q(z) + a(z). Factor i(p).
-(p - 2)*(p - 1)*(p + 3)
Suppose -37*n = -21*n - 96. Determine o, given that 153*o - 301*o + 140*o**5 - 375*o**4 + 240*o**2 + n*o**3 + 2*o**3 + 111*o**4 + 24 = 0.
-1, 2/7, 3/5, 1
Let h be -4*10/8 + -455. Let k = 460 + h. Factor -4/9*g + k - 2/9*g**2.
-2*g*(g + 2)/9
Let z = -54022 + 54035. Find k, given that 8*k**2 - 41/2*k - 1/2*k**3 + z = 0.
1, 2, 13
Suppose 21*v + 122 = -2*l, -149 = -2*l + 4*v - 121. Factor 2/5*i**5 + 342*i**l + 5400 - 4320*i + 998/5*i**3 + 82/5*i**4.
2*(i - 2)**2*(i + 15)**3/5
Let r(i) be the first derivative of 0*i - 127 + 3/17*i**6 - 2/17*i**2 + 2/17*i**3 + 10/17*i**5 + 21/34*i**4. Let r(c) = 0. What is c?
-1, 0, 2/9
Let v be (-2)/27 - (3 - 3973/783). Let l(s) be the first derivative of 2/3*s**3 - 7 - 12*s - s**v. Factor l(k).
2*(k - 3)*(k + 2)
Factor 5*k**4 + 360 - 674*k - 135*k**3 + 1068*k**2 - 411*k + 27*k**2 - 240*k**3.
5*(k - 72)*(k - 1)**3
Let k(h) = -9*h**2 + 20*h + 54. Let q(v) be the second derivative of -v**4/4 + 7*v**3/6 + 9*v**2 - 6*v - 2. Let s(w) = -4*k(w) + 11*q(w). Factor s(d).
3*(d - 3)*(d + 2)
Let w(h) be the second derivative of 0 - 1/35*h**6 + 1/10*h**5 + 5/14*h**4 - 6/7*h**3 - 120*h + 0*h**2 - 1/147*h**7. Suppose w(y) = 0. Calculate y.
-3, 0, 1, 2
Let j(c) be the third derivative of -c**7/210 - c**6/40 + 2*c**5/5 - 7*c**4/6 - c**2 + 397*c. Determine p, given that j(p) = 0.
-7, 0, 2
Let z(s) be the first derivative of -s**5/5 + 5*s**4/8 - s**3/2 + 41*s**2/2 - 124. Let p(q) be the second derivative of z(q). Factor p(n).
-3*(n - 1)*(4*n - 1)
Factor 2/9*z**4 + 52/9*z**3 + 0 + 56/9*z - 110/9*z**2.
2*z*(z - 1)**2*(z + 28)/9
Let p = 859925/4 + -214981. Factor -9/2 - 11/4*y - p*y**2.
-(y + 2)*(y + 9)/4
Let f(c) be the first derivative of -2*c**5/25 + 41*c**4/10 - 68*c**3 + 1836*c**2/5 - 3888*c/5 - 2912. Solve f(q) = 0 for q.
2, 3, 18
Solve 1/8*t**3 - 7/2*t**2 + 0*t + 0 = 0.
0, 28
Factor 288/7 + 3/7*m**2 - 150/7*m.
3*(m - 48)*(m - 2)/7
Let c(m) be the third derivative of m**6/84 - 4*m**5/35 - 13*m**4/7 - 176*m**3/21 - 12*m**2 + 24*m. Factor c(j).
2*(j + 2)**2*(5*j - 44)/7
Let k be (-336)/(-189) - 8/(-36). Let h(d) be the first derivative of -3/16*d**4 - 1/24*d**6 - 1/12*d**3 + 4 + 0*d**k + 0*d - 3/20*d**5. Solve h(t) = 0 for t.
-1, 0
Suppose 134*x + 36 = 143*x. Factor -x*f**3 + 3*f**5 - f**3 - 2*f + 5*f**4 - 8*f**2 + 3*f**2 + 4*f**3.
f*(f - 1)*(f + 1)**2*(3*f + 2)
Let m(w) be the third derivative of 0*w - 146*w**2 + 1/20*w**5 + 0 + 0*w**3 + 13/8*w**4. Determine k, given that m(k) = 0.
-13, 0
Let s(n) = -4*n + 16*n**2 + 3 + 2 - 3 + 1. Let y be s(1). Factor y*l**3 + 85*l**2 - 20 + 25*l**4 + 59*l**3 + 16*l**3.
5*(l + 1)**2*(l + 2)*(5*l - 2)
Suppose 2/15*s**3 + 3242/15*s + 108 + 1624/15*s**2 = 0. What is s?
