- 16*y**6/15 - 61*y**5/5 - 92*y**4/3 + 800*y**3/3 + 7*y**2 + 53. What is f in q(f) = 0?
-25, -4, 1
Let r be 4329/52 - 5/20. Factor -5*i**2 - 2*i - 65 - 110*i - r*i - 177 + 52.
-5*(i + 1)*(i + 38)
Let u be (-66)/(-30) - (-1 + (-2)/(-10)). Factor -3*o**u + 3*o**5 + 27*o**4 + 7894*o - 7894*o - 27*o**2.
3*o**2*(o - 1)*(o + 1)*(o + 9)
Solve 24/13*m + 54/13*m**4 - 20/13*m**3 - 4/13*m**5 + 2 - 80/13*m**2 = 0 for m.
-1, -1/2, 1, 13
Suppose -c = -2*a - 2*c + 17, -4*a + 3*c = -29. Find p such that -5*p - 4*p**5 + 2*p**2 + 5*p - a*p**4 + 6*p**2 + 4*p = 0.
-1, 0, 1
Suppose 4*f - 54 = 2*g, 9*f - 63105*g = -63109*g + 232. Find s such that 95/4*s**3 + 20*s**2 - 5/2*s**5 + f - 25/4*s**4 - 55*s = 0.
-4, -2, 1/2, 1, 2
Factor 0*d - 11/5*d**3 - 26/5*d**2 + 0 + 1/5*d**4.
d**2*(d - 13)*(d + 2)/5
Let w(j) be the first derivative of 745/3*j**3 - 3*j**5 - 150*j - 425/4*j**4 + 202 - 155/2*j**2. Suppose w(y) = 0. What is y?
-30, -1/3, 1
Let o(r) be the third derivative of r**8/1176 + 13*r**7/735 + 11*r**6/420 - 13*r**5/210 - r**4/7 - 2039*r**2. Let o(x) = 0. What is x?
-12, -1, 0, 1
Let f(n) = -170*n + 1703. Let q be f(10). Let k(o) be the first derivative of -20 + 0*o**2 + 0*o**q - 1/34*o**4 + 0*o. Factor k(b).
-2*b**3/17
Suppose -17*m + 5*m - 48 = 0. Let k(d) = 6*d**2 + 55*d - 78. Let z(u) = 4*u**2 + 28*u - 40. Let x(b) = m*k(b) + 7*z(b). Determine l, given that x(l) = 0.
2, 4
Suppose 0 = 5*b + g - 15, -5*g = -3*b + 1 - 20. Determine a so that 9 + 44*a - 54 - 15 - 2*a**b - 20 = 0.
2, 20
Let t(a) be the second derivative of -5*a**3/3 + 57*a**2 + 13*a - 1. Let s be t(11). Factor 2/3*v**5 + 4*v**3 + 0 - 8/3*v**s + 2/3*v - 8/3*v**2.
2*v*(v - 1)**4/3
Let v(r) be the second derivative of 30*r**2 + 0 - 1/4*r**5 + 40/3*r**3 + 5/4*r**4 - 131*r. Factor v(j).
-5*(j - 6)*(j + 1)*(j + 2)
Let c(z) be the first derivative of 9*z**3 + 1185*z**2 - 528*z - 128. Find x, given that c(x) = 0.
-88, 2/9
Suppose 0 = -f - 5*d + 15, 3*f = -16*d + 13*d + 9. Let l(z) be the first derivative of 0*z**4 + f*z**2 - 3 + 1/5*z**5 - 2/3*z**3 + z. Factor l(w).
(w - 1)**2*(w + 1)**2
Let x(n) be the second derivative of -2/25*n**5 + 0*n**2 - 1/5*n**3 + 13/30*n**4 + 0 - 31*n. Factor x(k).
-2*k*(k - 3)*(4*k - 1)/5
Let a(d) be the first derivative of -2/7*d - 1/14*d**2 - 43 + 1/21*d**3. Find p such that a(p) = 0.
-1, 2
Let h(n) be the first derivative of -3*n**4/16 - 271*n**3 - 415. Factor h(j).
-3*j**2*(j + 1084)/4
Let x be 36/45 + ((-3328)/(-585))/(-16). Find l such that 0 - 2/9*l**3 + 2/3*l**2 - x*l = 0.
0, 1, 2
Factor 0*n + 2/7*n**4 + 4/7*n**3 + 2/7*n**2 + 0.
2*n**2*(n + 1)**2/7
Solve 0 - 500/3*u + 254/3*u**2 - 2/3*u**3 = 0.
