11 = 0.
-15, -26/9
Let r(s) be the second derivative of -s**6/95 + s**5/190 + 52*s**4/57 + 236*s**3/57 + 112*s**2/19 - 6151*s. Find n such that r(n) = 0.
-4, -2, -2/3, 7
Find z such that -2/9*z**3 - 230/9*z**2 - 6272/3 - 6944/9*z = 0.
-56, -3
Let p(i) = i**2 - 8*i + 19. Let a be p(2). Let z be (8 - a)*3 + (-9)/12. Factor 21/8*x - 3/8 - z*x**2.
-3*(x - 1)*(6*x - 1)/8
Let l(t) be the second derivative of -t**8/6720 - t**7/560 - t**6/160 + 43*t**3/6 - t + 10. Let b(p) be the second derivative of l(p). Factor b(c).
-c**2*(c + 3)**2/4
Let f(g) = -29*g**3 - 12*g**2 + 23*g - 14. Let j(n) = n**4 - 52*n**3 - 24*n**2 + 46*n - 27. Let z(h) = 7*f(h) - 4*j(h). Solve z(d) = 0 for d.
-2, 1, 5/4
Suppose -2124*o + 2131*o - 84 = 5*r, 3*o + 2*r = -22. Find g such that 2*g - 1/3*g**4 + 1/3*g**5 + 1/3*g**o + 0 - 7/3*g**3 = 0.
-2, -1, 0, 1, 3
Let z(g) be the second derivative of -35/2*g**2 + 0 - 25/12*g**4 + 101*g + 30*g**3. Factor z(n).
-5*(n - 7)*(5*n - 1)
Factor -45*k**2 + 169*k**2 + k**3 + 126*k - 21*k**2 + 26*k - 76*k**2.
k*(k + 8)*(k + 19)
Let y = -2860 - -2860. Let n(i) be the third derivative of 0*i + 4*i**2 + y*i**3 + 0*i**5 + 0*i**6 + 0*i**4 + 1/840*i**7 + 0. Determine q so that n(q) = 0.
0
Let r(f) be the second derivative of -f**5/210 + f**4/126 + 22*f**3/63 - 40*f**2/21 + 2*f - 257. What is m in r(m) = 0?
-5, 2, 4
Let f(s) = 4*s**4 + 1354*s**3 - 8190*s**2 + 16438*s - 11066. Let v(g) = -g**3 + g**2 - g + 15. Let i(a) = -f(a) - 6*v(a). Let i(l) = 0. What is l?
-343, 2
Let s(d) be the first derivative of -7/25*d**5 + 0*d**2 + 78 + 0*d - 1/6*d**6 + 0*d**3 - 1/10*d**4. Factor s(v).
-v**3*(v + 1)*(5*v + 2)/5
Let n(k) be the first derivative of -5*k**4/12 + 140*k**3/9 + 155*k**2/2 - 6916. Solve n(v) = 0 for v.
-3, 0, 31
Let o(f) be the second derivative of f**5/4 + 15*f**4/2 + 355*f**3/6 + 195*f**2 + 852*f - 6. Suppose o(d) = 0. Calculate d.
-13, -3, -2
Let t(r) = -6*r**2 - 5160*r - 2182833. Let h(q) = q**2 + 14*q + 2. Let a(o) = -3*h(o) - t(o). Factor a(d).
3*(d + 853)**2
Let g = 6645/4432 + 3/4432. Factor -1 - 3*x - 1/4*x**4 - g*x**3 - 13/4*x**2.
-(x + 1)**2*(x + 2)**2/4
Let p(g) be the second derivative of g**5/90 - 19*g**4/27 + 29*g**3/3 - 198*g + 20. Factor p(o).
2*o*(o - 29)*(o - 9)/9
Suppose -j = 45*j + 56*j - 321 - 87. Solve -19/6*o**j + 64/3*o**3 - 166/3*o**2 + 16*o + 96 + 1/6*o**5 = 0.
-1, 4, 6
Suppose -15 - 33 = -12*l. Factor -449*k**4 + 19*k**3 - 67*k**3 + 452*k**l.
3*k**3*(k - 16)
Let y = 220 - 218. Factor -6*r**3 + 5*r**y - 23 - r**4 + 4*r**4 - 2*r**4 + 24*r - 13.
(r - 3)**2*(r - 2)*(r + 2)
Let p(l) be the first derivative of -8/9*l**3 - 1/2*l**2 - 1/4*l**4 + 2/3*l + 21. Suppose p(z) = 0. Calculate z.
