3 + 1/3*r**5.
(r - 1)**4*(r + 1)/3
Factor 1/3*q**4 + 2/3*q + 0 - 2/3*q**3 - 1/3*q**2.
q*(q - 2)*(q - 1)*(q + 1)/3
Let j(s) = 3 - 2*s - s**3 + 3*s**2 + 0*s + s. Let i be j(3). Factor i*c**2 - c + 2*c**4 + 3*c**3 - 4*c**5 - 2*c**2 + 2*c**4.
-c*(c - 1)**2*(2*c + 1)**2
Let v(z) be the first derivative of z**3/4 + 3*z**2/2 + 3*z + 2. Determine y so that v(y) = 0.
-2
Let o(v) be the first derivative of -1/3*v**3 + 0*v**2 + 0*v**6 + 0*v**5 + 0*v + 1/840*v**7 - 2 + 0*v**4. Let x(u) be the third derivative of o(u). Factor x(r).
r**3
Let r = 13/18 - 7/18. Factor 5/6*o**2 - 1/2*o - r.
(o - 1)*(5*o + 2)/6
Let y(t) be the first derivative of 0*t - 2/9*t**3 + 4 - 1/4*t**4 - 2*t**2 - 7/90*t**5. Let f(w) be the second derivative of y(w). Find d, given that f(d) = 0.
-1, -2/7
Let u(m) = 15*m**3 - 25*m**2 + 9*m - 1. Let p(a) = -a**3 - a**2. Let z = -5 - -3. Let v = -3 - z. Let f(b) = v*p(b) + u(b). Let f(l) = 0. Calculate l.
1/4, 1
Let t = -9 + 14. Determine m, given that -5 + 0*m**2 - t*m**3 + 5 - m**2 = 0.
-1/5, 0
Let r(k) be the third derivative of k**8/672 + k**7/1260 - 11*k**6/720 + k**5/120 + k**4/18 - k**3/9 - k**2. Suppose r(x) = 0. Calculate x.
-2, -1, 2/3, 1
Let a(u) be the third derivative of -u**5/15 + 2*u**3/3 + 2*u**2. Determine j so that a(j) = 0.
-1, 1
Let m(w) be the second derivative of -w**8/240 + w**7/168 + w**6/40 - w**5/24 - w**4/12 - 2*w**3/3 - w. Let a(o) be the second derivative of m(o). Factor a(x).
-(x - 1)**2*(x + 1)*(7*x + 2)
Suppose -2*a - a - 3*c + 6 = 0, 5*a - 4*c = -8. Suppose 0*t**2 - 21/4*t**5 - 3*t**3 + a - 12*t**4 + 0*t = 0. What is t?
-2, -2/7, 0
Let r(w) = 5*w - 1. Let f(m) = 9*m - 1. Let u(i) = -6*f(i) + 11*r(i). Let a be u(5). Let a*x + 2/5*x**2 + 0 = 0. Calculate x.
0
Let l(g) be the third derivative of 1/60*g**6 - 1/12*g**4 + 0 - 1/3*g**3 + 1/30*g**5 + 0*g + 2*g**2. Factor l(u).
2*(u - 1)*(u + 1)**2
Let y(i) = -i**3 - 5*i**2 - 9*i - 17. Let a be y(-4). Let d(o) be the second derivative of 0 - a*o + 1/3*o**3 + 1/18*o**4 + 2/3*o**2. Factor d(q).
2*(q + 1)*(q + 2)/3
Let c(p) be the second derivative of 9*p - 1/10*p**5 + 2/3*p**3 - 1/6*p**4 + 0 + 0*p**2. Solve c(t) = 0 for t.
-2, 0, 1
Let f(g) = g**2 - 6*g + 7. Let a be f(7). Let n = a - 10. Factor -i**2 - i**2 + 0*i - n*i + 2*i.
-2*i*(i + 1)
Let o(x) be the third derivative of -x**8/1344 + x**7/280 + x**6/480 - 7*x**5/240 + x**3/6 - 5*x**2. Suppose o(y) = 0. Calculate y.
-1, 1, 2
Suppose 4*d - 2*t = 18, 0*t = 3*d - 4*t - 16. Let x be 9/d + (-2)/8. Factor 0*a + 1/2*a**x + 0 - 3/2*a**3 + a**4.
a**2*(a - 1)*(2*a - 1)/2
Let v(p) = p - 5. Let n be 48/9 + 3/(-9). Let t be v(n). Determine a so that -1/5*a**5 - 1/5*a**3 + 0*a**2 + t*a - 2/5*a**4 + 0 = 0.
-1, 0
Let m(p) = -31*p**5 - 80*p**4 - 60*p**3 + 11*p. Let s(k) = -6*k**5 - 16*k**4 - 12*k**3 + 2*k. Let u(o) = -2*m(o) + 11*s(o). Let u(h) = 0. What is h?
