/105*x**7 + 2*x**2. Factor c(u).
-2*u**2*(u - 1)**2
Let u = -256 + 7681/30. Let h(d) be the second derivative of 0 + 0*d**2 + u*d**6 - 1/12*d**4 - 1/3*d**3 + 1/10*d**5 - 2*d. Factor h(r).
r*(r - 1)*(r + 1)*(r + 2)
Let n(q) be the second derivative of q**5/60 - q**4/36 - q**3/18 + q**2/6 - 4*q. Factor n(k).
(k - 1)**2*(k + 1)/3
Find h such that -12*h**5 + 7*h**4 + 8*h**3 - 19*h**2 + 4*h**4 + 4 + 9*h**4 + 4*h - 5*h**2 = 0.
-1, -1/3, 1
Let q(z) be the first derivative of -3*z**5/80 - z**4/16 - 4*z**2 + 2. Let h(y) be the second derivative of q(y). Factor h(g).
-3*g*(3*g + 2)/4
Let x be 5/12 - 24/(-96). Factor -x*t - 4/3 + 2/3*t**2.
2*(t - 2)*(t + 1)/3
Let o(p) be the third derivative of p**5/360 + p**4/72 + p**3/36 + 5*p**2. Factor o(a).
(a + 1)**2/6
Let h be (2 - (3 - 4))*1. Factor -57/2*m**h + 12*m - 69/2*m**2 + 6 + 165/2*m**4 - 75/2*m**5.
-3*(m - 1)**3*(5*m + 2)**2/2
Find v, given that 6*v**4 + 3*v + 4*v**5 - 6*v**2 - 6*v**5 - v**5 = 0.
-1, 0, 1
Let p(t) = t**2 + t - 1. Let d(u) = -21*u**4 + 36*u**3 - 6*u**2 - 3*u - 3. Let l(r) = -d(r) + 3*p(r). Determine h, given that l(h) = 0.
-2/7, 0, 1
Factor -105*f + 12*f**3 - 110*f**3 - 127*f - 60 + 448*f**2 + 92.
-2*(f - 4)*(7*f - 2)**2
Let i be (-2 - -1)*(15 + -10). Let o be 1/i*(-12)/4. Let -9/5*h**2 - o*h**5 - 11/5*h**4 + 0 - 2/5*h - 3*h**3 = 0. What is h?
-1, -2/3, 0
Let p be 1/(-7) - (-44)/14. Let -4*a**4 + 0*a**3 + 2*a**p + 2*a**4 + 4*a**4 = 0. What is a?
-1, 0
Find y such that -2/3*y**2 - 2/3 - 4/3*y = 0.
-1
Let i(t) be the first derivative of -t**4/4 + t**2 + t + 6. Let l be i(-2). Factor -2*m**4 + 0*m**2 + 0*m + 1/2*m**3 + 0 + 3/2*m**l.
m**3*(m - 1)*(3*m - 1)/2
Suppose -5*y + 28 = j, j = 3*j - 4*y + 14. Suppose 0 = 3*w + 4*d, -j*w = -4*w + 3*d + 13. Factor -3/2*a + 1/2*a**5 + a**3 - 1/2 - a**2 + 3/2*a**w.
(a - 1)*(a + 1)**4/2
Let k = 62/3 - 20. Find w such that -w + 1/3*w**3 + 0*w**2 - k = 0.
-1, 2
Suppose -9 - 7 = -4*x. Factor b**5 + 5 + 2*b**x - 4*b**2 - 4*b**3 + 2*b + b**5 + 0*b**5 - 3.
2*(b - 1)**2*(b + 1)**3
Let q(c) be the third derivative of 0*c**3 + 0*c + 0*c**4 - 6*c**2 + 1/60*c**6 - 2/315*c**7 - 1/90*c**5 + 0. Factor q(h).
-2*h**2*(h - 1)*(2*h - 1)/3
Let o(t) be the third derivative of t**5/6 + t**4/2 + 3*t**3/5 + 6*t**2. Factor o(v).
2*(5*v + 3)**2/5
Suppose -2*l = -0*l - 4. What is m in 8*m**l + 8*m**5 + 24*m**3 + 14*m - 14*m - 30*m**4 = 0?
-1/4, 0, 2
Let k(a) = -9*a**2 + 24*a - 17. Let y(f) = -f**2 + 3*f - 2. Let j(b) = 6*k(b) - 51*y(b). Let j(q) = 0. What is q?
-3, 0
Let m(f) be the second derivative of -f**7/16380 - f**6/2340 - f**5/780 + f**4/3 + 2*f. Let w(i) be the third derivative of m(i). Solve w(y) = 0 for y.
-1
Suppose 23 - 63 = -20*z. Let r = 31/33 + -3/11. Solve 2/9*k**z + 4/9 + r*k = 0.
