45 - 53*q**4/6 - 5*q - 12. Let j(g) be the third derivative of w(g). Factor j(t).
-(t + 4)*(t + 14)/3
Let y = -193 + 198. Let 3*p**4 + 2*p**5 - 11*p**y + 15*p**5 + 2*p**3 - 5*p**5 = 0. Calculate p.
-2, -1, 0
Let s(m) be the second derivative of m**5/20 + 215*m**4/12 + 107*m**3/3 + 35*m - 17. Solve s(p) = 0.
-214, -1, 0
Let a = 850/3 - 1133/4. Let j(x) be the second derivative of -a*x**4 + 0 + 0*x**2 - x**3 + x. Let j(u) = 0. What is u?
-6, 0
Factor -3720 + 30620*q - 12*q**2 + 7*q**2 - 30895*q.
-5*(q + 24)*(q + 31)
Let h be ((-8)/48 - 974/(-12)) + -5. Factor 183*o**2 + 8 + 40*o**3 - h*o - 117*o**2 - 110*o**2.
4*(o - 2)*(o + 1)*(10*o - 1)
Suppose -109*f + 146 = -36*f. Let d = -649 - -3259/5. Find n, given that 12/5 + d*n + 2/5*n**f = 0.
-6, -1
Let g(h) be the first derivative of 2*h**5/65 - 1072*h**4/13 + 764692*h**3/13 + 2300512*h**2/13 + 2302658*h/13 + 13857. Factor g(p).
2*(p - 1073)**2*(p + 1)**2/13
Let c(u) = -8*u + 7*u**2 + u**3 - 1 - 1 + 7*u. Let y be c(-6). Find m, given that -y*m**3 + 53*m - 1 - 7 - 13*m + 27*m**4 - 34*m**2 + 15*m**4 = 0.
-1, 2/7, 2/3, 1
Let p(a) be the second derivative of -a**5/20 - a**4/12 + 25*a**3/6 + 25*a**2/2 + 56*a + 6. Factor p(r).
-(r - 5)*(r + 1)*(r + 5)
Suppose 88/3 + 1/3*f**4 - 22*f**2 - 19/3*f**3 - 4/3*f = 0. Calculate f.
-2, 1, 22
Let v be (518/(-148) + (12 - 6 - -4))/(3/2). Suppose 1/3*d**3 + 40/3*d - 12 - v*d**2 = 0. What is d?
2, 9
Let u(j) be the first derivative of j**3/24 - 97*j**2/16 - 2118. Let u(m) = 0. What is m?
0, 97
Let h = 496 - 494. Suppose -302*v - h = -303*v. Suppose -58/7*g + 12/7 + 18/7*g**v = 0. Calculate g.
2/9, 3
Let q(k) be the second derivative of 6*k**3 - 1/24*k**4 - 324*k**2 + 1 - 27*k. Factor q(z).
-(z - 36)**2/2
Suppose -2*n = -2*j - 7*n + 33, 0 = 2*j - 2*n - 12. Suppose -19*c - j*c**2 - 10 + 26*c**2 + 8 + 4 = 0. Calculate c.
2/17, 1
Let 0 - 39/4*n**3 + 3*n - 1/4*n**4 - 23/4*n**2 + 3/4*n**5 = 0. What is n?
-3, -1, 0, 1/3, 4
Let d(b) be the first derivative of b**6/8 - b**5/3 - 175*b**4/24 + 10*b**3 + b**2 + b - 141. Let v(t) be the second derivative of d(t). Factor v(q).
5*(q - 4)*(q + 3)*(3*q - 1)
Let b(g) = g**3 - 8*g**2 + 6*g + 15. Let n be b(7). Suppose r - 5*p + n = -7, p - 3 = -4*r. What is s in -2/9*s**3 + 0*s**2 + 2/9*s**5 + 0*s**4 + 0*s + r = 0?
-1, 0, 1
Let f be 7950/350 + (4/(-14))/(-1). Suppose 46*g = 115 - f. Find k, given that -1/3*k**g + 16/3*k - 64/3 = 0.
8
Let a(l) be the third derivative of -25*l**8/336 - 17*l**7/21 - 13*l**6/24 + 16*l**5/3 - 5*l**4/2 - 78*l**2 + 2*l. Solve a(i) = 0 for i.
-6, -2, 0, 1/5, 1
Let l(r) = -425*r**3 - 1280*r**2 + 945*r + 560. Let s(h) = 52*h**3 + 160*h**2 - 118*h - 70. Let q(a) = 3*l(a) + 25*s(a). Determine t so that q(t) = 0.
-7, -2/5, 1
Let y be (-100)/36*(-726)/1210. Factor -11/6*z - 1/6*z**2 - y.
