ctor u(t).
-3*t**2
Let c be (-10)/12*6*-1. Suppose 6*b = c*w + b - 35, 3*w - b - 11 = 0. Factor 8*x + 7*x**2 - 5*x**3 + 2 + w - 6 - 2.
-(x - 2)*(x + 1)*(5*x - 2)
Let k(f) be the second derivative of -5/6*f**4 + 0*f**2 + 1/3*f**6 + 4*f + 0 + 3/10*f**5 + 1/3*f**3 - 4/21*f**7. Determine w, given that k(w) = 0.
-1, 0, 1/4, 1
Let h(r) be the second derivative of -r**7/70 + r**2 + 9*r. Let g(u) be the first derivative of h(u). Let g(k) = 0. What is k?
0
Let v(k) be the second derivative of k**7/245 + k**6/84 + k**5/105 + 13*k**2/2 - 9*k. Let j(c) be the first derivative of v(c). Factor j(m).
2*m**2*(m + 1)*(3*m + 2)/7
Solve -8*f + 0 - 1/2*f**2 = 0 for f.
-16, 0
Suppose 37 + x**3 + 5*x**2 - 33*x + 51 - 61 = 0. What is x?
-9, 1, 3
Let h(d) be the third derivative of d**9/7560 + d**8/4200 - d**7/2100 - d**6/900 - 2*d**3 - 12*d**2. Let s(y) be the first derivative of h(y). Factor s(c).
2*c**2*(c - 1)*(c + 1)**2/5
Let m(c) be the first derivative of c**6/6 + 3*c**5/5 + 3*c**4/4 + c**3/3 + 267. Find y such that m(y) = 0.
-1, 0
Let y be (-150)/(72/(-12)) - 22. Factor -12*m + 1/2*m**2 + 3*m**y + 1/2*m**4 + 8.
(m - 1)**2*(m + 4)**2/2
Let f(k) be the second derivative of k**5/90 + 4*k**4/3 + 64*k**3 + 1536*k**2 - 48*k. Suppose f(j) = 0. What is j?
-24
Suppose -18*k + 20 = -8*k. Factor 52 - 66 - 12*h + 54 - 4*h**k.
-4*(h - 2)*(h + 5)
Let h be 2 - (-1 + -1)*-1. Suppose -1 = -l - s, 5*l + 4*s + 26 - 32 = 0. Find m such that 1/3*m**4 + 0*m - 1/3*m**3 + 0 + h*m**l = 0.
0, 1
Let j(n) be the second derivative of n**6/2520 - n**5/120 - n**4/21 + 11*n**3/3 + 4*n. Let h(i) be the second derivative of j(i). Factor h(q).
(q - 8)*(q + 1)/7
Let s(j) be the second derivative of 2*j**4/3 - 22*j**3/3 + 74*j**2 - 16*j. Let z(w) = 7*w**2 - 45*w + 147. Let p(q) = -3*s(q) + 4*z(q). Factor p(x).
4*(x - 6)**2
Let h(f) be the third derivative of f**8/1344 + f**7/280 - 775*f**2. Find b such that h(b) = 0.
-3, 0
Let m(q) = -q**2 - 18*q - 26. Let f be m(-16). Suppose 6*r - 6 = f. Factor -2/3*z - 2/9*z**3 - 2/9 - 2/3*z**r.
-2*(z + 1)**3/9
Factor 1 - w**4 - w**2 + 3 + 11*w**3 + 0*w**3 - 2 - 8*w**3 - 3*w.
-(w - 2)*(w - 1)**2*(w + 1)
Let i(j) be the first derivative of 8/3*j + 2/9*j**3 + 26 + 5/3*j**2. Factor i(y).
2*(y + 1)*(y + 4)/3
Let b(z) be the first derivative of 1/5*z**3 + 0*z + 3/25*z**5 + 0*z**2 - 3/10*z**4 + 1. Factor b(g).
3*g**2*(g - 1)**2/5
Let z(o) be the third derivative of -1/4*o**4 + 0 - 1/105*o**7 + 2/3*o**3 + 21*o**2 + 1/20*o**6 + 0*o - 1/30*o**5. Find s such that z(s) = 0.
-1, 1, 2
Let y(j) be the third derivative of j**7/1890 - j**6/540 + j**5/540 - 81*j**2. Factor y(b).
b**2*(b - 1)**2/9
Let y(s) be the second derivative of -s**4/6 + 19*s**3/18 - s**2/2 - s + 13. Factor y(p).
-(p - 3)*(6*p - 1)/3
Solve -3/2*q**2 + 27*q - 108 = 0.
6, 12
Factor -96/5*q - 2/5*q**2 - 1152/5.
