h + 67*h = -2. Find v, given that 4*v**2 - 51*v + 39*v - 3*v**3 + 10*v**2 - 2*v**h = 0.
0, 2
Let i be (9/((-126)/16))/((-7)/((-105)/(-10))). Solve 9/7*z**2 + i + 1/7*z**3 + 20/7*z = 0.
-6, -2, -1
Let w(r) = 81*r**3 - 37*r**2 + 115*r - 7. Let x be w(3). Let d = 2195 - x. Find s, given that 2/3*s - 5/3*s**4 + 5/3*s**2 + 0 + 7/3*s**5 - 3*s**d = 0.
-1, -2/7, 0, 1
Factor -365 + 510 - 662 + c**2 + 1160*c - 645 + c**2.
2*(c - 1)*(c + 581)
Let b(x) = x**3 - x**2 + x - 1. Let h(f) = -7*f**3 + 15*f**2 + 16*f + 6. Suppose -v + 4*n = 10, -5*n = 4*v + v + 25. Let l(j) = v*b(j) - h(j). Factor l(s).
s*(s - 11)*(s + 2)
Let c(h) be the second derivative of -56*h + 5/4*h**3 + 0 - 13/24*h**4 + 7/120*h**5 + 9/4*h**2. Suppose c(x) = 0. What is x?
-3/7, 3
Suppose 35*m - 3711 = -16101. Let t = 354 + m. Solve 2/7*o**3 - 5/7*o**5 + 0*o**2 + 0 + 3/7*o**4 + t*o = 0.
-2/5, 0, 1
Suppose 1/2*u**4 + 0 - 32*u - 38*u**2 - 11/2*u**3 = 0. What is u?
-4, -1, 0, 16
Let k(y) be the second derivative of 0*y**2 + 1/15*y**3 + 20*y - 112/75*y**6 + 7/15*y**7 - 8/15*y**4 + 0 + 39/25*y**5. Find g such that k(g) = 0.
0, 1/7, 1
Let q(n) = -n**2 - 12*n - 17. Let b be q(-7). Suppose -13*o + 7*o = -b. Factor -3*h**2 - 7*h**4 - 9*h**o - 8*h**4 + 27*h**4.
3*h**2*(h - 1)*(4*h + 1)
Let c = -602 + 601. Let z be (c - -7)*((-50)/(-40) - 1). Factor 1/4*s**4 + 3*s + 13/4*s**2 + 1 + z*s**3.
(s + 1)**2*(s + 2)**2/4
Let u be (-10 - ((-11128)/(-80))/(-13))/(364/208). Solve -8/5 - u*p**3 + 0*p + 6/5*p**2 = 0.
-1, 2
Let u(k) = 28*k**3 - 26*k**2 - 28*k + 25. Let v(q) = -q**4 - q**3 + q**2 + q + 1. Let p(i) = 3*u(i) + 3*v(i). Factor p(z).
-3*(z - 26)*(z - 1)**2*(z + 1)
Let w(k) = -k**2 - 16*k - 15. Let i(u) be the first derivative of -2*u**3 - 40*u**2 - 74*u - 8. Let z(r) = -3*i(r) + 14*w(r). Factor z(p).
4*(p + 1)*(p + 3)
Let g(r) = -r**5 + r**4 - 2*r**3 - r**2 - r - 2. Let m(n) = -13*n**5 + 18*n**4 - 52*n**3 - 100*n**2 - 103*n - 58. Let i(l) = 14*g(l) - m(l). Factor i(o).
-(o - 5)*(o + 1)**3*(o + 6)
Let -168507/4 - 3/4*o**2 - 711/2*o = 0. Calculate o.
-237
Let r be 24/33408*328 - (-8)/(-116). Let l(g) be the first derivative of r*g + 0*g**2 - 18 - 1/18*g**3. Factor l(y).
-(y - 1)*(y + 1)/6
Let c(h) be the second derivative of h**7/5 + 109*h**6/75 + 41*h**5/50 - 437*h**4/30 - 154*h**3/5 - 72*h**2/5 - 3401*h. Find b, given that c(b) = 0.
-3, -1, -4/21, 2
Let j(x) be the second derivative of -2*x**3 + 0 + 0*x**2 - 2/15*x**6 - 1/5*x**5 - 21*x + 5/3*x**4. Let j(g) = 0. What is g?
-3, 0, 1
Suppose 8*t - 14*t = -90. Suppose 0 = -t*o + 6*o + 8*o. Solve o*l**2 - 1112*l**4 + 10*l + 6*l**2 + 1104*l**4 - 10*l**3 + 2 = 0 for l.
-1, -1/4, 1
Let c(f) = -4*f**2 - 496*f - 30736. Let p(z) = z**2 - 8. Let o(v) = -c(v) - 2*p(v). What is s in o(s) = 0?
