 the first derivative of r(c). Factor o(p).
p*(p - 1)*(p + 2)/4
Let h = -17 + 20. Let p be -1*5 - (2793/(-95) - -13). Factor p*l**h + 3/5*l + 6/5 - 9*l**2 - 21/5*l**4.
-3*(l - 1)**3*(7*l + 2)/5
Let r(m) be the second derivative of -m**5/160 + m**4/96 + m**3/24 - 2*m + 3. What is t in r(t) = 0?
-1, 0, 2
Let z(f) be the first derivative of 2*f**6/45 + f**5/18 - 7*f**4/72 - f**3/18 - 9*f**2/2 + 5. Let w(l) be the second derivative of z(l). Solve w(v) = 0.
-1, -1/8, 1/2
Suppose -7*r = -2*r - 75. Suppose 3*x = -5*a + r, 4*x + 14 = 5*a - 1. Factor 9*p**a - 5*p**3 - 4*p**2 + 8*p**3 - 8*p.
4*p*(p - 1)*(3*p + 2)
Find b, given that 44/3*b**3 - 64/3*b**2 + 20/3 - 34/3*b - 10/3*b**5 + 44/3*b**4 = 0.
-1, 2/5, 1, 5
Let l(z) be the first derivative of 5*z**3/3 + 35*z**2 + 75. Factor l(b).
5*b*(b + 14)
Let m = -763/5 - -764/5. Factor -2/5 + m*r**3 - 1/5*r + 2/5*r**2.
(r - 1)*(r + 1)*(r + 2)/5
Suppose -t = -2*n - 12, -3*n - 13 = -4*t - 2*n. Suppose -t*x = -6*x + 12, 2*x = -2*y + 10. Factor 1/3*k + 1/3*k**4 + 1/3*k**5 - 2/3*k**y - 2/3*k**3 + 1/3.
(k - 1)**2*(k + 1)**3/3
Let j(o) be the second derivative of 0*o**3 + 0 + 0*o**5 - 1/6*o**6 + 0*o**2 + 5/12*o**4 + 11*o. Factor j(z).
-5*z**2*(z - 1)*(z + 1)
Find w such that -1/5*w**2 + 0 + 1/5*w = 0.
0, 1
Let g(q) = q**3 + 4*q - 1. Let o(p) = 36*p**4 + 231*p**3 + 529*p**2 + 544*p + 193. Let b(y) = 3*g(y) - o(y). Factor b(t).
-(t + 2)**2*(6*t + 7)**2
Suppose 2/7*n**2 + 968/7 - 88/7*n = 0. What is n?
22
Factor -497 - 62*s**2 + 537 + 3*s**3 - 16*s - 9*s**3.
-2*(s + 1)*(s + 10)*(3*s - 2)
Let l(t) be the first derivative of t**3/5 + 18*t**2/5 + 96*t/5 - 398. Find f such that l(f) = 0.
-8, -4
Let m(o) be the third derivative of 0*o**3 + 1/180*o**5 + 1/72*o**4 + 38*o**2 + 0 + 0*o. Factor m(h).
h*(h + 1)/3
Let l(o) be the third derivative of o**5/150 - o**4/10 + o**3/3 - o**2 + 52. Factor l(w).
2*(w - 5)*(w - 1)/5
Let r(n) be the first derivative of -n**4/7 - 4*n**3/7 - 4*n**2/7 - 73. Determine x so that r(x) = 0.
-2, -1, 0
Suppose 0 = 4*h - 2*v - 228, 3*h + h - 5*v - 216 = 0. Suppose -5*d + h - 59 + 5*d**2 = 0. Calculate d.
0, 1
Let h(t) be the first derivative of -5*t**6/18 - 5*t**5/3 + 5*t**4/2 + 160*t**3/9 - 80*t**2/3 + 15. Find a such that h(a) = 0.
-4, 0, 1, 2
Let r = -103/21 - -16/3. Find g, given that 0*g - r + 3/7*g**2 = 0.
-1, 1
Let p = 1 - -2. Let l(y) = 52*y**2 - 108*y - 16. Let x(a) = -17*a**2 + 36*a + 5. Let n(i) = p*l(i) + 8*x(i). Factor n(r).
4*(r - 2)*(5*r + 1)
Let w = -2044 - -63354/31. Let b = w + 194/217. Suppose -2/7*q**4 + 2/7*q**2 + 0 + b*q**3 - 4/7*q**5 + 0*q = 0. What is q?
-1, -1/2, 0, 1
Let n(q) be the first derivative of -17*q**3/3 + 9*q**2/2 - 185. Factor n(x).