-(z + 1)*(z + 10)/6
Let i(p) = -7*p**4 + 11*p**2 - 4*p. Let r(j) = -422*j + 25*j**4 + 437*j - 42*j**2 + 2*j**4. Let h(t) = -15*i(t) - 4*r(t). Factor h(o).
-3*o**2*(o - 1)*(o + 1)
Let r be 82/8 - ((-18)/8)/(-9). Factor -10*t**3 - 8*t**3 - 60*t - 46*t**2 + r*t**3 + 18.
-2*(t + 3)**2*(4*t - 1)
Let a(g) = 20*g - 477. Suppose -1146*x = -1152*x + 144. Let z be a(x). Let 0 + h + 1/3*h**4 - 1/3*h**2 - h**z = 0. What is h?
-1, 0, 1, 3
Factor -2/11*l**2 - 1124/11 - 1126/11*l.
-2*(l + 1)*(l + 562)/11
Let c be 0/1 + (-4)/14 + 84760/88998. Factor 1/6*y**3 + c*y**2 + 1 - 11/6*y.
(y - 1)**2*(y + 6)/6
Suppose 11*a + 3744 = 19*a. Let k = a - 4679/10. Factor 3/10*z**4 + 1/2*z**3 + k*z**2 + 0 - 1/10*z.
z*(z + 1)**2*(3*z - 1)/10
Let x(q) = q**3 - 45*q**2 - 93*q - 45. Let b be x(47). Let o(c) be the second derivative of -3/16*c**b + 0 - 1/8*c**3 + 9*c - 1/32*c**4. Solve o(i) = 0 for i.
-1
Let z = 48602 + -48597. Suppose -6/11*m**4 - 4/11*m**3 + 0*m**2 + 0*m - 2/11*m**z + 0 = 0. What is m?
-2, -1, 0
Let i(v) = v**3 + v**2 - 1. Let a(m) = 5*m**3 + 13*m**2 + 12*m + 3. Let f = -117 + 80. Let h = f - -38. Let l(y) = h*a(y) - i(y). Factor l(j).
4*(j + 1)**3
Let r(i) = -3*i - 3. Let n(l) = 11*l + 12. Let y(t) = 2*n(t) + 9*r(t). Let k be y(-12). Factor 7*h**2 - 65*h + k*h - 3*h**2.
4*h*(h - 2)
Let x = 106 - 54. Factor -38 + 7*y**2 - x*y + 14 - 30*y.
(y - 12)*(7*y + 2)
Suppose 4*j - 8*j - 12 = 0. Let n(y) = 8*y**3 + 13*y**2 - 23*y - 43. Let s(p) = p**3 + p**2 - p - 1. Let h(q) = j*s(q) + n(q). Factor h(a).
5*(a - 2)*(a + 2)**2
Let n(l) be the second derivative of -l**6/420 - l**5/42 + l**4/84 + 5*l**3/21 - 9*l**2 - 198*l. Let m(t) be the first derivative of n(t). Factor m(u).
-2*(u - 1)*(u + 1)*(u + 5)/7
Let a = -6685 + 6689. Let c(m) be the first derivative of 0*m**2 - 1/5*m**3 + 5 - 12/25*m**5 + 3/5*m**a + 0*m. Suppose c(k) = 0. What is k?
0, 1/2
Factor -27 + 3622*q - 136*q**2 + 105*q**2 - 3904*q.
-(q + 9)*(31*q + 3)
Suppose 551 = 26*q + 3*q. Suppose 4*v - 19 + q = 0. Factor -2/9*d + v + 4/9*d**2 - 2/9*d**3.
-2*d*(d - 1)**2/9
Let k(u) be the third derivative of -5*u**7/168 + 289*u**6/96 + 2137*u**5/80 + 2037*u**4/32 + 279*u**3/4 - 15071*u**2. Solve k(y) = 0 for y.
-3, -3/5, 62
Let l(x) = x**3 - 8*x + 3. Let q be l(3). Factor -21*p**2 - 6*p**3 + q*p + 9 - 27*p**2 - p**4 + 40*p**2.
-(p - 1)*(p + 1)*(p + 3)**2
Let w be (39/(-6) + 6 + (-93)/(-186))/(-3). Suppose 0*l**2 + 0*l + 14/9*l**5 + w - 8/9*l**3 - 8/3*l**4 = 0. Calculate l.
-2/7, 0, 2
Let y = -148 + 150. Suppose 36*w**3 + 85*w**2 - 102*w**y - 52*w**2 + 30*w = 0. Calculate w.
0, 2/3, 5/4
Let t be 1 - (-21)/6 - (-30)/(-20). What is n in 88*n**2 - 12 - 48*n + 2*n**2 + 3*n**2 - 33*n**t = 0?
-2/11, 1, 2
Let m = 38033/8 + -4754. Let s(k) be the first derivative of m*k**4 + 5 - 1/4*k**2 + 1/3*k**3 - k. Factor s(l).