-3, -1, 0
Let l(r) be the first derivative of 0*r - 14/15*r**3 + 2/5*r**2 - 2 + 24/25*r**5 - 7/10*r**4. What is a in l(a) = 0?
-2/3, 0, 1/4, 1
Solve -g**3 + 3*g**2 - 7 - 7 + 9*g + 16 - g**4 - 4*g = 0.
-1, 2
Factor -106*r**4 - 2*r**2 + 107*r**4 - r**2 - 2*r.
r*(r - 2)*(r + 1)**2
Let i(x) = -6*x**2 + 3*x - 1. Let t(h) = 13*h**2 - 7*h + 3. Let j(a) = -9*i(a) - 4*t(a). Let q be j(-2). Factor 1/3*c**2 + 0*c + 0 - 1/3*c**q.
-c**2*(c - 1)/3
Let u(m) be the third derivative of -m**8/1008 + m**7/630 + m**6/360 - m**5/180 - 4*m**2. Solve u(c) = 0 for c.
-1, 0, 1
Let i(s) = 7*s**2 - 2*s - 13. Let k(m) = 3*m**2 - m - 6. Let a(d) = -2*i(d) + 5*k(d). Let x be a(3). Suppose -1/3*l**x + 0 + 1/3*l = 0. What is l?
0, 1
Suppose 0*n + 12 = 3*n. Suppose 0 = 3*f + 2*o - 7*o + 3, -4*f = -n*o - 4. Solve 0*a**2 + 2*a**2 - f*a**2 - 2*a + 4 = 0 for a.
-2, 1
Let n(q) = q**3 - 5*q**2 + 48*q - 64. Let g(k) = k**2. Let b(a) = -28*g(a) + 4*n(a). Suppose b(r) = 0. What is r?
4
Let y(l) be the third derivative of l**8/70560 - l**7/4410 + l**6/840 + l**5/10 + 6*l**2. Let g(w) be the third derivative of y(w). Find f, given that g(f) = 0.
1, 3
Let h(x) be the second derivative of -x**7/56 + 3*x**6/20 - 9*x**5/20 + 5*x**4/8 - 3*x**3/8 + 2*x - 1. Factor h(j).
-3*j*(j - 3)*(j - 1)**3/4
Determine s, given that -4*s**5 - s**4 + 2*s**5 - s**4 = 0.
-1, 0
Let o(b) = 2*b**2 + 2*b + 2. Let f = -15 - -12. Let l be o(f). Let -50*a**4 - 80/7*a - 470/7*a**3 - 290/7*a**2 - 8/7 - l*a**5 = 0. What is a?
-1, -2/7
Suppose -n + 4*k + 1 - 14 = 0, 8 = 2*k. Determine u, given that -n*u - 8*u**2 + 3*u - 2*u = 0.
-1/4, 0
Let o(r) be the third derivative of -r**5/540 + r**4/108 - r**3/54 + 50*r**2. Let o(b) = 0. Calculate b.
1
Let g(w) be the third derivative of -8/27*w**3 + 0 - 49/45*w**5 - 4*w**2 - 7/9*w**4 + 0*w - 343/540*w**6. Find x such that g(x) = 0.
-2/7
Let q(o) be the first derivative of -o**5/20 + o**4/4 - o**3/2 + o**2/2 - o/4 - 1. Factor q(m).
-(m - 1)**4/4
Let k(y) be the second derivative of -y**6/150 + 3*y**5/50 - y**4/5 + y**3/3 - 3*y**2/10 + y - 2. Factor k(u).
-(u - 3)*(u - 1)**3/5
Let z(c) be the second derivative of -3/14*c**4 - 1/105*c**6 + 0 - 2/7*c**2 - 5*c + 1/14*c**5 + 1/3*c**3. Suppose z(s) = 0. What is s?
1, 2
Let d be ((-2)/16)/(18/(-4)). Let y(r) be the second derivative of d*r**4 + 0 + 2*r + 1/18*r**3 - 1/3*r**2. Factor y(z).
(z - 1)*(z + 2)/3
Let l be (-4)/(-14) - (-432)/56. Let k = l - 6. Factor -2*b - 2*b**2 + k*b**2 + 0*b + 4*b**2 + 2*b**5 - 4*b**4.
2*b*(b - 1)**3*(b + 1)
Let n(u) = 0*u**2 + 2*u**2 - 18*u + 3*u**3 - 11*u**2 + 6*u. Let m(z) = -2*z**3 + 8*z**2 + 11*z + 1. Let x(a) = 4*m(a) + 3*n(a). Factor x(c).
(c + 1)*(c + 2)**2
Let c(x) be the second derivative of -x**4/9 + 16*x**3/9 - 32*x**2/3 - 9*x. Factor c(s).
