -m + 0 + 2 = 0. Let y(a) = m*n(a) - 3*f(a). Factor y(w).
-(w - 1)**4
Let o be ((-3)/27 - (0 + 1)) + 2. Let 22/9*w**2 - 2/3*w**3 + o - 8/3*w = 0. What is w?
2/3, 1, 2
Let u(h) = h**2 + h - 21. Let g(n) = -n**2 - n + 10. Let b(q) = -13*g(q) - 6*u(q). Let r(o) = -4*o**2 - 4*o + 2. Let y(j) = -3*b(j) - 5*r(j). Factor y(w).
-(w - 1)*(w + 2)
Let -9/2*g - 1/6*g**3 + 3/2*g**2 + 9/2 = 0. Calculate g.
3
Let m(w) = 6*w + 1. Let q be m(1). Let l be q/14 - (-1)/6. Factor 0*s + 0 + l*s**3 + 0*s**2 + 0*s**4 - 2/3*s**5.
-2*s**3*(s - 1)*(s + 1)/3
Suppose 5*a - 25 = -0*a. Let d = 7 - a. Let -j - 2*j**4 + 2*j**2 + 0*j**d - j + 2*j**3 = 0. What is j?
-1, 0, 1
Suppose 0 = -u - u - 8. Let l(i) = i**2 + 3*i - 4. Let s be l(u). Let -2/7*p**2 + 2/7*p + s = 0. Calculate p.
0, 1
Suppose 5*y - 3*d + d = -25, 4*d + 20 = -4*y. Let t(h) = -6*h**2 - h - 5. Let v(q) = -7*q**2 - q - 6. Let b(j) = y*v(j) + 6*t(j). Factor b(a).
-a*(a + 1)
Suppose -5*d - 1 = m, 3*d - 1 = 4*d. Let x = -2 + 2. Solve -7/2*k**5 - 8*k**m - 11/2*k**3 - k**2 + 0 + x*k = 0.
-1, -2/7, 0
Let n(u) be the third derivative of 6*u**2 + 0*u - 4/3*u**3 + 1/6*u**4 + 1/15*u**5 + 0. Factor n(y).
4*(y - 1)*(y + 2)
Let k(l) be the second derivative of -l**6/210 + l**5/35 - 5*l**4/84 + l**3/21 + 3*l. Factor k(j).
-j*(j - 2)*(j - 1)**2/7
Let q(t) = t + 15. Let o be q(-12). Suppose -o*l = f - l, 6 = 2*f + l. Suppose 500/3*a**3 + 20/3*a + 625/3*a**f + 1/3 + 50*a**2 = 0. What is a?
-1/5
Let m(b) be the third derivative of 0*b**3 - 1/660*b**6 + 0*b - 1/132*b**4 - 1/165*b**5 + 0 - 3*b**2. Find g, given that m(g) = 0.
-1, 0
Suppose 6 = -0*g + 2*g. Let a(i) be the second derivative of 0*i**2 + 0 - 1/6*i**4 + 1/3*i**g + 3*i. Factor a(r).
-2*r*(r - 1)
Let k = 199/3 - 66. Factor 0*c**2 - k*c**3 + 0*c**4 + 1/3*c**5 + 0 + 0*c.
c**3*(c - 1)*(c + 1)/3
Suppose -2*h**2 + 0*h**2 + h + 2*h**2 - 2 + h**2 = 0. What is h?
-2, 1
Let z(t) = t**5 + t**4 + 4*t**3 - 3*t. Let m(i) = -3*i**5 - 2*i**4 - 11*i**3 + 8*i. Let c = -10 + 7. Let s(k) = c*m(k) - 8*z(k). Factor s(o).
o**3*(o - 1)**2
Let b(t) be the third derivative of -1/24*t**3 + 0*t - 1/48*t**4 + 4*t**2 + 1/840*t**7 + 0 + 1/240*t**6 + 0*t**5. Factor b(f).
(f - 1)*(f + 1)**3/4
Suppose 2*s - 2 = 3*b - 4, 29 = b + 5*s. Factor -3*r**b + 2*r**3 - r**5 - r + 3*r**4.
-r*(r - 1)**2*(r + 1)**2
Let i(a) be the second