(l - 1)*(l + 1)*(l + 2)/2
Let b = -1323 + 1325. Suppose n + 3 = v, -3*n + 11 = -b*v + 4*v. Factor -1/9*m**2 + 1/3*m - 1/9*m**v + 2/9 - 1/3*m**3.
-(m - 1)*(m + 1)**2*(m + 2)/9
Let o be 2/(-3)*165/(-110)*(20 - 3). Let j(i) be the first derivative of -1/4*i**2 + 1/3*i + o + 1/18*i**3. Determine f, given that j(f) = 0.
1, 2
Suppose 8*z - 15 = 3*z. Suppose 2825*t - 1308*t = 1300*t. Suppose -3/2*i**z + 3/4*i**4 - 3*i**2 + 6*i + t = 0. What is i?
-2, 0, 2
Let p = -3464 + 3469. Let l(i) = -i - 1. Let s be l(-1). Determine a so that 15*a**p - 64 - 92*a**3 + 12*a**5 + 96*a + 36*a**4 + 28*a**2 + s*a**2 - 31*a**5 = 0.
-1, 1, 4
Determine b so that 0*b**2 + 0 - 3/4*b**4 - 219/4*b**3 + 0*b = 0.
-73, 0
Suppose 6*t = 4*t + 6. Suppose -4*v = -3*m - 6, -15 = t*m + 2*v - 27. Factor -162/7 - 2/7*u**m - 36/7*u.
-2*(u + 9)**2/7
Suppose 4*m = 48*n - 44*n - 12 - 16, -5*n + 35 = 0. Suppose 2*s + m + 1/3*s**3 + 5/3*s**2 = 0. What is s?
-3, -2, 0
Solve 81/2*h**2 + 987/2*h + 441 - 27/2*h**3 - 3/2*h**4 = 0.
-7, -1, 6
Let b = 378411/5 + -76453. Let i = b - -772. Factor -2*n**2 - i + 14/5*n + 2/5*n**3.
2*(n - 3)*(n - 1)**2/5
Let a(c) = 7 - 14*c + 25 + 33 + 2*c**2 + 36*c. Let p be a(-5). Suppose 0*j**2 + 0*j**4 - 3/8*j**p + 0 + 3/8*j**3 + 0*j = 0. Calculate j.
-1, 0, 1
Let p(q) be the first derivative of -q**6/33 - 4*q**5/55 + 29*q**4/22 + 20*q**3/11 + 7442. Let p(f) = 0. What is f?
-6, -1, 0, 5
Let s be (5 - 3) + -11 - -18. Let k be (s/(-15))/(114/(-380)). Factor -2/15*a**k + 2/5 - 4/15*a.
-2*(a - 1)*(a + 3)/15
Let 2001/4*d + 4005/8 - 3/8*d**2 = 0. What is d?
-1, 1335
Factor -524/9*v - 2/9*v**2 - 1040/9.
-2*(v + 2)*(v + 260)/9
Factor 21*j - 233*j**3 + 79 + 231*j**3 - 8*j**2 - 43 + 9*j.
-2*(j - 3)*(j + 1)*(j + 6)
Suppose -x = -2 - 6. Let w be (-1)/4 + ((-610)/x)/(-5). Factor -8*k**4 - 5*k + w*k**3 - k**5 - 5*k - 6*k + 2*k**5 + 8*k**2.
k*(k - 4)**2*(k - 1)*(k + 1)
Let b(j) be the third derivative of -j**6/12 - 11*j**5/4 + 35*j**4/3 + 30*j**3 + 194*j**2 + 2. Factor b(v).
-5*(v - 2)*(v + 18)*(2*v + 1)
Let t be (148/(-16))/((-2)/240). Factor 102*f - 10 - 1093*f**2 - t*f**2 + 2183*f**2.
-2*(f - 5)*(10*f - 1)
Factor -70225/4 - 1/4*x**2 - 265/2*x.
-(x + 265)**2/4
Let d be 10 - (-8)/(-40)*40. Let s(a) be the second derivative of 1/18*a**4 + 0 + 0*a**d - 1/6*a**3 + 1/60*a**5 - 21*a. Let s(q) = 0. What is q?
-3, 0, 1
Let m(a) = -2*a**2 + 7*a - 9. Let s be m(2). Let o(r) = -5*r - 13. Let v be o(s). Factor 6*k**3 - 6*k + 0*k**3 + 0*k**2 + 2*k**v - 2*k**4.
-2*k*(k - 3)*(k - 1)*(k + 1)
Let t(n) = n + 4. Let b be t(-1). Suppose -3*a = -4*k - 13, b = -a - k + 5. Factor 9*w**a + 21*w**5 + 3*w**3 - 44*w**4 - 4*w**4.
3*w**3*(w - 2)*(7*w - 2)
Let i = 115