m**2 + m + 4. Let f(y) = 20*y**3 - 60*y**2 + 35*y - 20. Let r(o) = -f(o) - 5*k(o). Determine t so that r(t) = 0.
0, 2/3, 4
What is f in -455*f**2 - 121/6*f**5 - 36 - 210*f - 2665/6*f**3 - 550/3*f**4 = 0?
-6, -1, -6/11
Solve -24 - 6*v**2 + 14*v**2 + 6*v + 2*v**2 - 7*v**2 = 0 for v.
-4, 2
Let q(l) be the first derivative of l**4/34 + 2*l**3/51 - 2*l**2/17 - 760. Factor q(r).
2*r*(r - 1)*(r + 2)/17
Let c(y) = 3*y**2 + 9*y**4 + 24 - 10 - 8. Let z(j) = -j**4 - j**3 - 1. Let v be (-11)/(-55) - 29/(-5). Let w(x) = v*z(x) + c(x). Suppose w(a) = 0. What is a?
0, 1
Let t(p) be the third derivative of -p**8/90720 + p**7/405 - 98*p**6/405 - 7*p**5/15 + p**3/6 + 133*p**2. Let j(w) be the third derivative of t(w). Factor j(b).
-2*(b - 28)**2/9
Suppose 10*h = 9*h. Suppose h = -3*m + 4*m - 3. What is v in -63*v**4 + 7*v**3 + 21*v**4 + 23*v**3 - m*v**2 - 33*v**4 = 0?
0, 1/5
Let p(c) be the third derivative of -c**5/150 + 401*c**4/10 - 482403*c**3/5 + 1089*c**2 - 4. Factor p(t).
-2*(t - 1203)**2/5
Let s(u) = -28*u**3 - 148*u**2 - 168*u + 32. Let h(y) = 9*y**3 + 50*y**2 + 56*y - 10. Let k = 441 - 425. Let n(g) = k*h(g) + 5*s(g). Let n(d) = 0. What is d?
-14, -1, 0
Suppose s - 9*r + 13*r + 26 = 0, -5*s - 2*r - 4 = 0. Factor 0*o - 4/9 + 4/9*o**s.
4*(o - 1)*(o + 1)/9
Let l(k) = -2*k**3 + 27*k**2 + 16*k - 59. Let d(t) = 5*t + 25*t**2 - 29 + 3*t - 12*t**2. Let g(h) = 5*d(h) - 3*l(h). Find o such that g(o) = 0.
-4/3, 2
Find k such that 440/9 - 497/9*k**2 + 19/3*k**4 + 1/9*k**5 - 34/3*k + 101/9*k**3 = 0.
-55, -4, -1, 1, 2
Suppose j = a - 4, -3*j + 6*j = a. Let f be (25/4 - a)/(4/32). Factor 1/3*s**f - 1/3*s - 1/9*s**3 + 1/9.
-(s - 1)**3/9
Let c(f) be the first derivative of -f**5/30 + 1141*f**4/8 - 162640*f**3 - 732736*f**2/3 + 6451. Suppose c(p) = 0. What is p?
-1, 0, 1712
Let d be (0 - -1*3*-12)/1. Let q = d - -48. Factor 4*c**4 - 3*c**4 + 12*c**3 + c**4 - 18*c**2 - 5*c**4 + q*c - 3.
-3*(c - 1)**4
Suppose 5*w = 5*v + 30, 3*v - 33 = w - 43. Let t(p) be the first derivative of 1/4*p**3 - 3/8*p**2 - 3/4*p - 9 + 3/16*p**w. Factor t(d).
3*(d - 1)*(d + 1)**2/4
Let q(r) = 10*r + 23. Let x be q(4). Let -h**4 + 27*h**2 + 3*h**5 + 275*h + x*h**3 - 257*h + 30*h**2 + 28*h**4 = 0. Calculate h.
-6, -1, 0
Factor 1/4*o**2 + o - 21/4.
(o - 3)*(o + 7)/4
Let r(g) be the first derivative of 5*g**4/12 + 25*g**3/9 + 35*g**2/6 + 48*g - 134. Let h(x) be the first derivative of r(x). Factor h(i).
5*(i + 1)*(3*i + 7)/3
Let i(k) be the second derivative of k**4/18 + 13*k**3/9 + 22*k**2/3 - 1517*k. Find j such that i(j) = 0.
-11, -2
Suppose -17*p + 103*p = 344. Let w(h) be the second derivative of -1/18*h**3 - 11*h + 0 - 1/36*h**p + 0*h**2. Factor w(j).
-j*(j + 1)/3
Let g(n) = -5*n**3 - 8*n**2 + 79*n + 146. Let s(m) = -21*m**3 - 33*m**2 + 318*m + 582. Let z(i) = 9*g(i) - 2*s(i). Factor z(c).