-2, -1, 1/3
Let h(j) be the first derivative of 7*j**3 - 6*j**3 - 12 + 65*j**2 + 36 + 76*j**2 + 6627*j + 52. Let h(a) = 0. What is a?
-47
Let v = -72 - -69. Let o(b) = -8*b**2 + 5*b + 77. Let n(l) = 4*l**2 - 3*l - 39. Let f(z) = v*o(z) - 5*n(z). What is a in f(a) = 0?
-3, 3
Let l(b) be the third derivative of -5/8*b**4 + 0*b**3 + 24*b**2 - 1/20*b**5 + 0 + 0*b. Let l(g) = 0. What is g?
-5, 0
Let a(g) be the second derivative of 1/5*g**5 + 0*g**2 + g + 34 - 2/3*g**4 + 0*g**3. Factor a(y).
4*y**2*(y - 2)
Let a be 77/35*10/2. Let a + 33*w - 9*w**2 - 30*w**4 + 23*w**4 + 19*w**4 - 48*w**3 + 1 = 0. Calculate w.
-1/2, 1, 4
Let m(f) = 14*f**2 - 2945*f - 2172676. Let c(o) = 5*o**2 + o. Let r(j) = 15*c(j) - 5*m(j). Determine y so that r(y) = 0.
-1474
Let j = -169 - -196. Factor 28*p**3 - 39 + 8*p + 43*p**2 + 86*p**2 - 2*p**4 - j*p**2 - 97.
-2*(p - 17)*(p - 1)*(p + 2)**2
Let h(m) be the third derivative of -m**9/20160 - m**8/1680 - m**7/420 - 169*m**5/60 - m**2 + 4. Let q(t) be the third derivative of h(t). Factor q(b).
-3*b*(b + 2)**2
Let j(z) = 17*z + 94. Let h be j(8). Let f = h + -230. Factor 2/21*y**2 + 0*y + f.
2*y**2/21
Suppose -2/3*n**3 - 32/3 - 2/3*n**4 - 8/3*n + 8*n**2 = 0. Calculate n.
-4, -1, 2
Let q(f) be the first derivative of -1/27*f**3 - 62 + 1/3*f - 1/9*f**2. Factor q(a).
-(a - 1)*(a + 3)/9
Let r(k) be the second derivative of -1/3*k**4 + 0*k**2 - 113*k - 2*k**3 + 0. Determine l so that r(l) = 0.
-3, 0
Find p, given that 770*p**2 - 34380*p**3 - 884*p + 119*p + 34375*p**3 = 0.
0, 1, 153
Let k(g) be the second derivative of g**5/8 - 10*g**4/3 - 175*g**3/12 - 45*g**2/2 + 1502*g. Find b such that k(b) = 0.
-1, 18
Let m(b) be the first derivative of 6*b**3 - 15 - 5*b - 1/4*b**4 - 54*b**2. Let t(z) be the first derivative of m(z). Factor t(k).
-3*(k - 6)**2
Factor 0*c + 2*c**2 + c**2 - 28*c - 313 - 164 - 122*c.
3*(c - 53)*(c + 3)
Let x(a) = 29*a + 172. Let i be x(-6). Let s be ((-3)/3 - i)*40/180. Suppose -s*w**2 + 4/9 + 2/9*w = 0. What is w?
-1, 2
Let f(l) be the third derivative of 0 - 1/76*l**4 - 154*l**2 + 4/57*l**3 - 1/570*l**5 + 0*l. Find x, given that f(x) = 0.
-4, 1
Let x(j) be the second derivative of -111*j - 1/10*j**5 + 0 - 39/2*j**4 - 1521*j**3 - 59319*j**2. Factor x(s).
-2*(s + 39)**3
Factor 93 - 1/2*h**3 - 16*h**2 - 25/2*h.
-(h - 2)*(h + 3)*(h + 31)/2
Let k(i) = i**3 - 56*i**2 + 612*i + 49. Let a be k(15). Factor 3/7*v**5 + 0 - 9/7*v + 0*v**a - 18/7*v**3 + 24/7*v**2.
3*v*(v - 1)**3*(v + 3)/7
Let t(l) be the third derivative of -l**6/1200 + 28*l**5/75 - 784*l**4/15 - l**2 + 594*l. Determine o, given that t(o) = 0.
0, 112
Let i(b) be the third derivative of b**8/672 - b**7/420 - b**6/48 + b**5/24 + b**4/12 - b**3/3 + 5*b**2 + 2*b + 5. Suppose i(w) = 0. Calculate w.
-2, -1, 1, 2
Let y be (-2)/3 - 102/(-18). Suppose 4*k - y = 7. Suppose 0*w**4 - k*w**5 + 0*w**4 + 7*w**3 + 2*w**3 + 6*w - 3*w**4 + 15*w**2 = 0. What is w?
