7*t - 135 = 0. Let h = -36 - t. Factor -3*f**2 - h*f + 9*f + 10*f - 5*f**3 - 2*f**2.
-5*f*(f - 1)*(f + 2)
Suppose 0 = -18*a + 22*a - 8. Factor 12*b + 8 - 12*b**2 - 15*b**2 + 37*b**a - 6*b**2.
4*(b + 1)*(b + 2)
Suppose 810*d**2 - 2080833*d + 2078358*d + 5*d**3 + 0*d**3 = 0. What is d?
-165, 0, 3
Let s(f) be the first derivative of f**8/2352 - f**7/1470 - f**6/140 + f**5/105 + f**4/21 + 4*f**2 - 26. Let k(m) be the second derivative of s(m). Factor k(j).
j*(j - 2)**2*(j + 1)*(j + 2)/7
Let m(r) be the first derivative of -5*r**6/6 - 13*r**5 + 5*r**4 + 260*r**3/3 - 6453. Let m(n) = 0. Calculate n.
-13, -2, 0, 2
Factor -60 + 131*m**3 - 229*m**3 - 185*m - 90*m**2 + 133*m**3.
5*(m - 4)*(m + 1)*(7*m + 3)
Let n = -3597/4 + 906. Let z = -133142 - -133144. Factor 15/4*y**z + n*y - 3/2.
3*(y + 2)*(5*y - 1)/4
Let r be 6/1 + 163/((-6846)/(-2196)). Let -r*a**3 - 144/7 - 36/7*a**4 + 816/7*a - 1012/7*a**2 = 0. What is a?
-6, 1/3
Let i(v) = v**4 + v**3 - v**2 - 10*v - 1. Let q(g) = 4*g**4 - 51*g**2 + 242*g - 387. Let x(j) = -3*i(j) + q(j). Factor x(o).
(o - 4)**2*(o - 3)*(o + 8)
Let 3074*y - 4*y**2 - 2990*y + 230 - 550 = 0. Calculate y.
5, 16
Let p(n) = 2*n**3 + 26*n**2 + 11*n - 22. Let l be p(-11). Find z, given that -35*z - 6*z**2 - l + 320 - 10*z = 0.
-7, -1/2
Suppose -3*o + 110 = 89. What is t in -o*t - 4*t**3 + t - 19*t**2 - 13*t**2 + 2*t**4 + 8 + 10*t**3 + 22*t**2 = 0?
-4, -1, 1
Let q(w) be the third derivative of w**5/140 - 31*w**4/56 - 19*w**3 - 246*w**2 - 2*w. Find x such that q(x) = 0.
-7, 38
Suppose -3*g = -6*g. Let q be -11*(70/(-22) + (-60)/(-20)). Solve -8/3*c**q - 8/3*c + g - 2/3*c**3 = 0.
-2, 0
Let 0*k**2 + 0*k**2 - 4*k - 902*k - 846*k - 383688 - 2*k**2 = 0. What is k?
-438
Let l = -96 + 30. Let q be 5/(5/(-2)) + l/(-27). Factor -2/9*p**2 - 2/9 + q*p.
-2*(p - 1)**2/9
Let w(c) be the first derivative of c**4/16 + 49*c**3/12 - 51*c**2/4 - 896. Factor w(q).
q*(q - 2)*(q + 51)/4
Let i(k) be the third derivative of k**6/600 - k**5/150 - k**4/6 - 4*k**3/5 + 69*k**2 - k. Let i(m) = 0. Calculate m.
-2, 6
Let f = 1452 - 1441. Let s(p) be the first derivative of 10*p - 10/3*p**3 + 5/2*p**2 + f - 5/4*p**4. Determine l, given that s(l) = 0.
-2, -1, 1
Suppose -96*w = -88*w - 32. Let u be 108/(-44)*(w/(-6) + -2). Solve -32/11*c**4 - 194/11*c**2 + u*c + 144/11*c**3 - 8/11 = 0.
1/4, 2
Let t(c) be the first derivative of -c**5/270 + 5*c**4/108 - 80*c**2 - 87. Let z(f) be the second derivative of t(f). Factor z(k).
-2*k*(k - 5)/9
Let g(l) be the second derivative of l**4/18 - 23*l**3/3 - 370*l**2/3 - 2003*l. Solve g(o) = 0 for o.
-5, 74
Let g = -194 + 187. Let x be (-656)/40 - g - -11. Factor -4/5*r**5 + 8/5*r**3 - x*r**2 + 4/5*r**4 - 4/5*r + 4/5.
-4*(r - 1)**3*(r + 1)**2/5
Let q(m) = -178363*m**3 - 4 + 178358*m**3 - 25*m**2 + 6*m + 0. Let i(t) = -t**3 - 5*t**2 - 1. Let y(f) = 20*i(f) - 5*q(f). Factor y(j).