-3*(c - 5)*(c + 2)*(c + 5)
Factor 1816*w**2 + 79152*w - 157666*w + 80334*w - 4*w**3.
-4*w*(w - 455)*(w + 1)
Let o be (-1 + 6)*1 - (-792)/72. Factor -8 - 21617*r**2 + 21633*r**2 + 4*r - o + 4*r**3.
4*(r - 1)*(r + 2)*(r + 3)
Factor 15*k**2 + 0 - 3/7*k**3 - 102/7*k.
-3*k*(k - 34)*(k - 1)/7
Let x = -164 + 357. Factor -6 + 6 - 8*d - 181*d**4 + x*d**4 + 24*d**2 - 26*d**3 - 2*d**5.
-2*d*(d - 2)**2*(d - 1)**2
Let b(d) be the third derivative of 1/240*d**5 + d**2 - 7*d + 0 + 5/48*d**4 + 3/8*d**3. Suppose b(k) = 0. Calculate k.
-9, -1
Suppose l + 4*f + 1 = 0, 4*l - 2*f + 28 - 42 = 0. Suppose -3*c**5 - 7*c**4 + 14*c**2 - 7 - 2 + 4*c**5 + 2*c**l + c**4 + c**4 - 3*c = 0. Calculate c.
-1, 1, 3
Factor -2/21*a**2 + 20/7*a - 96/7.
-2*(a - 24)*(a - 6)/21
Let q = -120 + 120. Suppose -s - 3*o + q*o - 3 = 0, -2 = 3*s + 2*o. Factor 2/9*y**3 + s*y**2 - 4/9 - 2/3*y.
2*(y - 2)*(y + 1)**2/9
Let b be 20/15 + 18203/1002. Factor -b*p - 3/2*p**2 - 18.
-3*(p + 1)*(p + 12)/2
Suppose -16*v - 12 + 60 = 0. Suppose 3*j - 4 - 7 = 2*b, 0 = -4*b - 5*j + 33. Solve -v + 7*d**2 + 3*d + d**3 - 10*d**2 + b = 0 for d.
1
Let g(x) = 39*x + 30. Let k(j) = -j**3 + j**2 + 2*j - 12. Let q be k(-3). Let n be g(q). Let -n + 732 - 3*v**4 + 10*v**3 - 15*v**5 + 8*v**4 = 0. What is v?
-2/3, 0, 1
Let r(y) be the first derivative of -y**5/20 + y**4/4 + 4*y**3 + 7*y**2/2 + 7*y - 79. Let o(t) be the second derivative of r(t). Factor o(u).
-3*(u - 4)*(u + 2)
Let 138*g**3 + 15962*g**4 - 31928*g**4 + 15963*g**4 = 0. What is g?
0, 46
Suppose -27*q + 83 - 29 = 0. Let s(o) = 31*o - 58. Let i be s(q). Suppose -3/8*n**2 - 3/2 + 15/8*n**i - 6*n - 75/8*n**5 + 123/8*n**3 = 0. Calculate n.
-1, -2/5, 1
Let p = 1343 - 1341. Let q(z) be the first derivative of 21/19*z**p - 36/19*z - 18 - 16/57*z**3 + 1/38*z**4. Find v such that q(v) = 0.
2, 3
Let v = -487 - -334. Let y be (-3)/((-6)/4) + v/(-18). Let -3 + 3*m**3 - 12*m**2 + 3*m**4 - 3/2*m**5 + y*m = 0. What is m?
-2, 1
Let f(g) be the second derivative of 3/4*g**4 + 1/120*g**6 + 0 - 1/8*g**5 + 7*g + 0*g**2 + 2*g**3. Let x(w) be the second derivative of f(w). Factor x(a).
3*(a - 3)*(a - 2)
Let k = 603 + -602. Let w be k*-4 - ((-300)/70 + 0). Factor -w*b**2 + 6/7*b + 8/7.
-2*(b - 4)*(b + 1)/7
Factor -38/5*s + 48 - 2/5*s**2.
-2*(s - 5)*(s + 24)/5
Factor 0 + 33/2*i + 1/4*i**3 - 17/4*i**2.
i*(i - 11)*(i - 6)/4
Let c(k) be the third derivative of -k**6/160 + 67*k**5/80 + k**4/8 - 67*k**3/2 - 2122*k**2. Factor c(b).
-3*(b - 67)*(b - 2)*(b + 2)/4
Let r(i) be the first derivative of -2*i**6/3 + 204*i**5/5 + 6*i**4 - 1192*i**3/3 - 810*i**2 - 612*i - 3534. Factor r(g).
-4*(g - 51)*(g - 3)*(g + 1)**3
Let l(s) be the third derivative of 1/96*s**6 + 0*s**3 + 0 + 47*s**2 + 5/48*s**5 + 5/24*s**4 - 2*s. Factor l(o).
