et d(x) = x**2 - 14*x + 19. Let r be d(13). Let h(f) = -f**2 + 6*f + 2. Let o be h(r). Find t, given that -2/3 + 2/3*t**o + 4/3*t - 4/3*t**3 = 0.
-1, 1/2, 1
Let x(n) be the first derivative of 7*n**5 - 5*n**4/2 - 35*n**3 + 50*n**2 - 20*n + 23. Factor x(w).
5*(w - 1)**2*(w + 2)*(7*w - 2)
Let l(k) be the first derivative of 3/4*k**4 + 0*k**3 - 9/2*k**2 + 6*k + 7. Find h such that l(h) = 0.
-2, 1
Let x(j) = j + 3. Let h be x(7). Let a be ((-4)/8)/(h/(-24)). Find n such that 2/5*n**2 + 4/5 + a*n = 0.
-2, -1
Let z be 0 - ((-18)/28 + 10/70). Let 0 - 1/4*m**2 + z*m = 0. What is m?
0, 2
Factor 2 - 5*c**3 + 2 - c**4 - 9*c**2 - 7*c - 6.
-(c + 1)**3*(c + 2)
Let p = 4013/7 + -573. Suppose 0 - p*j + 2/7*j**2 = 0. Calculate j.
0, 1
Suppose -5*y - 6 = -16. Suppose -6/11*b + 0*b**y - 4/11 + 2/11*b**3 = 0. What is b?
-1, 2
Let c(r) be the second derivative of 0*r**3 - 1/9*r**4 + 0*r**2 + 3/10*r**5 + 0 - 7/45*r**6 - 4*r. Factor c(n).
-2*n**2*(n - 1)*(7*n - 2)/3
Let o(p) be the first derivative of -p**6/8 - 9*p**5/10 - 27*p**4/16 + p**3 + 9*p**2/2 - 56. Determine c, given that o(c) = 0.
-3, -2, 0, 1
Let q(k) be the third derivative of -k**5/180 - k**4/36 - k**3/18 - 14*k**2. Factor q(a).
-(a + 1)**2/3
Let g = 5 - 3. Let f be (g/3)/(6/27). Factor 4 + 42*b**f + 48*b**2 - 56*b**4 + 8*b - 42*b**4 - 4.
-2*b*(b - 1)*(7*b + 2)**2
Let p(d) be the third derivative of -d**7/735 - d**6/420 + d**5/70 + 5*d**4/84 + 2*d**3/21 - 14*d**2. Factor p(r).
-2*(r - 2)*(r + 1)**3/7
Let l(t) be the second derivative of t**8/720 - t**7/210 + t**6/360 + t**5/180 - t**3/6 + t. Let j(w) be the second derivative of l(w). Factor j(p).
p*(p - 1)**2*(7*p + 2)/3
Find h such that -h**5 - 1 - h**4 - h + 16*h**2 - 14*h**2 + 0*h**3 + 2*h**3 = 0.
-1, 1
Let b = 1020/3521 + -2/503. Factor 0 - b*v**2 + 0*v.
-2*v**2/7
Suppose 4*u - 9 = 3. Factor -3*d**2 - 3*d**2 + 0*d**2 + u*d**2.
-3*d**2
Determine h, given that -280 + 4*h**2 + 278 + h**4 - 2*h**3 - 3*h**4 + h + h**5 = 0.
-1, 1, 2
Factor -1/4*r**2 - 11/2*r - 121/4.
-(r + 11)**2/4
Let z(n) be the first derivative of -2*n - 2 - 4*n**2 - 7/6*n**3. Let z(k) = 0. Calculate k.
-2, -2/7
Let a(v) be the third derivative of 0 - 1/112*v**8 - 1/70*v**7 + 0*v + 1/10*v**5 - 1/2*v**3 - 1/8*v**4 + 1/20*v**6 + 3*v**2. Factor a(z).
-3*(z - 1)**2*(z + 1)**3
Let u(q) be the second derivative of 2*q**6/15 + 3*q**5/5 - 5*q**4/3 - 2*q**3 + 8*q**2 + 32*q. What is d in u(d) = 0?
-4, -1, 1
Let 3*v**5 - v**2 - 3*v**3 + 2*v**2 + 0*v**3 - 9*v**4 + 8*v**2 = 0. What is v?
-1, 0, 1, 3
Let h be 36/(-27)*3/(-2). Let w(z) be the first derivative of 0*z + 1/2*z**3 + 3/4*z**h - 1. Factor w(j).
3*j*(j + 1)/2
Let b be (-6)/15 + (-196)/(-480). Let o(u) be the third derivative of 0*u + 0 - 1/15*u**3 + 1/300*u**5 + 4*u**2 + b*u**4. Factor o(t).