-810, -1
Determine s so that -150 - 32/3*s**5 + 298*s**4 - 1752*s**3 - 13772/3*s**2 - 2680*s = 0.
-1, -1/16, 15
Let z(j) be the third derivative of -j**9/453600 - j**8/50400 + j**7/9450 + j**5 - 10*j**2 + 6*j. Let s(w) be the third derivative of z(w). Factor s(u).
-2*u*(u - 1)*(u + 4)/15
Let v be 4*(-5 - (-115)/20). Let c(t) = -56*t - 3*t**2 + 13*t**2 - 3*t**2 + 193. Let o(l) = 6*l**2 - 56*l + 194. Let z(b) = v*o(b) - 2*c(b). Factor z(j).
4*(j - 7)**2
Let k(c) be the third derivative of 13122*c**8/49 + 64152*c**7/49 + 8127*c**6/5 + 2569*c**5/15 + 109*c**4/14 + 4*c**3/21 + 1489*c**2. What is p in k(p) = 0?
-2, -1, -1/54
Let n be (-1 - (-22)/2)*25/50. Suppose 2*a + 4 = 3*d, -2*a + 2*d - 8 = -2*d. What is h in -20 - 3*h**3 + n*h**a + 0 + 13*h**3 - 40*h - 15*h**2 = 0?
-2, -1, 2
Factor 23 + 30 - 252*o - 192 - 644 + 3*o**2.
3*(o - 87)*(o + 3)
Let j = -159940 - -1759360/11. Factor -6/11*q + 2/11*q**2 - j.
2*(q - 5)*(q + 2)/11
Factor -64/7*p**2 + 4/7*p**4 + 192/7 - 64/7*p + 16/7*p**3.
4*(p - 2)**2*(p + 2)*(p + 6)/7
Let o be (91/(-234))/(10 + -11). Let g(b) be the second derivative of 8/9*b**3 - 16/3*b**2 - 24*b + 0 + 1/30*b**5 + o*b**4. Determine n, given that g(n) = 0.
-4, 1
Suppose -4*p + 13*p - 963 = 0. Determine n, given that 52 - 15*n + 10*n**3 + 48*n**2 - p*n - 18*n**3 + 10*n**3 + 20*n = 0.
-26, 1
Let x(w) = 12*w**2 + 35*w + 37. Let u(k) = 35*k - 6 + 17 - 6 + 11*k**2 + 31. Let q(s) = -7*u(s) + 6*x(s). Solve q(a) = 0.
-6, -1
Let o = 3746243/13111826 + -1/1873118. Factor -18/7 + o*w**2 - 16/7*w.
2*(w - 9)*(w + 1)/7
Let n = 10279/7865 + -39/121. Let k = n + 2/5. Factor -12/13*o**4 + 8/13*o - 22/13*o**3 + k*o**5 + 8/13*o**2 + 0.
2*o*(o - 1)**2*(3*o + 2)**2/13
Let i(w) = -7*w**4 + 5*w**3 + 14*w**2 + 2*w. Let j(r) = 190*r**4 - 135*r**3 - 380*r**2 - 55*r. Let m = -127 - -72. Let f(x) = m*i(x) - 2*j(x). Factor f(l).
5*l**2*(l - 2)*(l + 1)
Let i = -1004999411/905850 - -1/82350. Let y = i + 1110. Factor 8/11 + 2/11*q**3 + 0*q - y*q**2.
2*(q - 2)**2*(q + 1)/11
Let d = -3653 - -3658. Let n(h) be the first derivative of 0*h**2 + 0*h**3 - 1/11*h**6 + 33 + 0*h**4 + 0*h - 2/55*h**d. Find i such that n(i) = 0.
-1/3, 0
Suppose -4*n = 2*d + 4 + 14, 4*n + 16 = 0. Let t be (108/432)/((-1)/d). Find u, given that 0 - t*u**4 + 5/4*u**3 + u - 2*u**2 = 0.
0, 1, 2
Let i = 27 + -24. Let x be (2/13 - 55/(-65))*5. Factor 0*y**5 + 46*y**3 - i*y**x - 40*y**3 - 3*y.
-3*y*(y - 1)**2*(y + 1)**2
Let h(p) be the first derivative of 2*p**5/5 + 131*p**4 + 1042*p**3/3 + 260*p**2 - 7809. Factor h(q).
2*q*(q + 1)**2*(q + 260)
Factor 2/9*u**2 + 1005362/9 - 2836/9*u.
2*(u - 709)**2/9
Let y be ((-270)/(-240))/(351/260). Let i(f) be the second derivative of -y*f**3 - 33*f + 5/12*f**4 + 0 + 0*f**2. Solve i(q) = 0.
0, 1
Let h = 274/13 + -256/117. Suppose -h*r - 86/9 + 2/9*r**3 - 82/9*r**2 = 0. What is r?