-2*(q + 24)**2/5
Let k be (444/(-777))/(1 + (-9)/7). Let y(g) be the first derivative of 1/36*g**4 + 0*g**3 + 8 - 1/6*g**k + 2/9*g. Factor y(h).
(h - 1)**2*(h + 2)/9
Let y(d) = -27*d**2 - 15*d - 3. Let n(x) = -7*x**2 - 4*x - 1. Let j be 304/72 + (-4)/18. Let p(z) = j*y(z) - 15*n(z). Solve p(g) = 0.
-1, 1
Let p(k) be the second derivative of -k**4/18 + 17*k**3/3 - 50*k**2/3 - 56*k - 1. Factor p(h).
-2*(h - 50)*(h - 1)/3
Suppose -91/4*m - 11/2*m**2 - 1/4*m**3 - 51/2 = 0. Calculate m.
-17, -3, -2
Suppose -19*j + 21*j = 4. What is a in -21*a**2 - 14 + 22*a**j + 3*a + 10 = 0?
-4, 1
Let l be (5 + (-3 - 1))/5. Let v(c) be the first derivative of 0*c - l*c**3 + 9/10*c**2 - 3. Find h such that v(h) = 0.
0, 3
Suppose 12 = -14517*f + 14523*f. Factor 3*a**f + 16/3 - 8*a.
(3*a - 4)**2/3
Let z(m) = 3*m**3 + 32*m**2 - 10*m + 11. Let t be z(-11). Solve -2/3*y**4 - 34/15*y**2 + 8/15 + t*y + 12/5*y**3 = 0.
-2/5, 1, 2
Let j(b) = -1 - 1 - 2 + 4*b - 1. Let r be j(2). Let 14*d**2 - 86*d**r - 28*d**4 - 27*d**2 + 22*d**3 - 31*d**2 - 8*d = 0. What is d?
-1, -2/7, 0
Let r(q) = -2*q**3 + 12*q**2 + 12*q + 8. Let o(g) = 3*g**2 + g + 2. Let l(h) = 4*o(h) - r(h). Solve l(u) = 0 for u.
-2, 0, 2
Let v = -49 - -69. Suppose -v = -4*m - 0*m. What is w in 6*w**2 - m*w**2 - 12*w + 4 - 1 + 8*w**2 = 0?
1/3, 1
Let j(f) = -f**3 - 11*f**2 - 11*f - 10. Let q be j(-10). Suppose -s - v + 6*v + 23 = q, 0 = 5*s + 4*v + 1. Let 1/4*d**s - d**2 + 0 + d = 0. Calculate d.
0, 2
Let g(l) be the second derivative of l**5/200 + l**4/30 + l**3/15 - 69*l + 2. Let g(q) = 0. Calculate q.
-2, 0
Let h(b) be the third derivative of 5*b**8/336 + 3*b**7/14 + 13*b**6/12 + 3*b**5/2 - 45*b**4/8 - 45*b**3/2 + 2*b**2 - 105. Determine u, given that h(u) = 0.
-3, -1, 1
Let v(b) = 4*b + 16. Let p be v(0). Let h be (p/(-12) - -1) + (-5)/(-9). Determine o, given that h*o - 4/9 + 2/9*o**2 = 0.
-2, 1
Let l(x) = 16*x + 7 + 2 - 15*x. Let c be l(-4). Suppose 6*j - 3*j - 3*j**2 + 8*j**2 - c*j = 0. What is j?
0, 2/5
Let s(d) be the first derivative of -3*d**4/16 - 5*d**3/4 - 21*d**2/8 - 9*d/4 - 36. What is l in s(l) = 0?
-3, -1
Let r(v) = -v**3 - v**2 + 5*v + 7. Let x be r(-4). Suppose 0 = 10*f - 5 - x. Factor 0 - 2/7*n**3 + 2/7*n**5 + 2/7*n**2 + 0*n - 2/7*n**f.
2*n**2*(n - 1)**2*(n + 1)/7
Let a = -41 + 45. Let 5723*m**a - 15*m**5 - 5670*m**4 - 2*m - 2*m**5 + 23*m**2 - 57*m**3 = 0. Calculate m.
0, 2/17, 1
Suppose -13*q = -9*q - 360. Factor 35*n**3 - 5*n**3 + q*n**2 + 5*n**3 + 5*n**4 + 29 + 11 + 100*n.
5*(n + 1)*(n + 2)**3
Let y(m) = -m**3 + m**2 - m. Let h(x) = 10*x**3 - 16*x**2 + 23*x - 8. Let l(r) = -4*h(r) - 36*y(r). Factor l(f).
-4*(f - 4)*(f - 2)*(f - 1)
Let v(r) be the third derivative of r**5/180 - r**4/18 + 2*r**3/9 - r**2 - 30. Factor v(n).