(t - 1)*(t + 2)/5
Let u(p) = -p**3 + p**2 - 1. Let t(k) = -3*k**3 - 6*k**2 - 21*k - 20. Let q(f) = -t(f) + 2*u(f). Let q(m) = 0. What is m?
-3, -2
Let 1/4*j**4 - 1/4*j**2 + 0*j - 1/4*j**3 + 1/4*j**5 + 0 = 0. What is j?
-1, 0, 1
Factor -1/2*d**3 + 0 + d - 1/2*d**2.
-d*(d - 1)*(d + 2)/2
Let a(d) = 4*d**2 - 4*d - 5. Let m(y) = y**2 - y - 1. Let x(l) = a(l) - 5*m(l). Factor x(o).
-o*(o - 1)
Let c = 151 + -146. Find n such that -4/9 + 10/9*n**c - 20/9*n**2 - 2*n + 8/9*n**3 + 8/3*n**4 = 0.
-1, -2/5, 1
Let o(f) = -5*f**2 - 3. Let k(y) be the second derivative of -8*y**2 - 13/6*y**4 + 0 + 0*y**3 - 3*y. Let c(q) = -3*k(q) + 16*o(q). Factor c(l).
-2*l**2
Let r(p) = -6*p - 1 + 4*p**3 + 1. Let y(n) = -9*n**3 + 13*n. Let h(z) = -13*r(z) - 6*y(z). Factor h(s).
2*s**3
Suppose 0 = t - 0*t + 141. Let m = t + 989/7. Factor -m*z + 0 - 4/7*z**2.
-2*z*(2*z + 1)/7
Suppose -2*o - o = 3*t - 18, -o - 3*t + 10 = 0. Suppose 9*p = o*p + 25. Factor -2/3 + 3*j + 14/3*j**3 - 16/3*j**2 + 1/3*j**p - 2*j**4.
(j - 2)*(j - 1)**4/3
Let d(a) be the first derivative of -2*a**3/21 - 2*a**2 - 14*a + 14. Determine m, given that d(m) = 0.
-7
Let k be (-259)/(-35) - (-2)/(-5). Suppose -3*n - 2*n + k = 2*s, 16 = 4*n - s. Let -3*y**3 + 9*y**2 - 6*y - 6*y**3 + 3*y**3 + 3*y**n = 0. Calculate y.
0, 1, 2
Find t, given that 3 - 16*t - 1 + 4*t**2 + 10 = 0.
1, 3
Let l(a) be the third derivative of -1/48*a**4 + 0*a**3 + 0 - 1/80*a**6 + 1/24*a**5 + 3*a**2 - 3/140*a**7 + 0*a. Suppose l(y) = 0. Calculate y.
-1, 0, 1/3
Let t(c) = 3*c. Let w be (4 + -2)/(1 + 1). Let z be t(w). Determine r so that 0*r**z + 2*r**2 - 3*r**3 + r**3 - 4*r**2 = 0.
-1, 0
Let s = -41 + 44. Factor -g**s - 1/2*g**2 + 1/2 + 0*g**4 + 1/4*g**5 + 3/4*g.
(g - 2)*(g - 1)*(g + 1)**3/4
Suppose 22 = 4*t - 2*s, -s + 4 = 4*t - 9. Factor 1/5*f**2 - 1/5*f**3 + 1/5*f + 0 - 1/5*f**t.
-f*(f - 1)*(f + 1)**2/5
Let x(m) be the third derivative of -m**6/30 + 2*m**5/15 + m**4/2 + 7*m**2. Suppose x(n) = 0. What is n?
-1, 0, 3
Suppose -2*m + 11 = -3. Suppose 3*p - 4*p**2 + m*p**2 + 0*p**2 = 0. Calculate p.
-1, 0
Suppose -8*f + 76 = -4*f. Let c = f + -37/2. Find m such that 0*m + 0 - m**3 - c*m**2 = 0.
-1/2, 0
Let c(q) be the third derivative of -q**9/302400 + q**7/25200 - q**5/20 + q**2. Let p(r) be the third derivative of c(r). Suppose p(f) = 0. Calculate f.
-1, 0, 1
Let b = -17 - -11. Let x = b + 8. What is d in -4*d**3 + x*d**2 + 2*d**3 + 0*d**3 = 0?
0, 1
Let t = -116 - -116. Factor 1/3*a + 1/3*a**5 + 0 - 2/3*a**3 + t*a**4 + 0*a**2.
a*(a - 1)**2*(a + 1)**2/3
Suppose 0 = -4*q + 2*q + 14. Suppose -p + q = 5*d + p, d + p + 1 = 0. Factor -1 + d*f - 3*f + 3*f**2 - 2*f.