-2, -1
Let r(n) be the second derivative of -n**7/360 + n**6/45 - n**5/30 - n**4/12 + 3*n. Let x(b) be the third derivative of r(b). Solve x(f) = 0 for f.
2/7, 2
Let c = 6 + -6. Solve 0*x**3 + c*x**3 - x**2 + x**3 = 0.
0, 1
Let z = -53 + 24. Let i = z + 29. Factor -1/2*n**4 + i - 3/2*n**2 + 1/2*n + 3/2*n**3.
-n*(n - 1)**3/2
Let -60/19 - 6/19*d**2 - 94/19*d = 0. Calculate d.
-15, -2/3
Let z(w) be the first derivative of 6*w**2 + 12/7*w**5 - 213/28*w**4 + 4 + 25/14*w**6 + 24/7*w - 10/7*w**3. Suppose z(b) = 0. What is b?
-2, -2/5, 1
Factor -10*i + 6 - 9*i**2 + 3*i**4 - 3*i**3 + 14*i - i.
3*(i - 2)*(i - 1)*(i + 1)**2
Factor -3/2*v**4 + 9/2*v + 15/2*v**3 + 0 - 21/2*v**2.
-3*v*(v - 3)*(v - 1)**2/2
Find c such that -12/5*c + 3/5*c**4 - 3/5*c**5 + 12/5 + 3*c**3 - 3*c**2 = 0.
-2, -1, 1, 2
Let w = -4/9 + 10/9. Factor w*i - 2/3*i**3 + 0 + 5/3*i**2 - 5/3*i**4.
-i*(i - 1)*(i + 1)*(5*i + 2)/3
Let r(f) = 4*f**2 + 7*f - 5. Let y(q) = -5*q**2 - 8*q + 6. Let t = 2 - 8. Let k(n) = t*r(n) - 5*y(n). Factor k(c).
c*(c - 2)
Let r(u) = -2*u**2 + 2*u - 7*u + 3*u. Let s(n) = -2*n**2 - 3*n - 1. Suppose 3*c + 3*b = -b - 9, 4*c - 3*b = -12. Let t(p) = c*r(p) + 4*s(p). Factor t(m).
-2*(m + 1)*(m + 2)
Let g(o) be the first derivative of o**5/120 - o**4/24 + o**3/12 - o**2 + 2. Let r(j) be the second derivative of g(j). Let r(y) = 0. What is y?
1
Solve 2/3*j + 1/6*j**3 - 2/3*j**2 + 0 = 0.
0, 2
Let o(r) be the third derivative of -r**6/1260 - r**5/420 - 5*r**3/6 - 4*r**2. Let h(m) be the first derivative of o(m). Let h(c) = 0. Calculate c.
-1, 0
Suppose -3*w**2 - 21/5*w**4 + 6/5*w**5 + 0 + 3/5*w + 27/5*w**3 = 0. Calculate w.
0, 1/2, 1
Factor -1/5*h**5 + 0*h + 0 - 2/5*h**4 + 0*h**2 - 1/5*h**3.
-h**3*(h + 1)**2/5
Let r = 394 + -2752/7. Suppose -4/7 - 2/7*a**2 - r*a = 0. What is a?
-2, -1
Let t(b) be the third derivative of 0 - 8*b**2 + 1/8*b**4 - 1/10*b**5 + 0*b**3 - 1/40*b**6 + 0*b + 1/35*b**7. Factor t(w).
3*w*(w - 1)*(w + 1)*(2*w - 1)
Let f be 1 - (-4 - (-3 - -1)). Factor 2/3*j**f + 4/3*j**2 + 2/3*j + 0.
2*j*(j + 1)**2/3
Let w be (-2)/11 + 560/660. Factor 4/9 + 2/9*i**2 - w*i.
2*(i - 2)*(i - 1)/9
Let p be 26/4 + (-7)/14. Suppose -3*f - 2*l = f - 18, 3*f + p = 5*l. Suppose -11*i + 14*i**f + 5 - 11*i**2 - 5 + 13*i = 0. Calculate i.
0, 2/7, 1/2
Let m(l) be the first derivative of -6*l**5/25 + l**4/10 + 2*l**3/5 - l**2/5 - 22. Solve m(p) = 0.
-1, 0, 1/3, 1
Solve 9*d**2 - 6*d**2 - 6*d**2 = 0 for d.
0
Let q(g) be the second derivative of 5*g**7/42 - g**6/3 + g**5/4 + 21*g. Factor q(f).
5*f**3*(f - 1)**2
Let v = 6721/30 - 224. Let b(d) be the third derivative of 1/50*d**5 - 1/15*d**3 + 0*d + 3*d**2 - v*d**4 + 0. Factor b(s).
2*(s - 1)*(3*s + 1)/5
Let h(x) be the first derivative of -1/4*x + 3/8*x**2 + 3 - 1/4*x**3 + 1/16*x**4. Factor h(m).
