2946. Factor 10 - 5/3*b**3 + x*b**2 - 55/3*b.
-5*(b - 3)*(b - 2)*(b - 1)/3
Let v(c) be the first derivative of 15 + c**5 + 0*c - 5/3*c**3 + 0*c**2 + 0*c**4. Let v(m) = 0. What is m?
-1, 0, 1
What is b in 0 - 1/6*b**4 + 1/6*b**5 - 4*b - 11/3*b**3 - 22/3*b**2 = 0?
-2, -1, 0, 6
Let i = 15465 + -15461. Factor 2*l**3 + i + 116/7*l**2 + 130/7*l.
2*(l + 1)*(l + 7)*(7*l + 2)/7
Let b(a) be the third derivative of a**8/3696 - a**7/462 + a**6/660 + 7*a**5/330 - a**4/88 - 3*a**3/22 - 100*a**2. Let b(x) = 0. Calculate x.
-1, 1, 3
Let u = 37/73 - 1/146. Factor -1 - 1/2*s + u*s**2.
(s - 2)*(s + 1)/2
What is v in -72/13 - 2/13*v**3 + 4/13*v**2 + 30/13*v = 0?
-4, 3
Factor 27 - 11*i**3 + 109/3*i**2 + 75*i + 2/3*i**4.
(i - 9)**2*(i + 1)*(2*i + 1)/3
Let m be 48/(-2) + 6344/260. Suppose 0 = -4*c - 0*c. What is y in -4/5*y**2 - 2/5*y - m*y**3 + c = 0?
-1, 0
Suppose 5*p + 6 = 7*p. Suppose l + 28 = p*l. Factor l - 2*x**2 - 5*x + 3*x**2 - 10.
(x - 4)*(x - 1)
Let f(j) = j**2 - j - 1. Let i(x) = 4*x**2 - x - 5. Let u = 28 + -23. Let d be u + -1 - (-1 - 15). Let l(b) = d*f(b) - 4*i(b). Factor l(z).
4*z*(z - 4)
Let w(i) be the third derivative of -1/140*i**5 + 0*i**3 - 12*i**2 - 1/56*i**4 + 0*i + 0. Factor w(h).
-3*h*(h + 1)/7
Let h = -2 - -2. Suppose 12 = 3*n - h. Let -k**3 + 2*k - 5*k + 4 + k**2 + n*k - 5 = 0. What is k?
-1, 1
Let m = 3 + 1. Let r = 346/431 + -6/2155. Factor 0 - r*l - 4/5*l**5 - 24/5*l**3 - 16/5*l**2 - 16/5*l**m.
-4*l*(l + 1)**4/5
Let c(t) be the first derivative of t**4/10 - 4*t**3/15 - t**2/5 + 4*t/5 + 122. Factor c(r).
2*(r - 2)*(r - 1)*(r + 1)/5
Let a be 5/3 - 272/1632. Let a*w**4 + 0*w + 0 + 3*w**3 - 6*w**2 - 3/4*w**5 = 0. What is w?
-2, 0, 2
Let t = 493 + -491. Let r(d) be the third derivative of 1/150*d**5 - 1/20*d**4 + 0 + 2/15*d**3 + 6*d**t + 0*d. What is p in r(p) = 0?
1, 2
Let v = 1301 + -1299. Solve 1/4*z**v + 25/4 + 5/2*z = 0.
-5
Let u = -681 - -683. Let c(b) be the second derivative of -3/40*b**5 + 5*b + 1/12*b**3 + 0 - 1/2*b**u + 1/6*b**4. Find d such that c(d) = 0.
-2/3, 1
Let t(r) = 6*r + 104. Let k be t(-17). Let b(h) be the first derivative of -3/4*h**4 - k*h**3 + 0*h**2 + 4 + 0*h. Let b(a) = 0. Calculate a.
-2, 0
Let b(o) be the first derivative of -2*o**5 - 24*o**4 + 40*o**3/3 + 757. Factor b(v).
-2*v**2*(v + 10)*(5*v - 2)
Let a(j) = 9*j**3 + 24*j**2 + 3*j - 24. Let f(r) = -17*r**3 - 47*r**2 - 4*r + 47. Let q(k) = -7*a(k) - 4*f(k). Solve q(c) = 0.
-4, -1, 1
Let n(v) = v**2 - 3*v - 2. Suppose 0 = -19*q + 15*q - 4. Let k be n(q). Determine s so that -2/3 - 6*s**4 + 20/3*s**k + 0*s**3 + 0*s = 0.
-1, -1/3, 1/3, 1
Factor -22326/7*t - 2/7*t**3 - 366/7*t**2 - 453962/7.
-2*(t + 61)**3/7
Let f(b) = b**2 + 14*b + 62. Let r(t) = -t - 1. Suppose 0 = -5*l - 5. Let n(i) = l*f(i) + 2*r(i). Suppose n(q) = 0. Calculate q.