-124
Let 7055/3*c - 6889/3 + 1/3*c**3 - 167/3*c**2 = 0. Calculate c.
1, 83
Let p(x) = 39*x**2 + 19*x + 5. Let z be p(-4). Let u = 4979/9 - z. Solve 4/9*y**2 + u*y + 2/9*y**3 + 0 = 0.
-1, 0
Let t = -15439 + 26141. Let -68*n**2 + 5*n**3 + 11*n**3 - t*n + 10718*n = 0. What is n?
0, 1/4, 4
Let h = -49237 + 442619/9. Let c = h - -58. Let 2/9*u - 2/9*u**3 + 8/9 - c*u**2 = 0. What is u?
-4, -1, 1
Let h(u) = 694 - 769 - u**3 - 37*u**2 + 0*u**3 + 118*u. Let t be h(-40). Determine f, given that -3/5*f**4 + 3/5*f**3 + 0 + 3/5*f**2 - 3/5*f**t + 0*f = 0.
-1, 0, 1
Let a = -1/1652 + 207/826. Let n(k) = -k**2 - 7*k - 3. Let g be n(-1). Factor a*v**2 + 1/4*v - 1/4*v**g - 1/4*v**4 + 0.
-v*(v - 1)*(v + 1)**2/4
Let a(u) = -48*u**3 - 147*u**2 - 6*u + 201. Let y(f) = -7*f**3 - 21*f**2 - f + 29. Let v(z) = 4*a(z) - 27*y(z). Suppose v(m) = 0. What is m?
-7, -1, 1
Suppose -214*f**3 + 29635200 - 2475*f**2 + 70508*f**2 + 4021920*f + 5*f**4 + 50407*f**2 + 1524*f**3 = 0. Calculate f.
-84, -10
Let l(k) be the third derivative of 2028/7*k**3 + 0*k - 122*k**2 - 13/7*k**4 + 1/210*k**5 + 0. Factor l(v).
2*(v - 78)**2/7
Let q(p) = p**3 - p**2 - 2*p. Let g be (70/30 + 6/(-2))*9. Let a(z) = -6*z**3 + 5*z**2 + 11*z. Let b(j) = g*a(j) - 33*q(j). Factor b(v).
3*v**2*(v + 1)
Let b(h) = 23 - 58 + 4*h**2 + 13 + 19 + 35*h - 12*h. Let w be b(-6). Let -42/5*d**w + 0 - 8/5*d + 32/5*d**2 + 18/5*d**4 = 0. Calculate d.
0, 2/3, 1
Let i be 9/((-189)/7)*(-12)/20. Let m(p) = -p**3 + 14*p**2 - 12*p - 13. Let q be m(13). Factor i*y**3 + 1/5*y + 2/5*y**2 + q.
y*(y + 1)**2/5
Let z(j) = 6*j**2 + 22*j - 101. Let m be z(7). Let c = m - 344. Determine x so that 8/7*x**2 + 0 - 2/7*x**c - 8/7*x = 0.
0, 2
Let d = -171/427 - -1623/854. Solve 0 + 1/4*m**3 - 5/4*m**2 + d*m = 0.
0, 2, 3
Let m(d) be the third derivative of -4/3*d**3 - 1/6*d**4 + 0 + 2*d**2 + 1/30*d**6 + 2/15*d**5 + 2*d. Determine k so that m(k) = 0.
-2, -1, 1
Let q = 0 - -2. Let l be (-14)/(-4) + (-3)/q. Factor r**l + 33 + 3 + 0 + 7*r + 5*r.
(r + 6)**2
Let r(s) = -s**3 - 395*s**2 - 1539*s + 9777. Let p be r(-391). Solve 3/2*k**p - 3/2 + 1/2*k**3 - 1/2*k = 0.
-3, -1, 1
Let x(v) be the first derivative of -v**5/12 - 5*v**4/12 + 20*v**3 + 183*v**2/2 + 181. Let h(j) be the second derivative of x(j). Suppose h(b) = 0. What is b?
-6, 4
Let t be 42/(-7) + (-519)/(-1 + 2). Let g = 528 + t. Factor 8/3*i**2 - 10/3*i - 2/3*i**g + 4/3.
-2*(i - 2)*(i - 1)**2/3
Let h = 2804 - 2802. Let z(s) be the first derivative of 9/2*s**h + 39 - 30*s + s**3. Factor z(w).
3*(w - 2)*(w + 5)
Factor 19771*s + 19776*s - 4*s**2 + 36 - 39547*s.
-4*(s - 3)*(s + 3)
Let t(p) be the second derivative of -p**5/240 - p**4/24 + p**3/2 - 51*p**2/2 + 10*p + 2. Let m(w) be the first derivative of t(w). Let m(i) = 0. What is i?