5*j*(j - 1)*(j + 6)
Let f be (2 - 4015/2009)/(240/160). Let b = 1146/2009 + f. Suppose 0 + 0*a**2 - b*a - 8/7*a**4 + 12/7*a**3 = 0. Calculate a.
-1/2, 0, 1
Let k(t) = t**2 - 20*t + 11. Let n be k(13). Let l be (-20)/n - (-142)/8. Factor -2*j**2 + j**2 - l*j + 2 + 17*j.
-(j - 1)*(j + 2)
Let w be 122/(-42) - 21/(-14)*20/10. Let p(r) be the third derivative of 8/21*r**3 + 43*r**2 + 1/105*r**5 + 0*r + 0 - w*r**4. Suppose p(u) = 0. What is u?
2
Let y(p) be the first derivative of p**4/54 - 2*p**3/3 + 9*p**2 - 164*p - 47. Let w(x) be the first derivative of y(x). Factor w(u).
2*(u - 9)**2/9
Let g(q) = -15*q**3 + 5235*q**2 + 335*q - 21160. Let f(u) = u**3 - 374*u**2 - 24*u + 1512. Let k(t) = -55*f(t) - 4*g(t). Factor k(c).
5*(c - 74)*(c - 2)*(c + 2)
Let z(i) = i**3 - 4*i**2 + 3*i + 3. Let j be z(3). Let p(f) = f**2 + 5*f - 3. Let o be p(-6). Let -5*d**3 - 4*d**3 - 2*d + o*d**2 + 8*d**j = 0. What is d?
0, 1, 2
Suppose -4*w + 16 = 2*i, 3*w = 7 - 1. Let q = -185 + 187. What is a in -i*a**q + a**2 - 3*a**3 + 6*a**3 + 48 - 12 - 24*a = 0?
-3, 2
Let b be 8/(-6)*(10295/(-142) + 71). Suppose 19/4*u - 9/4 + 1/4*u**3 - 11/4*u**b = 0. Calculate u.
1, 9
Solve 28/3*s**2 + 6*s**3 + 2/3*s**4 + 0*s + 0 = 0 for s.
-7, -2, 0
Let h(f) be the third derivative of -f**7/105 - 61*f**6/360 - 7*f**5/20 + 3*f**2 + 762*f. Determine a, given that h(a) = 0.
-9, -7/6, 0
Let s = -250 + 252. Factor 14*p**2 - 13*p - 4*p**s - 10*p**3 - 5*p**4 + 5*p**5 - 5 + 18*p.
5*(p - 1)**3*(p + 1)**2
Let v be (-53)/(-28) - (6996/10164 + 18/(-33)). Factor 3/2*w**2 + v - 1/8*w**3 + 27/8*w.
-(w - 14)*(w + 1)**2/8
Let o(j) be the second derivative of j**7/21 + 2*j**6/3 + 21*j**5/10 - 2*j**4/3 - 28*j**3/3 - 1574*j. Factor o(t).
2*t*(t - 1)*(t + 2)**2*(t + 7)
Let l be ((-3031)/14 - -4)*-2. Let z be (l/510)/((-5)/(-4)). Suppose -z*t + 1/3 + 1/3*t**2 = 0. What is t?
1
Let b(w) = w - 119 - 5*w + 2*w + 14 - 2*w. Let a be b(-27). Solve -8/3 - 2/3*u**4 - 4/3*u**a + 2*u**2 + 8/3*u = 0.
-2, 1
Let l = 1490 - 129. Let r = -9523/7 + l. Factor 4/7 + r*a**2 + 8/7*a.
4*(a + 1)**2/7
Suppose 2*l - 4*l = -52. Factor -2*z**3 + l*z**2 + 1670*z + 1669*z - 3311*z.
-2*z*(z - 14)*(z + 1)
Let t(q) = 5*q**5 + 9*q**4 + 6*q**3 - q**2 - 3*q. Suppose -9 + 13 = 2*z. Let h(j) = -4*j**5 - 8*j**4 - 6*j**3 + 2*j. Let v(x) = z*t(x) + 3*h(x). Factor v(g).
-2*g**2*(g + 1)**3
Let k be 3/(-2 - 14/(-4)). Let l(y) = 28*y + 4. Let m be l(k). Factor 20*n**2 - 50 + m*n**3 - 55*n**3 - 27*n + 6*n - 14*n.
5*(n - 2)*(n + 1)*(n + 5)
Let z(a) = -a**2 - 2*a + 15. Let g(x) = x**2 - 18658*x - 17428535. Let h(l) = g(l) + 6*z(l). Let h(o) = 0. What is o?
-1867
Let d(b) be the third derivative of -b**7/105 - b**6/30 + 3*b**5/10 + 3*b**4/2 + 3*b**2 + 206. Factor d(w).