-8
Let s(q) = -q**3 + 4*q**2 - 7. Let d be s(3). Suppose -d - 18 = -4*t. Factor 3*m + 6*m + 2*m**2 + 6 - t*m + 4*m.
2*(m + 1)*(m + 3)
Let g(m) = -m**3 + 4*m**2 + 7*m - 7. Let i be g(5). Suppose -8 + 2 = -i*a. Determine v, given that -v**3 + 2*v**4 - a*v**3 - v**3 + 4*v - 2*v**2 = 0.
-1, 0, 1, 2
Let y = -25 + 29. Suppose -8 = -l + y*l + 2*w, 3*l = -3*w - 12. Determine o, given that -o**2 + o**5 - 5*o**5 + l*o**3 + 3*o**3 + 5*o**5 - 3*o**4 = 0.
0, 1
Let r(a) = 2*a**4 + 23*a**3 + 26*a**2 + 35*a - 3. Let c(m) = -14 + m**3 - 4*m + 13 + 6*m - m. Let o = 10 + -8. Let y(w) = o*r(w) - 22*c(w). Factor y(f).
4*(f + 1)**2*(f + 2)**2
Factor 14/9*n**3 + 0 - 8/3*n - 80/9*n**2.
2*n*(n - 6)*(7*n + 2)/9
Factor 11*u**2 - 8*u**2 - u**4 + u**5 - 12*u**3 - 3*u**2.
u**3*(u - 4)*(u + 3)
Suppose 2*v = -m - 20, -7 = 2*v - 3. Let l = -142/9 - m. Solve l*y**3 + 2/9*y**2 - 8/9 - 8/9*y = 0 for y.
-2, -1, 2
Let y(t) be the second derivative of -t**4/6 - 182*t**3/3 - 8281*t**2 - 38*t. Determine n so that y(n) = 0.
-91
Let z(a) be the second derivative of -a**7/42 + a**6/15 - a**5/20 - 49*a. Factor z(x).
-x**3*(x - 1)**2
Suppose 63*t + 8 = 93 + 41. Factor -6/5*y + 0 - 3/5*y**t.
-3*y*(y + 2)/5
Let r(w) be the third derivative of w**5/15 - 3*w**4/2 - 44*w**3/3 - 61*w**2 - 2. Suppose r(v) = 0. Calculate v.
-2, 11
Let w(y) = 8*y**2 + y - 2. Let m(r) = 55*r**2 - 7*r + 1. Let d(c) = 4*m(c) - 28*w(c). Determine l, given that d(l) = 0.
-15, 1
Let d(f) be the first derivative of 0*f**2 - 2/9*f**3 + 8/3*f + 22. Factor d(p).
-2*(p - 2)*(p + 2)/3
Let s(d) = -94*d - 92. Let q be s(-1). Let g(n) be the first derivative of 8/5*n**5 + 26/3*n**3 + q*n - 4 - 6*n**4 - 6*n**2. What is w in g(w) = 0?
1/2, 1
Let h(l) = -10*l**2 + 4*l. Let n(u) = 21*u**2 - 8*u. Let t(m) = 5*h(m) + 2*n(m). Factor t(p).
-4*p*(2*p - 1)
Let q(u) = u - 15. Let c be q(6). Let o = 11 + c. Let -3*r**o - 3*r**2 + 6*r**5 + 3*r**2 + 9*r**4 = 0. What is r?
-1, 0, 1/2
Let b(z) be the second derivative of z**7/168 - 2*z**6/15 + 61*z**5/80 + 23*z**4/24 - 20*z**3/3 - 16*z**2 - 2*z - 48. Suppose b(p) = 0. What is p?
-1, 2, 8
Let z(y) = y**2 + y + 7. Let c be z(0). Let q = 221 - 219. Let u + 3*u - c*u - 3*u**q = 0. Calculate u.
-1, 0
Suppose 1/5*f**4 + f**3 + 0 + 0*f + 4/5*f**2 = 0. Calculate f.
-4, -1, 0
Let j(m) be the second derivative of -2*m**5/5 - m**4/3 + 2*m**3 - 2*m - 41. Suppose j(w) = 0. Calculate w.
-3/2, 0, 1
Let c(w) be the third derivative of w**5/15 - w**4/8 + w**3/2 - 2*w**2. Let f be c(1). Let 9/7*x**2 + 9/7*x**3 + 0 + 3/7*x + 3/7*x**f = 0. Calculate x.
-1, 0
Let r(k) be the first derivative of -k**6/36 + k**5/5 + 17*k**4/12 + 28*k**3/9 + 13*k**2/4 + 5*k/3 + 71. What is q in r(q) = 0?
-1, 10
Let c be 4 + -5 + 4 - 1. Factor 3*o**2 + 12 - 7*o**2 + o**c.