(f - 1)*(3*f + 1)
Let a(f) be the first derivative of -7*f**4/16 - 4*f**3/3 - 11*f**2/8 - f/2 - 8. Factor a(y).
-(y + 1)**2*(7*y + 2)/4
Suppose o = -2*o - 54. Let a be o/(-10) - (-2)/(-10). Factor 4/5 - a*n**2 - 14/5*n.
-2*(n + 2)*(4*n - 1)/5
Let c = 16 - -7. Let s be 12/(-21) - c/(-28). Factor 0 + 0*q + s*q**3 - 1/2*q**2.
q**2*(q - 2)/4
Let t(u) be the third derivative of -121*u**5/80 - 11*u**4/16 - u**3/8 + 6*u**2. Factor t(w).
-3*(11*w + 1)**2/4
Let o(u) be the second derivative of 1/195*u**6 + 5*u + 0 + 1/13*u**2 - 1/39*u**4 + 0*u**3 + 0*u**5. Factor o(a).
2*(a - 1)**2*(a + 1)**2/13
Let w(g) be the third derivative of g**6/720 + 2*g**3/3 - 4*g**2. Let o(c) be the first derivative of w(c). Factor o(y).
y**2/2
Let x be (-1)/(-5 - (-1 - -2)). Let h(s) be the third derivative of s**2 + 0 + x*s**3 - 1/60*s**5 + 0*s + 0*s**4. Factor h(g).
-(g - 1)*(g + 1)
Let h(q) = -9*q**5 + 6*q**3 + 12*q**2 + 3*q + 6. Let k(v) = -v**5 + v**4 + v**3 + v**2 + 1. Let a(j) = h(j) - 6*k(j). Factor a(n).
-3*n*(n - 1)*(n + 1)**3
Let g(n) be the third derivative of -n**8/84 + 2*n**7/35 - n**6/10 + n**5/15 - 9*n**2. Determine j so that g(j) = 0.
0, 1
Factor 6*r - 9*r + 3*r**3 + 4*r**2 - 4 - 7*r**3 + 7*r.
-4*(r - 1)**2*(r + 1)
Let k(u) = 2*u**3 - 2*u**2 - 4*u - 2. Let o(q) = 4 + 5 - 2*q**2 - 7*q**3 + 8*q**2 + 16*q + 3*q**2. Let b(i) = -9*k(i) - 2*o(i). Find v, given that b(v) = 0.
-1, 0, 1
Let z(m) be the second derivative of 4*m - 1/3*m**3 + 0 - m**2 + 1/6*m**4 + 1/10*m**5. Suppose z(l) = 0. Calculate l.
-1, 1
Let u(q) be the third derivative of q**7/420 + q**6/180 - q**3/3 - 3*q**2. Let z(x) be the first derivative of u(x). Suppose z(w) = 0. Calculate w.
-1, 0
Suppose 0 = -3*p - p + 16. Let s(u) = -u**4 + 4*u**3 + 2*u**2 + 1. Let m(b) = 6*b**4 - 21*b**3 - 11*b**2 - b - 6. Let q(v) = p*m(v) + 22*s(v). Factor q(i).
2*(i - 1)*(i + 1)**3
Let n(y) be the first derivative of -3/13*y**2 - 4 + 2/39*y**3 + 0*y. Factor n(u).
2*u*(u - 3)/13
Let o(i) be the third derivative of -i**5/270 + i**4/27 - i**3/9 + i**2. Factor o(z).
-2*(z - 3)*(z - 1)/9
Let y = -747 + 749. Determine s so that -1/3*s**y + 0 + 2/3*s - 1/3*s**3 = 0.
-2, 0, 1
Let x = 26 + -24. Let n be (-14)/6 - (9 + -12). Factor 1/3*k + 1/3 - n*k**x.
-(k - 1)*(2*k + 1)/3
Let l(s) be the first derivative of s**6/9 + 8*s**5/15 + 2*s**4/3 - 4. Factor l(r).
2*r**3*(r + 2)**2/3
Let c(v) be the first derivative of 5*v**4/16 + v**3/12 - 5*v**2/8 - v/4 - 42. Determine d, given that c(d) = 0.
-1, -1/5, 1
Let x = 29/21 - 2/21. Factor -3/7*i**2 + x*i - 6/7.
-3*(i - 2)*(i - 1)/7
Let b(p) be the second derivative of -p**9/30240 + p**8/13440 + p**7/5040 - p**6/1440 + 7*p**4/12 + p. Let u(c) be the third derivative of b(c). Factor u(z).
-z*(z - 1)**2*(z + 1)/2
Suppose -1/2 - 2/5*r + 1/10*r**2 = 0. What is r?
-1, 5
Suppose -12 = 4*r - 0*r. Let x = r + 8. Factor 128/9*n**2 + 2*n**x + 32/9