-x*(17*x - 9)
Suppose 3 + 33 = 4*t. Let b = t - 9. What is l in 6*l**5 - 11*l**3 - 8*l - 2*l**5 - 4*l**4 + 20*l**2 + b*l**5 - l**3 = 0?
-2, 0, 1
Factor 21/2*w + 3/2*w**2 - 12.
3*(w - 1)*(w + 8)/2
Let o = 664 + -654. What is t in 2/5*t**2 + o - 4*t = 0?
5
Let a(y) = 4*y + 2. Let d be a(1). Suppose 9*s**2 - 14*s**2 + d*s**2 - 1 = 0. Calculate s.
-1, 1
Let i(c) = 21*c**2 - 633*c. Let t(x) = -3*x**2 + 90*x. Let l(m) = 2*i(m) + 15*t(m). Determine y so that l(y) = 0.
0, 28
Let c(r) be the first derivative of -9*r**4/2 - 80*r**3 + 83*r**2 - 28*r - 469. Factor c(j).
-2*(j + 14)*(3*j - 1)**2
Let u(s) = s**2 - s - 1. Let y(j) = 2*j**3 - 35*j**2 - 43*j - 3. Let h(i) = 6*u(i) - 2*y(i). Factor h(q).
-4*q*(q - 20)*(q + 1)
Let d(a) = -a**3 + 4*a**2 - 2. Let t(k) = 4*k**3 - 17*k**2 + 9. Let l be ((-6)/(-2))/(((-4)/(-6))/2). Let x(g) = l*d(g) + 2*t(g). Factor x(i).
-i**2*(i - 2)
Let s be (-36)/(-110)*23*400/2760. Find d, given that 34/11*d**3 - 10/11*d**4 - s*d**2 + 0*d + 0 = 0.
0, 2/5, 3
Let n(v) be the third derivative of 1/35*v**7 - 3*v**3 - 1/112*v**8 - 13/8*v**4 + 0 - v**2 + 3/20*v**6 + 2*v - 1/5*v**5. Solve n(s) = 0 for s.
-1, 2, 3
Let h = 36 - 26. Let o be -1 + 5/(h/8). What is i in 9*i**o - 21*i**3 - 28*i**2 + 12 + 4 = 0?
-2, -1, 2/3
Let b(f) be the second derivative of f**4/12 - 31*f**3/3 - 63*f**2/2 + 332*f. Factor b(s).
(s - 63)*(s + 1)
Let p(f) be the third derivative of f**9/4536 + f**8/2520 + f**3/2 + 13*f**2. Let q(x) be the first derivative of p(x). Factor q(c).
2*c**4*(c + 1)/3
Let z(w) = 2*w**2 + 6*w - 8. Let k(l) = -24 + 4*l**2 + 13*l - 2 + 9. Let t(f) = 2*k(f) - 5*z(f). What is m in t(m) = 0?
-3, 1
Let k(v) be the third derivative of 7*v**2 + 1/600*v**6 + 1/150*v**5 + 0 + 0*v**3 + 1/120*v**4 + 0*v. Factor k(g).
g*(g + 1)**2/5
Let x(m) be the first derivative of -2*m**5/5 + 20*m**4 - 26*m**3 + 518. Factor x(q).
-2*q**2*(q - 39)*(q - 1)
Let z(t) = 20*t**2 - 40*t - 12. Let d(h) = -8*h**2 + 16*h + 5. Let s(j) = 12*d(j) + 5*z(j). Factor s(y).
4*y*(y - 2)
Let i = -28048 - -139658/5. Let c = i + 117. Find s, given that 12/5*s + 12/5 + c*s**2 = 0.
-2
Factor -992 - 671 + 582 - 156*d**2 + 1596*d - 363 + 4*d**3.
4*(d - 19)**2*(d - 1)
Let q(z) be the first derivative of -z**4/4 - z**3/2 + 5*z - 23. Let s(l) be the first derivative of q(l). Solve s(t) = 0.
-1, 0
What is h in -1/5*h**2 + 14/5*h - 49/5 = 0?
7
Let v(h) be the first derivative of -5*h + h**5 + 5*h**2 - 5/2*h**4 - 46 + 0*h**3. Let v(c) = 0. Calculate c.
-1, 1
Factor 8*c + 26/3*c**3 + 0 - 49/3*c**2 - 1/3*c**4.
-c*(c - 24)*(c - 1)**2/3
Let p(t) be the first derivative of 48/11*t**3 - 648/55*t**5 + 27/11*t**6 - 2 - 9/11*t**4 + 1/11*t**2 - 8/11*t. Find x such that p(x) = 0.
-1/3, 1/3, 4
What is m in 157577*m**5 - 2*m**2 - 6*m**4 + m - m + 6*m**3 - 157575*m**5 = 0?