-3*(o - 2)*(o + 2)
Let c(m) be the third derivative of -m**6/480 - m**5/120 + m**4/24 + m**3/3 - 36*m**2 + 2*m. Factor c(y).
-(y - 2)*(y + 2)**2/4
Let y(s) = s**2 + 8*s + 12. Let n be y(-4). Let p be -1 + n + (-134)/(-26). Factor -2/13*b**5 + 0*b**2 + 0 - 4/13*b**4 - p*b**3 + 0*b.
-2*b**3*(b + 1)**2/13
Suppose -1/2*k**3 + 6*k**2 - 27/2*k - 20 = 0. What is k?
-1, 5, 8
Let l(z) = z**4 + 28*z**3 - z**2 - 35*z - 7. Let n(y) = -y**3 + 2*y + 1. Let s(j) = 5*l(j) + 35*n(j). Determine a so that s(a) = 0.
-21, -1, 0, 1
Let q(o) be the first derivative of -14*o**6/9 - 8*o**5/15 + 7*o**4 + 80*o**3/9 + 8*o**2/3 + 892. Solve q(r) = 0 for r.
-1, -2/7, 0, 2
Factor -5*w**2 + 0 + 0*w + 0*w**3 + 15/4*w**4 + 5/4*w**5.
5*w**2*(w - 1)*(w + 2)**2/4
Suppose 2*m = 2*k - 7*k - 5, -3*m = 0. Let l be 0/k - -3 - (-264)/(-96). Factor -1/4*b**2 - 1/2*b - l.
-(b + 1)**2/4
Let s(z) = -5*z**3 - 11*z**2 + 18*z + 28. Let k(r) = 81*r**3 + 177*r**2 - 288*r - 450. Let h(n) = 2*k(n) + 33*s(n). Factor h(w).
-3*(w - 2)*(w + 1)*(w + 4)
Let a = -2512/15 + 619/105. Let i = -161 - a. What is k in 2/7 + 2/7*k**5 + 4/7*k**2 - 6/7*k**4 - 6/7*k + i*k**3 = 0?
-1, 1
Suppose -l + j = -6, 8*l + j + 6 = 6*l. Factor -3/2*z**2 - 1/2*z**3 + l - z.
-z*(z + 1)*(z + 2)/2
Let v(j) = j**3 - j + 1. Let b(q) = -q**4 + 43*q**3 - 429*q**2 + 1287*q - 1151. Let c(n) = b(n) - 5*v(n). Find k, given that c(k) = 0.
2, 17
Suppose r = -5*l - 10, 6*l = 2*l - 5*r - 8. Let w be (4/5)/l*-10. Suppose 13*z + 8*z**4 - 5*z + w*z - 4 - 4*z**2 - 12*z**3 = 0. Calculate z.
-1, 1/2, 1
Factor 194*h - 14*h**3 - 5 - 7 - 228*h - 34*h**2 - 2*h**4.
-2*(h + 1)**2*(h + 2)*(h + 3)
What is r in 20*r**3 - 2/9*r**5 - 22/9*r**4 + 334/9*r - 388/9*r**2 - 34/3 = 0?
-17, 1, 3
Let t be 1/(((-30)/(-36))/(10/6)). Factor -29 - 32*m + 251*m**2 - 263*m**t + 9.
-4*(m + 1)*(3*m + 5)
Suppose -l - 2*l = 39. Let q be (-2 - (-165)/42)*(-11 - l). Factor 3/7*v**2 + q + 18/7*v.
3*(v + 3)**2/7
Let b(o) be the first derivative of o**4/18 - 4*o**3/9 - 7*o**2/9 - 59. Factor b(j).
2*j*(j - 7)*(j + 1)/9
Let x(m) be the second derivative of m**4/24 - 2*m**3 + 23*m**2/4 - 33*m. Factor x(l).
(l - 23)*(l - 1)/2
Let j be 16/10 - (-8)/20. Let o(t) be the second derivative of -1/54*t**4 + 0*t**j + 1/27*t**3 + 6*t + 0. Determine v so that o(v) = 0.
0, 1
Let p(q) = -q**3 + 9*q**2 + q - 8. Let h be p(9). Suppose 3*d - 5 = h. Solve o - 17*o**2 - 2*o**3 + 17*o**d + o**5 = 0.
-1, 0, 1
Suppose 1226 + 46 = 12*j. Suppose j - 104 = z. Factor 0*m - 3/5*m**z + 12/5.
-3*(m - 2)*(m + 2)/5
Factor 4*j**4 + 340*j**2 + 17280*j + 27648 + 61*j**3 - 3*j**4 + 13*j**3 + 1100*j**2 + 432*j**2.
(j + 2)*(j + 24)**3
Suppose 8*k - 40 = -o + 13*k, 0 = 3*o + k + 8. What is y in 1/8*y**2 - 1/8*y**5 - 1/8*y**4 + 