5*o*(o + 1)*(o + 4)/4
Let c(q) be the third derivative of q**6/1020 - 19*q**5/255 - 47*q**4/68 + 246*q**3/17 - 2681*q**2. Find p such that c(p) = 0.
-6, 3, 41
Let d(p) = 2*p - 16. Let f be d(9). Factor 30*r - 808*r**3 + 405*r**3 + 399*r**3 - f*r + 24.
-4*(r - 3)*(r + 1)*(r + 2)
Suppose 185*s - 309 = 246. Factor -38/3*c**2 + 0 - 8/3*c - s*c**3.
-c*(c + 4)*(9*c + 2)/3
Let v = -135 + 137. Factor -5*o**v - 201*o + 3*o**2 + 27*o - 133*o - 10082 + 23*o.
-2*(o + 71)**2
Solve 277/7*q**3 - 36*q**2 - 348/7*q - 32/7 - 30/7*q**4 = 0.
-2/3, -1/10, 2, 8
Let 2274*h**2 + 751*h**2 + 459040*h + 299006 + 58608 + 5*h**3 + 98406 = 0. Calculate h.
-302, -1
Let w(m) = -379*m + 2655. Let i be w(7). Factor 8/7 - 2/7*k**i + 0*k.
-2*(k - 2)*(k + 2)/7
Let q(i) be the second derivative of i + 0*i**2 + 27 - 2/5*i**6 + 0*i**3 + 1/5*i**5 + 0*i**4. Factor q(a).
-4*a**3*(3*a - 1)
Let g = 58823 + -235291/4. Let v be (2/6)/((-16)/(-72)). Determine f, given that -3*f - g*f**4 - 13/4*f**2 - v*f**3 - 1 = 0.
-2, -1
Solve 80*h - 75*h**3 - 1592276*h**2 - 5*h**5 + 1592316*h**2 - 58*h**4 + 18*h**4 = 0 for h.
-4, -1, 0, 1
Let m = -156097 - -1092701/7. Suppose 6/7*k**3 + 5/7*k**5 + m*k**2 - 11/7*k - 19/7*k**4 - 3/7 = 0. What is k?
-1, -1/5, 1, 3
Let w be (-6 + 21 - 2) + (-11 - -3). Suppose -q = 2*x - 25, 4*x - 75 = -4*q + x. Factor w*m**5 - 32*m**3 - 10*m**2 + 25*m + q + 18*m**4 - 23*m**4 + 2*m**3.
5*(m - 3)*(m - 1)*(m + 1)**3
Let j(o) = -1 + 3*o + 11*o + 4 - 16. Let c be j(5). Factor -57 + c + d**2 - 3*d.
d*(d - 3)
Let n be (-21 - 14471/(-435)) + 16/(-10). Factor 16/3 + n*h + 8*h**2 + 1/3*h**4 + 8/3*h**3.
(h + 2)**4/3
Factor -2101 - 13*w**3 + 2557*w + 526 - 317*w**3 - 900*w**2 - 5*w**4 - 196*w + 449*w.
-5*(w - 1)**2*(w + 5)*(w + 63)
Let r(z) be the third derivative of z**7/2415 - z**6/460 + z**4/69 + 538*z**2 - 1. Determine t, given that r(t) = 0.
-1, 0, 2
Let x(g) be the first derivative of -1/4*g**3 + 5/16*g**4 + 5/2*g + 126 - 13/8*g**2 + 1/20*g**5. Factor x(z).
(z - 1)**2*(z + 2)*(z + 5)/4
Factor 176/3 - 2*v - 2/3*v**2.
-2*(v - 8)*(v + 11)/3
Let h(m) be the first derivative of m**4 + 76*m**3/3 - 2752*m**2 + 52224*m + 4165. Factor h(c).
4*(c - 16)**2*(c + 51)
Factor -7*x**3 - 7*x**4 + 4742*x**2 + x**5 - 4718*x**2 + 33*x**3 + 16*x**4.
x**2*(x + 2)*(x + 3)*(x + 4)
Let a(x) be the third derivative of -x**6/660 - 17*x**5/165 - 265*x**4/132 - 200*x**3/11 + 7*x**2 + 11*x. What is z in a(z) = 0?
-24, -5
Suppose 0 = -13*r + 11*r + 6. Factor -1 + 21*m**3 - 3*m**r + 24*m**2 + 1 + 9*m - 3*m**5.
-3*m*(m - 3)*(m + 1)**3
Let v be (-9 - (7 - 31)) + (0 - 4) - 8. Factor 0 - 5/4*j**2 - 1/4*j**4 + 1/2*j + j**v.
-j*(j - 2)*(j - 1)**2/4
Solve -8/15*k + 2/15*k**2 - 14/5 = 0 for k.
-3, 7
Let k be