r.
1, 8
Suppose -5*f + 8 = -z - 3*z, -3*f - 3*z = -21. Let a(i) = -i**3 - i**2 - 3*i - 1. Let y be a(-2). Factor -3*k**3 + 0*k**4 - k**4 + 12*k - y*k - k**f + 1 + k**2.
-(k - 1)*(k + 1)**2*(2*k + 1)
Let v = 91 - 91. Suppose v*q + 4168 - q**2 - 4152 + 6*q = 0. Calculate q.
-2, 8
Let r(u) be the third derivative of u**5/420 + 95*u**4/21 + 72200*u**3/21 + 41*u**2 + 56*u. Suppose r(a) = 0. What is a?
-380
Let -27990*y**2 - 9500*y + 240*y**5 - 1346 + 207 + 139 - 94*y**4 - 23905*y**3 + 238*y**4 + 136*y**4 = 0. Calculate y.
-10, -2/3, -1/4, 10
Let g(n) = n**2 + 3*n + 1. Let i(p) = -20*p**2 + 116*p + 154. Let d(y) = -36*g(y) - 2*i(y). Factor d(u).
4*(u - 86)*(u + 1)
Let t(j) be the first derivative of -j**4/12 + 182*j**3/9 - 2635*j**2/2 - 11532*j + 851. Find w, given that t(w) = 0.
-4, 93
Let r(b) = -b**3 - 1002*b**2 + 6081*b - 196. Let j be r(6). Factor -8/5 + 1/5*s**3 - 4/5*s + 6/5*s**j - 1/5*s**4.
-(s - 2)**2*(s + 1)*(s + 2)/5
Let -303601/8 + 551/4*k - 1/8*k**2 = 0. Calculate k.
551
Let r be (-6 - (-216)/32)*12. Let t be (r/12)/((-858)/(-208)). Factor 4/11*a - 4/11*a**3 - 2/11*a**2 + t*a**4 + 0.
2*a*(a - 2)*(a - 1)*(a + 1)/11
Let p be (9 - 441/56)/((-87)/(-12) + -7). Factor -3/2*j - p*j**2 + 3/2*j**3 + 9/2.
3*(j - 3)*(j - 1)*(j + 1)/2
Let p = 267 + -265. Let f be ((-112)/(-49) - p)/((-4)/(-28)). Determine o, given that -12/7 + 2/7*o**f + 10/7*o = 0.
-6, 1
Determine a so that 24*a**2 + 14*a**2 - 57*a**2 + 38*a**4 - 2*a**5 + 19*a**2 + 40*a**3 = 0.
-1, 0, 20
Suppose 69740*z = 69751*z. Let s(y) be the first derivative of 33 + 63/5*y**5 - 39/4*y**4 + 6*y**2 - 12*y**3 + z*y. Determine u so that s(u) = 0.
-2/3, 0, 2/7, 1
Factor -54000 - 106*c**3 + 3940/3*c**2 + 4200*c - 8*c**4 + 2/3*c**5.
2*(c - 10)**3*(c + 9)**2/3
Let q(i) be the second derivative of 3/100*i**5 - 81/10*i**2 + 27/10*i**3 - 9/20*i**4 - 44*i + 0. Factor q(x).
3*(x - 3)**3/5
Suppose 64*b + 88 = 86*b. Let n(q) be the second derivative of 3*q - 5/18*q**b - 1/45*q**6 + 2/9*q**3 + 0*q**2 + 2/15*q**5 + 0. Factor n(z).
-2*z*(z - 2)*(z - 1)**2/3
Let h(k) be the first derivative of 2*k**3/21 + 76*k**2/7 + 438*k/7 - 1657. Factor h(f).
2*(f + 3)*(f + 73)/7
Let r = 276 + -276. Suppose r = 8*l - 8*l - 3*l. Determine f so that 1/7*f**3 + 0*f**2 + l + 0*f**4 - 1/7*f**5 + 0*f = 0.
-1, 0, 1
Let y be -1 - -7 - -1 - (3 + 0). Let z(t) be the first derivative of 54*t**2 + 21*t**y + 12 - 212/3*t**3 + 36/5*t**5 - 16*t. Factor z(u).
4*(u - 1)*(u + 4)*(3*u - 1)**2
Let d(k) = -k**3 - 11*k**2 - 30*k + 8. Let c be d(-4). Solve 5 - c*j + 1469*j**2 - 1472*j**2 + 7 = 0.
-6, 2/3
Suppose -5*u + 13 = 3. Suppose f = -0*h - h + 27, -42 = -u*f + 2*h. Factor -f + 4*n**3 + n**2 + 0 + 8 + 11*n**2.