(m - 1)**3/4
Let n be (-2934)/(-315) - 2/(-5). Let m = 78/7 - n. Suppose -6/7*f**3 - 4/7*f - m*f**2 + 0 = 0. What is f?
-1, -2/3, 0
Suppose 3*o - 2 - 22 = -5*w, -w = -o. Suppose 0*v + v = 0. What is m in 2*m**w + v*m**3 - 3*m**3 - m**3 = 0?
0
Suppose 0 = -5*c + 2*s - 0 + 12, 5*s + 5 = 0. Factor -3 - 3*k**c + 21*k**3 + 14*k**3 + 2 - 34*k**3 + 3*k.
(k - 1)**3
Let y = 6 - 8. Let f be 52/(-30)*-3 + y. Factor -1/5 - 8/5*b - f*b**2.
-(4*b + 1)**2/5
Let k be ((-2)/21)/(8/(-14)). Let n(z) be the third derivative of 0*z**4 + 0*z + k*z**3 - z**2 + 0*z**6 + 1/210*z**7 - 1/30*z**5 + 0. Factor n(v).
(v - 1)**2*(v + 1)**2
Let l(n) be the third derivative of n**8/80640 + n**7/10080 - n**5/15 + 2*n**2. Let r(b) be the third derivative of l(b). Factor r(c).
c*(c + 2)/4
What is m in -16/11*m**4 - 34/11*m - 56/11*m**2 - 8/11 - 2/11*m**5 - 4*m**3 = 0?
-4, -1
Let n(i) = -7*i**2 - 7*i + 4. Let b(q) = 22*q**2 + 22*q - 12. Let f(r) = -5*b(r) - 16*n(r). Solve f(s) = 0 for s.
-2, 1
Let h(g) = -g**3 - 6*g**2 + g + 13. Let d(q) = 3*q**2 - 6. Let s(o) = -2*o - 8. Let b be s(-6). Suppose 12 - 40 = b*k. Let p(v) = k*d(v) - 3*h(v). Factor p(n).
3*(n - 1)**2*(n + 1)
Let m(u) be the third derivative of 2*u**7/21 - u**6/8 - 3*u**5/4 - 5*u**4/12 + 6*u**2 + 1. Find n, given that m(n) = 0.
-1, -1/4, 0, 2
Let r(w) = -w**4 - w + 1. Let i(s) = 8*s**4 - 6*s**3 - 92*s**2 - 105*s - 31. Let d(a) = -i(a) + r(a). Suppose d(x) = 0. What is x?
-2, -2/3, 4
Factor 0*h**2 + 4/3*h**3 + 2/3*h**4 - 2/3 - 4/3*h.
2*(h - 1)*(h + 1)**3/3
Let y be (4*(-7)/84)/((-1)/6). Let o(g) be the first derivative of y*g**2 - 2/3*g**3 + 1 + 0*g. Factor o(h).
-2*h*(h - 2)
Factor 0*q - 1/2*q**2 + 1/2.
-(q - 1)*(q + 1)/2
Let c(q) be the second derivative of -5*q**4/12 - 25*q**3/6 + 36*q. Solve c(g) = 0 for g.
-5, 0
Suppose -3*w + 0*w - 4*y + 210 = 0, -3 = y. Let t be w/30 - (-2)/10. Factor -8/3*r**2 - t*r - 2/3.
-2*(2*r + 1)**2/3
Let o(d) be the first derivative of 4/5*d**5 - 6*d**2 + 3*d**4 - 8*d - 7 + 4/3*d**3. Factor o(y).
4*(y - 1)*(y + 1)**2*(y + 2)
Let g be (52/16 - 4)*-8. Let q(s) be the first derivative of -2/3*s**3 + 1/2*s**2 + 1 - 1/2*s**4 + 1/6*s**g + 1/5*s**5 + s. Factor q(t).
(t - 1)**2*(t + 1)**3
Let g = -265/3 + 91. Factor 2/3*t**2 - g*t + 8/3.
2*(t - 2)**2/3
Find b, given that 3*b + 3/2*b**3 + 0 - 9/2*b**2 = 0.
0, 1, 2
Let t(p) be the first derivative of p**6/3 - 4*p**5/5 + 4*p**3/3 - p**2 - 11. Factor t(a).
2*a*(a - 1)**3*(a + 1)
Let c = -42 + 128/3. Suppose -10 = -3*j - 1. Factor -c*y**j + 4/3*y**2 - 2/3*y + 0.
-2*y*(y - 1)**2/3
Let p be 1 - -1 - 5/5*-3. Let r(j) be the first derivative of 2 - 4/15*j**3 + j**2 + 6/25*j**p + 3/5*j**6 - 2/5*j - 7/5*j**4. Find y, given that r(y) = 0.
-1, 1/3, 1
Suppose -10 - 10 = -5*m. Let -5*n**3 + 0*n - 2*n**3