(n - 2)**2/3
Suppose 0 = -3*w + 8 - 2. Factor -3*t**w + 3*t**2 + 1 + t**2 + t - 3*t.
(t - 1)**2
Find m, given that 5/2*m**3 + 30*m**2 - 135/2*m + 35 = 0.
-14, 1
Let c(r) be the first derivative of -3 + 7/15*r**3 + 2/5*r + 9/10*r**2. Factor c(d).
(d + 1)*(7*d + 2)/5
Let t = 157 - 155. Let -108*n**2 - 4*n**4 - 9*n - 44*n**3 + 44*n**2 - 76*n**t - 91*n = 0. What is n?
-5, -1, 0
Let w(z) be the second derivative of z**4/3 + 32*z**3 + 94*z**2 - 4*z - 13. What is m in w(m) = 0?
-47, -1
Let i(v) = -9*v**3 - v**2 - v. Let j be i(-1). What is x in 3*x**4 + j*x**3 + 10*x - 5*x - 5*x = 0?
-3, 0
Let l = -9 + 11. Suppose a + 0*a = l. Let 4 - 4 + 118*f**2 - 126*f**a + 4*f = 0. What is f?
0, 1/2
Let f(s) = -s**3 + 1. Let k(v) be the first derivative of 19*v**4/2 - 50*v**3 + 90*v**2 - 43*v - 11. Let l(w) = -3*f(w) - k(w). Find h, given that l(h) = 0.
2/7, 2
Suppose -6 = 3*i, 3*c - 230 = -2*i - 0*i. Let v be 7*16/728 - (-14)/c. Solve -1/3*x**3 - v*x - 2/3*x**2 + 0 = 0 for x.
-1, 0
Let w(u) be the second derivative of -u**6/900 + u**5/300 + u**4/30 + 13*u**3/6 - 7*u. Let i(y) be the second derivative of w(y). Find j, given that i(j) = 0.
-1, 2
Let i(s) = 234*s**2 + 3 + 120*s - 4 - 4 - 189*s**2. Let q(b) = b**3 + b**2 + b + 1. Let y(r) = i(r) + 5*q(r). Factor y(m).
5*m*(m + 5)**2
Let l(q) = -q - 5. Let t be l(-7). Suppose -5*h + t = -13. Factor -a**4 + 1 - 1 - a**2 + h*a**3 - a**3.
-a**2*(a - 1)**2
Let w be (-5 + 4 - -5)/2. Find r such that -3*r**w + 50*r**3 - 92*r**3 + r**4 + 43*r**3 + 2 - r = 0.
-2, -1, 1
Suppose -20 = -5*b - 5*j, -3*b - 4*j = -2*b - 4. Determine i so that 3/2*i**3 + 3/2 + 3/2*i**b - 3/4*i**5 - 3/4*i - 3*i**2 = 0.
-1, 1, 2
Let h = 2948 - 2948. Let s = -12/7 - -45/14. Factor 0 + 0*u**4 + h*u + 3/2*u**3 - s*u**5 + 0*u**2.
-3*u**3*(u - 1)*(u + 1)/2
Let l(m) be the second derivative of m**7/273 - 8*m**6/195 + 5*m**5/26 - 19*m**4/39 + 28*m**3/39 - 8*m**2/13 - 256*m. Factor l(y).
2*(y - 2)**3*(y - 1)**2/13
Let v(k) be the third derivative of -k**7/210 - k**6/24 + k**5/60 + 5*k**4/24 + 79*k**2. Solve v(i) = 0 for i.
-5, -1, 0, 1
Suppose 4*a - 12 = 0, 18*f - 16*f + 4*a = 16. Factor -2/15*o**f + 2/15*o**3 + 2/15*o**4 + 0 - 2/15*o.
2*o*(o - 1)*(o + 1)**2/15
Let a(y) be the first derivative of -43 + 4/5*y**5 + 0*y + 0*y**2 - 2/3*y**6 + y**4 - 4/3*y**3. Determine r, given that a(r) = 0.
-1, 0, 1
Factor 27556/3*o**2 + 1328/3*o + 16/3.
4*(83*o + 2)**2/3
Suppose -10*i + 20*i = 40. Let p(r) be the second derivative of 7*r - 1/10*r**5 + r**3 + 2*r**2 + 0 + 0*r**i. Factor p(f).
-2*(f - 2)*(f + 1)**2
Suppose -y + 5 = -d - 16, 5*d + 65 = -5*y. Let c = 19 + d. Factor 3*j**c - 5*j**2 + 0*j**2 - 2*j**2.
-4*j**2
Factor -2/11*f**5 - 20/11*f**4 - 160/11*f - 