-1, 0, 2
Let k = 18/985 - -50091/7880. Suppose -3/8*i**4 - 9/4 - k*i - 51/8*i**2 - 21/8*i**3 = 0. Calculate i.
-3, -2, -1
Let i = 649 - -96. Suppose -673 = -g + 2*n, -2*g - 2*n + 583 = -i. Solve 405*q**3 + 82*q**2 - 20 + 173*q - g*q**2 + 27*q = 0 for q.
2/9, 1
Let r(d) = 19*d + 27. Let h be r(8). Factor -170 - 27*l - 284*l**3 - 46*l**2 - 64*l**5 + 240*l**4 + h*l**2 + 85 + 87.
-(l - 2)*(l - 1)*(4*l - 1)**3
Determine z so that 956*z - 1761*z**2 + 4*z**3 - 1829*z**2 + 6400 + 724*z + 3734*z**2 = 0.
-16, -10
Let y(a) be the first derivative of 2*a**5/5 + 26*a**4 - 214*a**3/3 + 54*a**2 + 50. Factor y(r).
2*r*(r - 1)**2*(r + 54)
Let k(d) be the second derivative of 5*d - 7 + 1/25*d**5 + 0*d**2 - 8/15*d**3 + 1/2*d**4. Solve k(j) = 0.
-8, 0, 1/2
Let b(k) be the first derivative of 1/6*k**4 + 1/15*k**5 + 0*k + 29 - 1/3*k**2 - 1/9*k**3. Factor b(a).
a*(a - 1)*(a + 1)*(a + 2)/3
Let t(a) be the first derivative of -a**6/120 - a**5/30 - a**4/24 + 3*a**2/2 - 5*a + 103. Let z(g) be the second derivative of t(g). Solve z(b) = 0.
-1, 0
What is y in -1017/4 - 507/2*y + 3/4*y**2 = 0?
-1, 339
Let 5*j**4 + 233*j**2 + 12*j**4 - 3*j**4 - j**5 - 193*j**2 - 44*j**3 = 0. Calculate j.
0, 2, 10
Let h(f) be the first derivative of 5*f**4/4 - 455*f**3/3 + 665*f**2 - 880*f + 2868. Suppose h(n) = 0. Calculate n.
1, 2, 88
Let g be ((-19)/(-4) - (-104)/(-26))/((-2313)/(-1028)). Suppose 0 + 1/3*x + g*x**2 = 0. Calculate x.
-1, 0
Let y = -419231/28 + 63185/4. Determine w, given that -y + 372/7*w - 6/7*w**2 = 0.
31
Let t(p) be the second derivative of -p**6/15 + 51*p**5/10 - 167*p**4/2 - 659*p**3/3 + 1110*p**2 + 9800*p. Find o such that t(o) = 0.
-2, 1, 15, 37
Suppose 3*p = 5*y - 135, p - 4*y = 4*p + 108. Let l be 7/(210/p) + 1 + 1. Suppose 0 - 1/3*b**5 + 4/3*b**4 + l*b**2 - 5/3*b**3 + 0*b = 0. Calculate b.
0, 1, 2
Suppose 0 = -21*m + 91*m - 35*m - 18*m. Let b(d) be the third derivative of -1/1020*d**6 + 0*d**4 - 1/170*d**5 - 31*d**2 + 0*d**3 + m + 0*d. Factor b(q).
-2*q**2*(q + 3)/17
Let 1/4 - 49/8*g**2 - 47/8*g = 0. What is g?
-1, 2/49
Let a(s) = s**2 + s + 1. Let z = 3 + -4. Let o(c) = 20*c**2 + 16*c. Let n(d) = z*o(d) + 4*a(d). What is v in n(v) = 0?
-1, 1/4
Find n, given that -116*n**2 - 123*n**2 - 2010*n + 475*n**2 - 121*n**2 - 120*n**2 = 0.
-402, 0
Let i(q) be the second derivative of -q**4/6 - 6646*q**3/3 - 11042329*q**2 + 31*q - 81. Determine f, given that i(f) = 0.
-3323
Let h(g) be the third derivative of g**7/490 + g**6/168 + g**5/280 + 215*g**3/6 + 107*g**2. Let v(m) be the first derivative of h(m). Factor v(x).
3*x*(x + 1)*(4*x + 1)/7
Let b(i) = 2*i**2 + 137*i + 159. Let a be b(-62). Let s = a + 647. Determine u so that 1/7*u**3 + 0*u + 3/7*u