z**5 - 1/2*z**4. Suppose u(s) = 0. What is s?
-2, 1, 3
Let b = 45126 - 586636/13. Factor -b*o**3 - 154/13*o - 32/13*o**2 - 196/13.
-2*(o + 2)*(o + 7)**2/13
Suppose -4*m = -8, 3*a = 3*m + 20 + 124. Let v = -45 + a. Factor -5*n**4 - 105*n**3 - v + 10*n**2 - 4*n**5 + 95*n**3 + 5*n + 9*n**5.
5*(n - 1)**3*(n + 1)**2
Suppose 728*m = 729*m - 36. Let l be (-48)/14 - (-3)/(27/m). Let -2/7*c**5 + 2/7*c + 0 + l*c**4 - 4/7*c**2 + 0*c**3 = 0. What is c?
-1, 0, 1
Suppose s - 1607 = 3*g, 3*g + 3351 = 2*s + 122. Let u = 1622 - s. Factor -1/4*t**3 - 1/4*t**2 + u + 1/2*t.
-t*(t - 1)*(t + 2)/4
Let o(w) be the second derivative of w**9/25704 - w**8/4760 + w**7/3570 - 23*w**3/2 + 102*w. Let p(h) be the second derivative of o(h). Factor p(b).
2*b**3*(b - 2)*(b - 1)/17
Let b be ((-1)/(-6))/(6/108). Let w(q) be the first derivative of -2*q**4 + 20/3*q**b - 8*q - 2*q**2 + 8. Find a such that w(a) = 0.
-1/2, 1, 2
Factor -546*p**2 - 29523*p - 2*p**4 - 29371*p + 62422*p - 76*p**3.
-2*p*(p - 4)*(p + 21)**2
Let f(z) be the third derivative of -z**7/630 + z**6/36 - z**5/20 - 13*z**4/18 - 16*z**3/9 + 6*z**2 - 247*z. Determine j so that f(j) = 0.
-1, 4, 8
Let s be 17408/(-11424)*27/(-8). Let l be 146/70 + (-2)/(-10). Determine b, given that 12*b + s + l*b**3 + 64/7*b**2 = 0.
-3/2, -1
Let t = -64 - -70. Suppose -5*l = -m - 48, 5*l - m = -t*m + 60. Factor 6*x**2 + 10*x**3 + 4*x**2 - 5*x**4 - l*x**2.
-5*x**3*(x - 2)
Let y(w) be the second derivative of -w**6/6 + 2*w**5 - 25*w**4/12 - 125*w**3/3 - 21*w + 2. Factor y(i).
-5*i*(i - 5)**2*(i + 2)
Suppose 118*c - 106*c = 60. Let r(j) be the second derivative of -1/14*j**3 + 0*j**4 + 0*j**2 + 3/140*j**c + 0 + 15*j. Factor r(h).
3*h*(h - 1)*(h + 1)/7
Factor 402000*y - 5*y**4 - 779*y**3 - 237296 - 1221*y**3 + 35291 - 197990*y**2.
-5*(y - 1)**2*(y + 201)**2
Let v = -607 + 656. Let a be 212/(-252) - (-14)/v - -1. Factor a + 2/9*k**2 + 2/3*k.
2*(k + 1)*(k + 2)/9
Suppose 3*h - 5*w = 67, 4*h + 3*w = 7*w + 76. Let j be (6/(-20))/((336/(-20))/h). Let 0*g + 0 + 1/4*g**4 - j*g**5 + 1/4*g**3 - 1/4*g**2 = 0. What is g?
-1, 0, 1
Suppose 259/6*o**2 - 18 - 83/2*o + 101/6*o**3 - 1/2*o**4 = 0. Calculate o.
-3, -1/3, 1, 36
Let x = 23 + -13. Suppose -2 = 4*q - x. Factor -4*r + 0*r**q + 9*r + 7*r + 3*r**2.
3*r*(r + 4)
Let u(o) be the second derivative of 3*o**7/98 + 23*o**6/70 - 327*o**5/140 + 17*o**4/28 + 33*o**3/7 + 7866*o. Determine n, given that u(n) = 0.
-11, -2/3, 0, 1, 3
Let p(r) be the second derivative of -9/2*r**3 - 73*r + 0 + 57/4*r**2 - 1/8*r**4. What is b in p(b) = 0?
-19, 1
Let d = 5190 + -5184. Let n(p) be the first derivative of 49 + 0*p - 2*p**5 + 0*p**2 + 0*p**4 + 5/6*p**d + 0*p**3. Factor n(z).
5*z**4*(z - 2)
Let g(b) = -9*b**2 - 24*b + 4. Let m be g(-4). Let x be ((-22)/m)/((-5)/(-96)). Factor 18/5*n**2 - 2/5*n**3 + 32/5 - x*n.