4*(n - 1)*(n + 2)**2
Let g be (-2)/10 + 2212/(-4340). Let x = 314/93 + g. Factor -x*q + 26/9*q**2 + 8/9 + 2/9*q**4 - 4/3*q**3.
2*(q - 2)**2*(q - 1)**2/9
Let 4/3*w**4 - 16/3*w**2 + 14/3*w**3 - 8*w - 2/3*w**5 + 0 = 0. Calculate w.
-2, -1, 0, 2, 3
Suppose 44 = 20*j - 16. Suppose -2*l = -j*p + 6, -10 = -3*p - 2*p. Determine f, given that l*f**2 + 1/5*f + 0 - 1/5*f**3 = 0.
-1, 0, 1
Let x = -5204 + 5207. Let s(q) be the first derivative of 8 - 11/20*q**4 + 3*q**x + 54/5*q - 81/10*q**2 + 1/25*q**5. Let s(f) = 0. What is f?
2, 3
Let a(p) be the first derivative of -5*p**3/3 - 845*p**2/2 - 840*p - 1266. Factor a(m).
-5*(m + 1)*(m + 168)
Let b(i) be the second derivative of -i**4/54 + 257*i**3/27 - 2405*i - 1. Factor b(x).
-2*x*(x - 257)/9
Let h(m) be the first derivative of m**4/2 - 8*m**3/3 - 29*m**2 - 48*m - 533. Suppose h(f) = 0. Calculate f.
-3, -1, 8
Factor -50/3*s**2 + 2/3*s**3 + 392 + 224/3*s.
2*(s - 14)**2*(s + 3)/3
Suppose 44/9*i**3 - 152/9*i + 106/9*i**2 + 2/9*i**4 + 0 = 0. What is i?
-19, -4, 0, 1
Let l be (-6)/(-243)*6/4. Let p(u) be the third derivative of 12*u**2 + l*u**3 + 0*u**4 + 0*u + 0 - 1/270*u**5. Factor p(r).
-2*(r - 1)*(r + 1)/9
Let 1 - 5*u**3 - 1 - 1242*u**2 + 1267*u**2 + 2470*u**2 = 0. Calculate u.
0, 499
Let y(q) be the third derivative of 5*q**2 + 1/210*q**5 + 0*q - 1/21*q**4 + 0 + 1/7*q**3. Factor y(k).
2*(k - 3)*(k - 1)/7
Suppose -2595 = -44*b + 3345. Factor -262*k + b*k - 3 + 9*k**2 + k**3 - 5*k**3 + 137*k.
-(k - 3)*(k + 1)*(4*k - 1)
Let d(t) be the second derivative of -t**6/15 - 7*t**5/8 + 79*t**4/8 + 203*t**3/12 - 65*t**2/4 - 1575*t. Let d(l) = 0. Calculate l.
-13, -1, 1/4, 5
Suppose -189 = 4*b - 395 + 194. Let m(g) be the first derivative of -24*g - 45/2*g**2 + 2*g**b - 1. Factor m(k).
3*(k - 8)*(2*k + 1)
Suppose -65 = 29*i + 80. Let r be (-5)/2*(i + 3). Let 1/8*a**r - 1/2*a + 1/2*a**4 + 0 - 1/2*a**2 + 3/8*a**3 = 0. Calculate a.
-2, -1, 0, 1
Let c be (-9)/(-15)*(91 + -92) + (-32)/(-10). Factor -49/5 + 7*u + 1/5*u**3 + c*u**2.
(u - 1)*(u + 7)**2/5
Let t(o) = o**3 - 77*o**2 + 130*o - 2. Let w(a) = 2*a**3 - 157*a**2 + 256*a - 5. Let m(s) = -10*t(s) + 4*w(s). Factor m(v).
-2*v*(v - 69)*(v - 2)
Let f(n) = -116*n - 926. Suppose 14*j = 20*j + 48. Let x be f(j). Factor 23/3*t + 8/3*t**4 + 34/3*t**2 + 1/3*t**5 + 8*t**3 + x.
(t + 1)**3*(t + 2)*(t + 3)/3
Let j(k) be the second derivative of k**6/900 - 11*k**5/300 - k**3/6 - 47*k**2/2 - 242*k. Let x(y) be the second derivative of j(y). What is d in x(d) = 0?
0, 11
Suppose 28 = 48*v - 70 + 2. Let y(x) be the second derivative of 0 + 1/51*x**3 + 3*x + 0*x**v + 121/170*x**5 - 11/51*x**4. Factor y(u).
2*u*(11*u - 1)**2/17
Let q be (-31967)/7377 - 44/(-6). Factor -5/6*u**q - 59/6*u - 19/3*u**2 + 5.
-(u + 3)*(u + 5)*(5*u - 2)/6
Factor 2/19*y**2 + 32/19*y + 56/19.