0, 2, 125
Let z(y) be the second derivative of y**5/160 + 3*y**4/32 - 7*y**3/16 - 33*y**2/2 + 15*y + 1. Let q(j) be the first derivative of z(j). Factor q(x).
3*(x - 1)*(x + 7)/8
Let c(f) be the first derivative of 1/34*f**4 - 42/17*f - 46/51*f**3 - 52 + 43/17*f**2. Factor c(u).
2*(u - 21)*(u - 1)**2/17
Let u = -40 + 36. Let b be -5*2/(-20)*-1 - u. Solve -9/2*f - b*f**2 - 1 = 0.
-1, -2/7
Suppose -3*d = 4*x - 0*x + 257, -15 = -3*d. Let o = 73 + x. Factor -16*g**3 - g**5 - 4*g**4 - g**o + 14*g**3.
-2*g**3*(g + 1)**2
Let x = 7473 + -291445/39. Let z(w) be the second derivative of 1/130*w**5 + 17*w + 1/26*w**4 + x*w**3 + 0 + 0*w**2. Find n, given that z(n) = 0.
-2, -1, 0
Let x(w) = -w**3 + w - 1. Let o(v) = 24*v**3 + 153*v**2 + 2499*v + 13221. Let l(n) = o(n) + 21*x(n). Find a such that l(a) = 0.
-20, -11
Let y = -683988 + 683996. Solve -y - 4/9*m**2 + 76/9*m = 0 for m.
1, 18
Let a be -1 + 5 + (8 - 21). Let c be 3/a + 32/6. Suppose 15*g + 5*g - 5*g**2 - 30*g - c = 0. Calculate g.
-1
Let j(i) be the second derivative of 3*i**7/14 + 4*i**6 - 239*i**5/20 - 33*i**4/2 + 94*i**3/3 + 60*i**2 - 185*i - 5. Solve j(x) = 0 for x.
-15, -2/3, 1, 2
Let z(c) be the third derivative of c**5/12 - 10355*c**4/6 + 42890410*c**3/3 - 1559*c**2. What is f in z(f) = 0?
4142
Let m = 29 + -26. Let u be 6*2/m*(0 - -9). Suppose -19*c + 162*c**3 - 10*c - u*c**2 - 11*c + 16 - 108*c**4 = 0. What is c?
-1/2, 2/3
Let y(w) = -7*w**4 + 116*w**3 - 66*w**2 + 126*w + 108. Let v(b) = 6*b**4 - 106*b**3 + 66*b**2 - 126*b - 108. Let d(q) = -13*v(q) - 12*y(q). Factor d(c).
2*(c - 3)**2*(c + 3)*(3*c + 2)
Let z = -1699 - -664. Let a = -5167/5 - z. Solve -1/5*p**3 + 0 + a*p - 7/5*p**2 = 0.
-8, 0, 1
Let m be (5 + (-50)/12)/(75/45). Solve 2*y**3 - m*y**4 - 5/2*y**2 + 0 + y = 0.
0, 1, 2
Let g = 319 - 321. Let f(q) = 12*q**2 - 897*q + 16428. Let u(r) = 3*r**2 - 224*r + 4107. Let j(m) = g*f(m) + 9*u(m). Factor j(c).
3*(c - 37)**2
Let x(t) be the third derivative of 2*t**7/245 + 11*t**6/105 + 47*t**5/105 + 2*t**4/7 - 24*t**3/7 + t**2 + 48. Determine r so that x(r) = 0.
-3, -2, 2/3
Let j(h) be the second derivative of h**5/4 - 3005*h**4/6 + 899990*h**3/3 + 1812020*h**2 - 6264*h. Factor j(b).
5*(b - 602)**2*(b + 2)
Let z(d) be the first derivative of -2*d**5/55 + 23*d**4/22 - 12*d**3/11 - 92*d**2/11 + 16*d + 889. Suppose z(m) = 0. Calculate m.
-2, 1, 2, 22
Determine h, given that -8*h**3 + 337 + 19*h**3 - 19*h**2 + 7*h**4 + h**5 - 373 - 60*h = 0.
-3, -2, -1, 2
Let t(q) be the first derivative of -7/22*q**4 + 12/11*q + 34/33*q**3 - 87 + 2/55*q**5 - 17/11*q**2. Suppose t(w) = 0. What is w?
1, 2, 3
Let s(z) be the second derivative of -z**6/10 - 201*z**5/5 - 12015*z**4/2 - 364366*z**3 - 2114907*z**2/2 - 876*z. Factor s(b).
-3*(b + 1)*(b + 89)**3
Let v be -3*(1 - (-26)/(-3)). Suppose -2*h - v = -63. Determine i so that -2*i**2 + 3*i**2 + h*i - 3*i**2 - 3*i**2 = 0.