-6, 2
Let t(f) be the third derivative of -f**5/15 - 43*f**4/8 - 377*f**3/6 - f**2 - 246*f. Let t(j) = 0. Calculate j.
-29, -13/4
Let p(w) = -4*w**2 - 27*w - 16. Let m be p(-6). Suppose -5*y + 2 + 8 = 0. Factor -59*a**2 - 6 + 3*a + 31*a**m + 31*a**y.
3*(a - 1)*(a + 2)
Let n(x) = -7*x**2 + 213*x + 787. Let t(j) = -12*j**2 + 419*j + 1573. Let r(d) = 5*n(d) - 3*t(d). Let r(w) = 0. Calculate w.
-4, 196
Suppose -12*f + 5*b = -8*f - 71, 92 = 3*f + 4*b. Factor -d**4 - 8*d**4 + 6*d**3 + 7*d**4 + 12*d**2 - 2*d**4 - 44*d + f + 6*d**3.
-4*(d - 3)*(d - 1)**2*(d + 2)
Find g such that 104/5*g**3 + 2/5*g**2 - 104/5*g - 2/5*g**4 + 0 = 0.
-1, 0, 1, 52
Let q(i) be the second derivative of -i**6/15 - 51*i**5/40 - 107*i**4/24 + 5*i**3/2 + 766*i. Let q(z) = 0. What is z?
-10, -3, 0, 1/4
Let h be -3 - (-4 + 1 + 10/(-5)). Factor 108152*q - 108117*q + 6*q**h - q**2.
5*q*(q + 7)
Suppose 2*l + 4*d = 338, 4*l - 3*l - 177 = 2*d. Factor l - 337*k + 4*k**2 + 3427 + 577*k.
4*(k + 30)**2
Let x(n) = 19237*n - 57709. Let y be x(3). Factor -2/3*q**y + 242/9*q - 80/9.
-2*(q - 40)*(3*q - 1)/9
Suppose 1/3*x**4 + 5/3*x**3 + 2 - 7/3*x**2 - 5/3*x = 0. What is x?
-6, -1, 1
Let k(q) be the first derivative of -11/9*q**3 + 83 + 13/3*q**2 + 1/12*q**4 - 16/3*q. Let k(l) = 0. What is l?
1, 2, 8
Let y(i) = 13*i**2 + 34*i + 6. Let v(x) = x**3 - x**2 - x + 2. Let b(l) = v(l) + y(l). Let u be b(-8). Factor -3/4*m**2 + 3/4 + u*m.
-3*(m - 1)*(m + 1)/4
Let j(y) be the third derivative of 0*y + 2 + 1/12*y**5 - 1/8*y**4 - 1/210*y**7 - 75*y**2 - 1/120*y**6 + 0*y**3. Factor j(w).
-w*(w - 1)**2*(w + 3)
Let i(f) be the first derivative of 27*f**5/5 - 303*f**4/4 - 338*f**3 - 258*f**2 + 168*f + 924. Find k, given that i(k) = 0.
-2, -1, 2/9, 14
Factor 84*t**3 + 26*t + 80*t**2 - 11*t**5 + 13*t**5 - 16*t**4 + 33*t**4 + 15*t**4.
2*t*(t + 1)**3*(t + 13)
Let c(g) be the first derivative of -g**4 + 0*g - 6*g**2 + 27 - 16/3*g**3. Suppose c(m) = 0. Calculate m.
-3, -1, 0
Let c(l) = -10*l + 4. Let t be c(1). Let k be (1*3)/(t/(-36)). Suppose -14*v**3 - 5*v**2 + k*v**3 - v**2 - 6*v**3 - 4*v = 0. Calculate v.
-2, -1, 0
Factor -4410*g - 3402/5*g**2 + 18522/5 - 166/5*g**3 - 8/15*g**4.
-2*(g + 21)**3*(4*g - 3)/15
Let y(i) be the second derivative of 0*i**2 + 0 - 5*i**3 + 1/10*i**5 + 190*i - 1/3*i**4. Factor y(l).
2*l*(l - 5)*(l + 3)
Let h(b) = b**2 + 2*b - 22. Let y be h(-12). Suppose y*c = -57 + 547. Solve 8/3*q**4 - 16/3*q**2 + 4/3*q + 4/3*q**c - 8/3*q**3 + 8/3 = 0.
-2, -1, 1
Let g = 35732 - 315995/9. Let b = g - 621. Factor 5/9*d**4 - 13/9*d**3 + 0 + 4/9*d + b*d**2.
d*(d - 2)*(d - 1)*(5*d + 2)/9
Let w = 222045 - 444081/2. Find u such that 24*u - w*u**2 - 39/2 = 0.
1, 13/3
Let p(x) be the first derivative of -x**3/18 - 29*x**2 - 347*x/6 - 623. Suppose p(v) = 0. What is v