2*(y + 2)*(y + 14)/19
Find d, given that 37953*d**3 - 1157*d + 38071*d**3 + 104*d**5 + 313*d + 168 - 74564*d**3 + 972*d**4 - 1860*d**2 = 0.
-7, -3, -1/2, 2/13, 1
Suppose -44 = -147*m + 103*m. Let s(g) be the first derivative of -2*g + 2*g**2 - 2/3*g**3 + m. Factor s(n).
-2*(n - 1)**2
Let t(a) be the second derivative of 0 + 1/28*a**4 + 34/7*a**3 + 1734/7*a**2 - 88*a. Factor t(s).
3*(s + 34)**2/7
Let w(h) be the first derivative of 0*h + 17 + 8*h**2 + 4/3*h**3. Suppose w(x) = 0. What is x?
-4, 0
Let s be 532 + 7/(-35)*5. Let -18*a**4 - s*a + 531*a - a**5 - 81*a**3 = 0. Calculate a.
-9, 0
Let l(w) be the third derivative of 2*w**7/105 + 11*w**6/40 + 91*w**5/60 + 17*w**4/4 + 20*w**3/3 - w**2 - 218. Let l(i) = 0. Calculate i.
-4, -2, -5/4, -1
Let j(h) be the second derivative of -13 + 9/4*h**4 + 169/2*h**2 + 1/20*h**5 + 65/2*h**3 + 3*h. Factor j(r).
(r + 1)*(r + 13)**2
Let l be -113 - -156 - 4280/100. Let s = -3/8 - -23/40. Determine i, given that 0*i - s + l*i**2 = 0.
-1, 1
Suppose 0 = -11*j + 79 + 53. Suppose 28*h**4 + h**2 - j*h**4 + 4*h**3 - 15*h**4 - 6*h**2 + 0*h**2 = 0. What is h?
-5, 0, 1
Let p(a) be the second derivative of -2*a**6/105 + 71*a**5/35 - 58*a**4 - 1152*a**3/7 + 15552*a**2/7 - 10506*a. Determine h, given that p(h) = 0.
-3, 2, 36
Let x(b) be the first derivative of -b**5/20 - 107*b**4/4 + 216*b**3 - 650*b**2 + 868*b - 4452. Factor x(g).
-(g - 2)**3*(g + 434)/4
Let c = -1001 - -1002. Let u(y) be the first derivative of 4/5*y**3 + c + 4/25*y**5 + 0*y**2 + 0*y + 4/5*y**4. Let u(w) = 0. What is w?
-3, -1, 0
Let i be (11 + 455/(-49))/(-2 - -3). Let h(m) be the first derivative of 2/35*m**5 - 4/21*m**3 - 1 - 2/7*m**4 + 18/7*m + i*m**2. Solve h(o) = 0.
-1, 3
Suppose 52 = -13*k + 182. Solve -6*j**3 - 8*j - 18*j - 34*j + k*j**3 - 8*j**2 = 0.
-3, 0, 5
Let j(l) be the first derivative of l**6/6 - 14*l**5/5 + 18*l**4 - 176*l**3/3 + 104*l**2 - 96*l - 1596. Factor j(f).
(f - 6)*(f - 2)**4
Let j = -44580 + 178321/4. Factor 1/4*o - j*o**2 + 3/2.
-(o - 3)*(o + 2)/4
Let r(o) = -14*o**3 - 152*o**2 + 122*o + 292. Let x(f) = -12*f**3 - 151*f**2 + 124*f + 291. Let l(d) = -7*r(d) + 8*x(d). Determine h, given that l(h) = 0.
-1, 2, 71
Let j = 3197/7196 + 550/1799. Let -11/8*f + j*f**2 + 3/4 - 1/8*f**3 = 0. Calculate f.
1, 2, 3
Suppose -2*f = -14*f + 24. Let v be (f/(-2))/(-4 - 1375/(-345)). Let 64*u**4 + 36*u**5 - 16*u**3 - v*u + 69*u = 0. What is u?
-2, 0, 2/9
Let y(f) be the second derivative of 0*f**2 + 4/7*f**3 + 0 + 5/14*f**6 - 9/7*f**4 + 91*f + 9/14*f**5. Determine o, given that y(o) = 0.
-2, 0, 2/5
Let g(d) = -2*d**3 + 17*d**2 + 11*d - 16. Let r be g(9). Factor -25*p**2 + 6*p + 5 + 44*p**r - 18*p**2.
(p + 1)*(p + 5)
Let b be 21/(-56)*(-268)/201. Determine a so that 13/2 - 7*a + b*a**2 = 0.
1, 13
Let s(z) = -3*z + 2. Le