-2*(n - 4)**2*(n - 1)/5
Factor 4/9*t**4 + 0 - 56/3*t - 40/9*t**3 - 212/9*t**2.
4*t*(t - 14)*(t + 1)*(t + 3)/9
Let j(z) = z**2 + 345*z + 1368. Let r be j(-4). Let q be (0 - -60) + 0 + 0. What is v in -2*v**2 - 8*v**3 + 0*v**2 - r*v**2 - v**3 + q*v**4 = 0?
-1/4, 0, 2/5
Suppose 4*o + o - 165 = 0. Let g(p) = -40*p - 103*p - 15*p**2 - 225 - 97*p. Let d(k) = -k**2 - 15*k - 14. Let r(h) = o*d(h) - 2*g(h). Factor r(u).
-3*(u + 1)*(u + 4)
Let a be ((-900)/(-40))/(-15)*8/(-3). Let b(o) be the second derivative of 0*o**2 + 0 - 10/3*o**3 + 55/3*o**a + 19*o - 121/4*o**5. Solve b(l) = 0.
0, 2/11
Suppose -4*t = 5*f - 19 - 0, -t + 4*f = -10. Find s such that s**4 - t*s**5 + 15*s**2 + 10*s**4 + 6*s - 26*s**4 = 0.
-2, -1, -1/2, 0, 1
Let n(p) be the second derivative of -1/15*p**3 + 0*p**2 + 122 - 1/120*p**4 - 2*p. Find h such that n(h) = 0.
-4, 0
Let t(l) be the second derivative of -2*l**6/135 - 101*l**5/30 + 383*l**4/27 - 205*l**3/9 + 154*l**2/9 - 1322*l. Determine g, given that t(g) = 0.
-154, 1/2, 1
Let f be ((-9)/(-6))/(3/68). Suppose -2*i + 0*u - 4*u = -f, 0 = -3*u + 15. Solve -5 + i + 3*c**3 - 2 = 0.
0
Let n be 2 - 1*4968/16. Let t = 309 + n. Suppose 0*s + 0 - s**3 - t*s**4 + 0*s**2 + 3/2*s**5 = 0. What is s?
-2/3, 0, 1
Let w be (0 - (-20)/495)*(13 - (-255)/(-30)). Factor -w*n**4 - 20/11*n**3 + 0 + 2*n**2 + 0*n.
-2*n**2*(n - 1)*(n + 11)/11
Let j(r) be the second derivative of -r**6/45 + r**5/2 + 16*r**4 + 108*r**3 - 609*r. Find b, given that j(b) = 0.
-6, 0, 27
Let f = 20990/3 - 6984. Let v(h) be the second derivative of -16*h**2 + 0 - 12*h - 5*h**5 - f*h**4 - 56/3*h**3 - 16/15*h**6 - 2/21*h**7. Factor v(l).
-4*(l + 1)**2*(l + 2)**3
Suppose 2*y - 26 = -2*k, -2*k + 60 - 43 = -y. Determine b, given that 0 + 2/5*b**4 + 4/5*b**y - 16/5*b - 8/5*b**2 = 0.
-2, 0, 2
Solve -928 - 333*b - 977 - b**2 + 11*b**2 + 953*b - 5*b**2 = 0 for b.
-127, 3
Let p be ((-2)/21)/((-72)/28*(-10)/(-140)). Let a(x) be the first derivative of 6 + 1/18*x**4 + 10/9*x + 11/9*x**2 + p*x**3. Find u, given that a(u) = 0.
-5, -1
What is f in 1088/11 - 2/11*f**4 - 68/11*f**3 - 606/11*f**2 - 412/11*f = 0?
-17, -16, -2, 1
Let s = -247537 - -495089/2. Let s + 5*y - 5/2*y**2 = 0. Calculate y.
-1, 3
Suppose 2*q + 5*n - 2*n = 6, n = 0. Factor k**5 + k**3 - 6*k**4 + 9*k**q - 14*k**3 + 16*k**2 - 6*k**3 + 33*k + 0*k**5 + 14.
(k - 7)*(k - 2)*(k + 1)**3
Let t(l) = l**3 + 8*l**2 + l. Let o(f) = -80*f**2 - 500*f - 738. Let m(q) = 2*o(q) - 2*t(q). Solve m(z) = 0 for z.
-82, -3
Let m(c) be the third derivative of -17*c**2 - 1/420*c**8 + 0*c**4 + 2/525*c**7 - 1/75*c**5 + 0*c**3 + 0*c + 1/150*c**6 + 0. Let m(i) = 0. What is i?
-1, 0, 1
Suppose 4*u - 4 = 4*l, -2*u + l = -3 - 2. Suppose 0 = 12*n - 9*n + u*z + 8, 0 = -4*z - 20. Solve -n*w**2 - 50 + w**2 - 58 - 25*w - 11*w = 0.