0, 1
Determine o so that 214*o + 21*o**5 + 67*o + 272*o**3 + 148*o**3 - 528*o**2 - 48 - 153*o**4 + 7*o = 0.
2/7, 1, 2
Suppose -2*x - q + 4 = 0, 4*x - 28*q + 25*q - 28 = 0. Factor 0*y**2 + 8/5*y**x + 4/5*y**3 + 0*y + 4/5*y**5 + 0.
4*y**3*(y + 1)**2/5
Let n(d) be the first derivative of 2*d**3/21 + 17*d**2/7 + 32*d/7 + 11. Let n(c) = 0. Calculate c.
-16, -1
Let t be 5/77 - 256/(-704). Let f(i) be the first derivative of 1 - t*i**2 - 4/7*i - 2/21*i**3. Factor f(k).
-2*(k + 1)*(k + 2)/7
Let l(f) = 35*f**2 + 84*f + 32. Let w(k) = 315*k**2 + 755*k + 285. Let m(x) = 35*l(x) - 4*w(x). Solve m(v) = 0 for v.
-2, -2/7
Let k(s) = 87*s**2 - 36*s - 2. Let y(x) = -718 + 79*x**2 + 715 + 94*x**2 - 72*x. Let g(w) = -11*k(w) + 6*y(w). What is v in g(v) = 0?
2/9
Let d = -2/5811 + 31292/5811. Let k = d + -62/13. What is z in 16/13*z**3 - k*z**5 - 8/13*z + 2/13 - 4/13*z**2 + 2/13*z**4 = 0?
-1, 1/4, 1
Let b(g) be the third derivative of g**7/1785 - 3*g**6/340 + 11*g**5/510 + 7*g**4/68 + 134*g**2. Let b(o) = 0. What is o?
-1, 0, 3, 7
Let p(u) be the second derivative of -1/6*u**3 + 0 - 1/8*u**4 - u + 1/15*u**5 + 3/2*u**2. Let r(b) be the first derivative of p(b). Factor r(m).
(m - 1)*(4*m + 1)
Let n(y) be the first derivative of 5*y**4/4 - 253*y**3 + 1512*y**2/5 - 604*y/5 + 105. Factor n(b).
(b - 151)*(5*b - 2)**2/5
Let p(s) = -4*s**2 + 10*s - 1. Let i(d) = -d**2 + 1. Let u be ((-2)/(-4))/(-5 + 22/4). Let g(r) = u*i(r) + p(r). Find b, given that g(b) = 0.
0, 2
What is s in 62*s**2 + s**3 - 56*s**2 - 32 - 2*s**3 = 0?
-2, 4
Let s(o) be the first derivative of 3*o**4/8 + 30*o**3 - 328. Find m such that s(m) = 0.
-60, 0
Suppose -9 = -5*s + 1. Let 0*z**2 + 6*z - 12 + 16 + s*z**2 = 0. What is z?
-2, -1
Let l be 4 - (-4 + 7)*1. Let t(x) be the first derivative of l + 0*x - 4*x**2 + 20/3*x**3. Factor t(u).
4*u*(5*u - 2)
Let t(r) be the third derivative of -r**7/1008 + r**5/48 - 5*r**4/72 + r**3 + 15*r**2. Let z(q) be the first derivative of t(q). Let z(h) = 0. What is h?
-2, 1
Let m(i) be the third derivative of i**6/180 - i**5/18 - 2*i**4/9 + 4*i**3/3 + 152*i**2. Factor m(s).
2*(s - 6)*(s - 1)*(s + 2)/3
Suppose 8543*t - 166 = 8460*t. Factor 1/9*c**3 - 1/3*c**t + 8/9 - 2/3*c.
(c - 4)*(c - 1)*(c + 2)/9
Determine b, given that 0 + 2/7*b**4 + 20/7*b**3 - 2/7*b**2 - 20/7*b = 0.
-10, -1, 0, 1
Let v = -799/3 - -289. Factor 0*i - 16/3*i**2 - 56/3*i**3 + v*i**4 + 0 - 6*i**5.
-2*i**2*(i - 2)**2*(9*i + 2)/3
Let g(s) be the second derivative of -s**5/20 + s**4/12 - s**3/6 - 3*s. Let m be g(0). Suppose -y**2 - 2*y**2 + m*y**2 = 0. Calculate y.
0
Solve 0*o + 70440*o**3 - 70441*o**3 - 3*o**2 - 2*o = 0 for o.
-2, -1, 0
Determine j, given that -27/4*j + 51/8 + 3/8*j**2 = 0.
1, 17
Let z(o) be the second derivative of 5*o**4/3 + 76*o**3/3 - 32*o**2 - 13*o - 2. Let z(v) = 0. C