0, 4
Let v(k) be the first derivative of 0*k - 12 - 1083/2*k**2 - 38*k**3 - 3/4*k**4. Let v(y) = 0. What is y?
-19, 0
Suppose -3*r + 4 = g, 3*g - 22394 = -r - 22414. Let 3/2*z**r + 307/2*z**2 - 53/2*z**3 + 147 - 623/2*z = 0. What is z?
2/3, 3, 7
Let y be 2/(-12)*-3*8. Let h = 12 - 8. Determine a, given that -a**5 - 84*a**h - 80*a**y + 166*a**4 - a**3 = 0.
0, 1
Let q(w) be the first derivative of -w**4/42 - 62*w**3/21 - 961*w**2/7 + 54*w - 101. Let r(i) be the first derivative of q(i). Factor r(p).
-2*(p + 31)**2/7
Determine o so that 168/5 - 3/5*o**3 + 54/5*o**2 - 36*o = 0.
2, 14
Let i = 179523 - 179519. Factor 0 + 12/7*f**3 - 2/21*f**5 + 0*f**2 - 2/7*f**i + 0*f.
-2*f**3*(f - 3)*(f + 6)/21
Suppose -616*r + 331*r = -452*r + 36072. Find w, given that r + 24*w + 2/3*w**2 = 0.
-18
Let r(s) = -2*s - 30. Let w be r(-8). Let d(a) = -a**2 - 17*a - 39. Let p be d(w). Factor 0*c - 2/11*c**2 + 4/11*c**p - 2/11*c**4 + 0.
-2*c**2*(c - 1)**2/11
Let b = 60679 - 546017/9. Determine a, given that 98/9*a**2 + 26/9*a**3 - 2/3*a**4 + b*a + 28/9 = 0.
-1, -2/3, 7
Let g = 2712 + -2709. Let n(h) be the first derivative of 16 - 1/3*h**g + 2/3*h + 1/15*h**5 - 1/12*h**4 + 1/6*h**2. Solve n(i) = 0 for i.
-1, 1, 2
Determine j, given that -184/7*j**3 - 16192/7*j - 4584/7*j**2 - 15488/7 - 2/7*j**4 = 0.
-44, -2
Let a(w) be the third derivative of w**8/672 + w**7/42 + 2*w**6/15 + 19*w**5/60 + 5*w**4/16 - 4*w**2 - 258. Factor a(h).
h*(h + 1)**2*(h + 3)*(h + 5)/2
Suppose 2 = -2*z + s, -2*z = 10*s + 1258 - 1322. Factor 57*r + 3/2*r**z + 1083/2.
3*(r + 19)**2/2
Let k be 10071/135 - 2/(-5). Determine q, given that 145*q - k + 151*q**3 + 18*q**2 - 83*q**2 - 156*q**3 = 0.
-15, 1
Suppose -5*p = 85*l - 89*l - 96, -3*l = -3. What is z in -4/5 - 125*z**2 + p*z = 0?
2/25
Let h(d) be the third derivative of d**5/210 + 1019*d**4/42 + 1038361*d**3/21 - 27*d**2 - 3*d - 9. Factor h(s).
2*(s + 1019)**2/7
Let k = 3402 - 3396. Let m(o) be the second derivative of 0*o**2 + 0*o**3 + 0 + 2/63*o**7 + 0*o**5 + 15*o + 2/45*o**k + 0*o**4. Factor m(g).
4*g**4*(g + 1)/3
Let d(g) = g**5 - 27*g**4 + 34*g**3 + 6*g**2 - 29*g + 9. Let z(a) = -a**5 + 2*a**4 + a**3 + a**2 - 2*a + 1. Let j(o) = -d(o) - 3*z(o). What is b in j(b) = 0?
-12, -1, 1/2, 1
Determine k so that -5/3*k**3 - 37/3*k**2 - 44/3*k - 4 = 0.
-6, -1, -2/5
Let q(v) = 2*v**3 - 72*v**2 - 190*v - 131. Suppose h + 4*h + 25 = 0. Let y(t) = -3*t**3 + 144*t**2 + 381*t + 261. Let b(i) = h*y(i) - 9*q(i). Factor b(x).
-3*(x + 1)*(x + 2)*(x + 21)
Let o(l) be the third derivative of 0*l**3 - 1/350*l**7 + 0*l**4 + 3/100*l**5 + 0*l + 0 - 115*l**2 + 1/100*l**6. Factor o(h).
-3*h**2*(h - 3)*(h + 1)/5
Let i(d) be the first derivative of d**4/4 + 11*d**3 + 67*d**2/2 + 220*d + 304. Let u be i(-31). Fact