-6
Let w = 182/129 - 139/129. Solve -1/9*i**2 + 1/9 + 1/3*i**3 - w*i = 0 for i.
-1, 1/3, 1
Let f(b) = -b**2 + 142*b + 2017. Let o be f(-13). Factor -3/2*j**o + 0 + 3/2*j.
-3*j*(j - 1)/2
Suppose 7*x - 11*x + 5*g = -337, 2*x - 161 = -5*g. Factor -32*y - 42*y**2 - 120 - x*y + 84*y**2 - 37*y**2.
5*(y - 24)*(y + 1)
Solve 164/3*b - 1/3*b**5 - 12*b**4 + 0 - 108*b**2 + 197/3*b**3 = 0.
-41, 0, 1, 2
Factor 11*v**3 - 2*v**3 - 8*v**3 + 729 + 1008*v + 275 + 255*v**2.
(v + 2)**2*(v + 251)
Let l(p) be the first derivative of -16*p**3 + 6*p**4 + 44 - 12*p + 20*p**2 - 4/5*p**5. Factor l(s).
-4*(s - 3)*(s - 1)**3
Suppose 0 = -25*i + 38*i + 273. Let b(l) = -2*l**4 - 8*l**3 + 13*l**2 - 6*l + 14. Let x(z) = -z**3 + 2. Let o(w) = i*x(w) + 3*b(w). Let o(s) = 0. Calculate s.
-3, 0, 1/2, 2
Let p(w) = -w**3 + 7*w**2 - 4*w. Let x be p(6). Suppose 10*t = x*t - 6. What is z in -6*z**2 + 3 + 0 + 0*z**2 - 5*z + z**t + 7*z**2 = 0?
-3, 1
Let b = -227 + 229. What is n in 6 + b - 14 - 5*n**4 + 10*n**2 + 1 = 0?
-1, 1
Let q be -5*(-5)/50*4. Factor -624*x**5 + 30*x**4 - 4*x**3 - 80*x - x**3 + 619*x**5 - 120*x**q.
-5*x*(x - 4)**2*(x + 1)**2
Let h = 4/324433 - -4904453633/2271031. Let m = -2159 + h. Determine b so that m*b**3 + 8/7*b - 10/7*b**2 - 2/7 = 0.
1/2, 1
Let t = 81273/14 - 40514/7. Solve -5/2*v**4 + 0 + t*v**3 + 20*v - 35*v**2 = 0 for v.
0, 1, 2, 4
Let j(s) = -378*s**2 - 1233*s - 12. Let m(l) = -379*l**2 - 1229*l - 10. Let q(g) = 14*j(g) - 15*m(g). Factor q(r).
3*(r + 3)*(131*r - 2)
Let r be (638/87 + -7)/(4 - (-34)/(-9)). Factor 39/2*o - r*o**2 + 0.
-3*o*(o - 13)/2
Let s(m) = -m**3 + 45*m**2 - 124*m - 88. Let i be s(42). Let x be ((-1555)/(-225) - 7)/(i/10). Determine c, given that -1/9*c**2 - 1/9*c + x = 0.
-2, 1
Let s(t) be the first derivative of -5*t**3/9 - 335*t**2/2 - 3940*t/3 - 3669. Suppose s(w) = 0. Calculate w.
-197, -4
Factor 0 + 156/7*d**2 - 320/7*d + 2/7*d**3.
2*d*(d - 2)*(d + 80)/7
Let q(r) = -r**2 + 31*r - 126. Let g be q(24). Suppose 28*o - g = 7*o. Suppose 0*n**o - 3/7*n + 2/7 + 1/7*n**3 = 0. What is n?
-2, 1
Let u(q) be the third derivative of -1/120*q**7 + 1/20*q**5 + 0 + 26*q**2 + 0*q**3 - 1/24*q**4 + 3/160*q**6 + 0*q. Let u(a) = 0. Calculate a.
-1, 0, 2/7, 2
Let p(q) be the second derivative of -1/16*q**4 - 15/8*q**2 - 32*q - 2 + 7/12*q**3. Find j, given that p(j) = 0.
5/3, 3
Let r(v) be the third derivative of v**6/30 + 19*v**5/5 - 21*v**4 - 944*v**3/3 - 3589*v**2. Factor r(p).
4*(p - 4)*(p + 2)*(p + 59)
Let -490 + 2697*k**5 - 2677*k**5 - 433*k**3 - 945*k - 1762*k**3 + 105*k**4 + 3505*k**2 = 0. What is k?
-14, -1/4, 1, 7
Let g = 980586 + -4898128/5. Factor g + 1/10*a**2 + 98/5*a.
(a + 98)**2/10
Let a be (-2308