-2*w*(w - 3)*(w + 2)*(w + 3)
Suppose -9*c - 4*c = -26. Find l, given that 5 + 40 - 14 - 5 - 2*l**c - 10 + 4*l = 0.
-2, 4
Let c(t) = -33*t**3 - 27*t**2 - 22*t - 26. Let y be c(-12). Find j such that 53230*j**3 - 376*j**2 + 512 - y*j**3 + 1152*j - 8*j**4 - 2*j**4 = 0.
-8, -2/5, 2
Let o(z) = -8*z**3 - 2*z**2 + z + 2. Let q be o(-1). Let d be -1 + q + (4 - 2). Factor -d*x**3 - 33*x + 5 + 40*x**2 + 2 - 8*x**3 + 2.
-(x - 1)*(4*x - 3)**2
Solve 230*h - 1/3*h**2 - 39675 = 0.
345
Suppose 3 + 1 = 2*w + 3*m, 4*w - m = 36. Factor 4*a**3 - 20*a + 2*a + a**3 - w*a**2 - 6*a**3 + 27*a**2.
-a*(a - 18)*(a - 1)
Factor 2/21*y**2 + 2637414/7 + 2652/7*y.
2*(y + 1989)**2/21
Let h(k) be the third derivative of 41/28*k**4 + 0 - 65*k**2 + 0*k + 1/140*k**5 + 1681/14*k**3. Factor h(p).
3*(p + 41)**2/7
Factor 2*u**3 + 1161/2*u + 315 + 431/2*u**2.
(u + 2)*(u + 105)*(4*u + 3)/2
Suppose 0 = -819*r - 808 + 1179 + 2086. Factor -1/2*l + 1/2*l**r + 1/2 - 1/2*l**2.
(l - 1)**2*(l + 1)/2
Let i(m) be the first derivative of 77 - 15/8*m**2 + 1/8*m**3 + 27/8*m. Factor i(l).
3*(l - 9)*(l - 1)/8
Let c(t) = 7*t**2 + 23*t + 10. Let v(j) = -3*j**2 - 9*j - 4. Let y(n) = 4*c(n) + 10*v(n). Factor y(i).
-2*i*(i - 1)
Let k(x) be the third derivative of -x**5 - 2/105*x**7 + 0*x + 0*x**3 - 7/30*x**6 - 90*x**2 - 3/2*x**4 + 0. Factor k(a).
-4*a*(a + 1)*(a + 3)**2
Let s(i) = -96*i**2 + 1120*i - 1108. Let o(v) = -89*v**2 + 1120*v - 1109. Let m(f) = 14*o(f) - 13*s(f). Factor m(n).
2*(n - 1)*(n + 561)
Let l(j) be the third derivative of 5776/27*j**3 + 1/270*j**5 + 0*j + 0 - 49*j**2 + 38/27*j**4. Factor l(g).
2*(g + 76)**2/9
Let j(h) be the second derivative of -5*h**7/42 + 7*h**6/3 - 21*h**5/2 + 20*h**4/3 + 215*h**3/6 - 75*h**2 - 4303*h. Suppose j(i) = 0. Calculate i.
-1, 1, 3, 10
Let n(t) be the second derivative of 0 + 149*t - 1/24*t**3 - 3/80*t**5 - 1/120*t**6 + 0*t**2 - 1/16*t**4. Factor n(j).
-j*(j + 1)**3/4
Let d(o) = -28*o**4 - 99*o**3 - 162*o**2 - 88*o - 15. Let w(s) = 32*s**4 + 99*s**3 + 162*s**2 + 87*s + 16. Let g(t) = -4*d(t) - 3*w(t). Factor g(q).
(q + 1)**2*(q + 4)*(16*q + 3)
Let y = -2 - -5. Let d be (3/(-8) - 90/144) + 3. Suppose 0*k**y + 0*k**3 + 25 + 9*k**3 - 4*k**3 + 55*k + 35*k**d = 0. What is k?
-5, -1
Suppose -6246 = -4*y + 56*y + 3111 - 11541. Factor -9*m**3 - y*m + 75/2*m**2 + 6.
-3*(m - 2)**2*(6*m - 1)/2
Let g(k) be the first derivative of -1/4*k**4 + 0*k**2 + 0*k + k**3 + 42. Factor g(i).
-i**2*(i - 3)
Let k = -2051/3 - -684. Let w(l) be the first derivative of -4 + 0*l**2 - 2/9*l**6 + 0*l + 0*l**3 - 1/12*l**4 + k*l**5. Solve w(p) = 0 for p.
0, 1/4, 1
Let v = -162 - -166. Determine a, given that -a**2 + 0*a + 106*a**3 + a - 107*a**3 + a**v = 0