-4*(s - 4)**2/3
Let g(v) be the second derivative of -6*v**6/5 + 21*v**5/20 + 17*v**4/12 - v**3/6 - v**2/2 - 4*v. Solve g(p) = 0.
-1/3, 1/4, 1
Let l(s) = 20*s + 2*s**2 - 7*s + 8 - 6*s. Let o be l(-3). Find i, given that 4/3*i + 0 + 10/3*i**4 + 6*i**3 + 14/3*i**2 + 2/3*i**o = 0.
-2, -1, 0
Let x(w) = -2*w**3 - w**2 + 2*w + 8. Let m(n) = n**3 - n - 4. Let q(y) = 7*m(y) + 4*x(y). Factor q(p).
-(p - 1)*(p + 1)*(p + 4)
Let k(u) be the first derivative of 4*u**5/25 - 4*u**4/5 + 16*u**3/15 + 29. What is a in k(a) = 0?
0, 2
Let b(t) be the third derivative of -t**8/1344 - t**7/840 + t**6/160 + t**5/48 + t**4/48 + 11*t**2. Solve b(p) = 0.
-1, 0, 2
What is r in -r**3 + 0 + 1/2*r**2 + 0*r + 1/2*r**4 = 0?
0, 1
Let j(b) be the first derivative of 2*b**5/35 - 2*b**4/7 + 10*b**3/21 - 2*b**2/7 + 1. Factor j(p).
2*p*(p - 2)*(p - 1)**2/7
Let x(o) = 3*o**2 - 1. Suppose 3*m + m - 5*h - 24 = 0, -5*m + 4*h = -21. Let l be x(m). Solve 2/7*y + 2/7*y**4 + 0 - 2/7*y**3 - 2/7*y**l = 0 for y.
-1, 0, 1
Factor 4/7 - 4/7*z**2 - 2/7*z + 2/7*z**3.
2*(z - 2)*(z - 1)*(z + 1)/7
Let f(k) be the second derivative of -1/12*k**3 + 4*k + 0 + 1/24*k**4 + 0*k**2. Factor f(i).
i*(i - 1)/2
Let 0*n + 0 - 1/2*n**2 - 5/4*n**3 + 3/4*n**4 = 0. What is n?
-1/3, 0, 2
Suppose -16 = -4*b + 4*t, -5*t - 8 = b - 0*b. Let d be (-4)/10 + (-6)/(-5). Find n such that -2/5 + d*n - 2/5*n**b = 0.
1
Let x(v) be the first derivative of v**4/22 + 4*v**3/33 - 4*v**2/11 - 16*v/11 - 46. Let x(i) = 0. Calculate i.
-2, 2
Let l(a) = a. Let n be l(4). Let y be (-2 - (-4)/n) + 1. Factor 0 + 0*h**4 + y*h**2 - 2/3*h**5 + 4/3*h**3 - 2/3*h.
-2*h*(h - 1)**2*(h + 1)**2/3
Factor 6*y + 14/3*y**2 + 4/3.
2*(y + 1)*(7*y + 2)/3
Let j = 2 - 14. Let u be 9/j - (-30)/8. What is x in -2 + 20*x**2 + 4 + 10*x**4 - 20*x**u - 11*x + x - 2*x**5 = 0?
1
Let i be (2 + 3)*(-6)/(-5). Suppose -3*t - 6 = -i*t. Let 8*l + 2*l + 6*l - 11*l**2 - 21*l**t - 2 = 0. What is l?
1/4
Let s(w) = 3*w**3 + 9*w**2 + 6. Let b(t) = -t**2 - 1. Let f(r) = -6*b(r) - s(r). Factor f(m).
-3*m**2*(m + 1)
Let k(i) = 4*i**2 - 3*i + 4. Let f(h) = 4*h**2 - 2*h + 4. Let s(p) = -5*f(p) + 6*k(p). Solve s(c) = 0.
1
Let c(x) = x**3 - 3*x**2 + 3*x + 4. Suppose 4*m + 4 - 16 = 0. Let w(a) = 1. Let p(i) = m*c(i) - 15*w(i). Factor p(r).
3*(r - 1)**3
Let n(q) be the third derivative of -5*q**8/336 + q**7/14 - q**6/8 + q**5/12 + 2*q**2. Factor n(h).
-5*h**2*(h - 1)**3
Let x(j) = 20*j**2 - 40*j - 36. Let a(h) = -h**2 + h + 1. Let m(r) = 24*a(r) + x(r). Factor m(p).
-4*(p + 1)*(p + 3)
Let d = 15 + -13. Let -3*v**4 - 4*v**4 - d*v**4 + 5*v**4 + 2*v**5 = 0. Calculate v.
0, 2
Let d(b) be the second derivative of 2*b**7/3 - 4*b**6 + 10*