-1, 43
Let o = -601673/13 - -46283. Let -o*g**4 + 0 - 2/13*g**3 + 6/13*g**2 - 2/13*g**5 + 4/13*g = 0. What is g?
-2, -1, 0, 1
Let n = -539356 - -2696808/5. Solve -12/5*w**2 + 0*w + 12/5*w**5 + 28/5*w**4 - n*w**3 + 0 = 0.
-3, -1/3, 0, 1
Let c(z) be the third derivative of -z**6/72 - 5*z**5/12 - 125*z**4/24 - 22*z**3/3 - 75*z**2. Let x(w) be the first derivative of c(w). Factor x(v).
-5*(v + 5)**2
Suppose -12180*w**3 + 1368 + 12176*w**3 - 572*w**2 + 2088 + 600*w = 0. Calculate w.
-144, -2, 3
Let x(r) be the third derivative of -r**7/140 + 9*r**6/20 - 48*r**5/5 + 64*r**4 + 16*r**2 - 2*r. Solve x(k) = 0.
0, 4, 16
Let f(n) be the second derivative of -n**5/4 - 25*n**4/6 - 20*n**3 - 13180*n. Factor f(o).
-5*o*(o + 4)*(o + 6)
Let v(d) be the third derivative of -2*d**5/165 + 125*d**4/44 + 94*d**3/33 + 112*d**2 + 2*d + 1. Let v(h) = 0. What is h?
-1/4, 94
Let k(f) = 904*f - 52. Let h be k(4). Factor 0*b**3 - 3*b**3 - 13*b - 14*b**2 - 3558 + h.
-(b + 2)*(b + 3)*(3*b - 1)
Factor 2/5*h**3 - 24/5*h**2 - 324/5 - 198/5*h.
2*(h - 18)*(h + 3)**2/5
Let w(p) be the third derivative of -p**5/180 - 301*p**4/36 - 601*p**3/18 + 1738*p**2. Factor w(u).
-(u + 1)*(u + 601)/3
Suppose 1476 + 864 = 13*u. Let -108*j - u*j**2 - 56*j**3 - 92*j - 4*j**4 + 8*j**3 = 0. What is j?
-5, -2, 0
Let k(q) be the third derivative of q**7/168 - q**6/24 + q**5/12 - 55*q**3/3 - 2*q**2 + 24. Let s(o) be the first derivative of k(o). Factor s(b).
5*b*(b - 2)*(b - 1)
Factor -866396/3*d**2 + 2/3*d**5 + 289814*d + 95252*d**3 - 96774 + 506*d**4.
2*(d - 1)**3*(d + 381)**2/3
Suppose 29 = 2*y - 5*j, 16*j + 93 = 4*y + 13*j. What is q in -y*q**2 - 8*q - 12*q + 26*q**2 + 4*q = 0?
-16, 0
Let x = -18 + 13. Let t = 9 + x. Let 8*u - 15*u**2 + 20*u**2 - 3*u - 5*u**3 - 5*u**t = 0. Calculate u.
-1, 0, 1
Let s = 2562795/2 - 1281397. What is k in -31/2*k - s*k**3 + 0 - 16*k**2 = 0?
-31, -1, 0
Let q be (96/80)/(-2 - (-22)/10). Let i(g) be the third derivative of 0 + 7/108*g**4 + 0*g + 1/54*g**5 + 26*g**2 + 1/9*g**3 + 1/540*g**q. Solve i(b) = 0 for b.
-3, -1
Let u(g) = -g**3 - 6*g**2 + 11*g - 28. Let t be u(-8). Suppose 99*m**4 + 20*m**2 + 30*m**3 - 94*m**4 - 13 - t - 30*m = 0. Calculate m.
-5, -1, 1
Let h(s) be the first derivative of -8/5*s**5 + 4*s + 4/3*s**3 - 2*s**4 + 5*s**2 + 47 - 1/3*s**6. Factor h(b).
-2*(b - 1)*(b + 1)**3*(b + 2)
Let x = -285231/8 + 35481. Let c = 174 + x. Suppose -3/8*g**4 + 3/4*g - c*g**3 + 3/8*g**5 + 0 + 3/8*g**2 = 0. What is g?
-1, 0, 1, 2
What is s in -11/4*s**3 + 1/6*s**5 + 2 + 7/12*s**4 + 13/3*s - 5/6*s**2 = 0?
-6, -1, -1/2, 2
Suppose -j = 3*j, 5*b = -j + 15. Let h be 25/(-5) + (-12)/9*(-133)/28. Factor -16/3*c**2 + 14/3*c + h*c**4 - 2/3*c**5 + 4/3*c**b - 4/3.
-2*