06)*(p - 2)**3/15
Suppose 0 = 35*a - 27*a - 32. Suppose -3*t - 3*u = -a*u - 7, 2*t + 2*u = 2. Factor -3/5*p**t + 3/5*p + 0.
-3*p*(p - 1)/5
Let s(b) be the second derivative of b**6/1080 - 43*b**5/180 + 1849*b**4/72 + 44*b**3/3 + 57*b. Let r(g) be the second derivative of s(g). Factor r(a).
(a - 43)**2/3
Suppose -5*x - 700 = -5*g, g + 3 = 7. Let t = x - -139. Factor c**t + 3*c**3 + 8*c**3 + 4*c**4 - 16*c**2.
4*c**2*(c - 1)*(c + 4)
Solve 255/2*t**5 - 6 + 252*t - 261/2*t**4 - 759/2*t**3 + 273/2*t**2 = 0 for t.
-1, 2/85, 1, 2
Let g(f) be the first derivative of -f**6 + 16*f**5/5 - 11*f**4/3 + 16*f**3/9 - f**2/3 - 1626. Factor g(k).
-2*k*(k - 1)**2*(3*k - 1)**2/3
Let o(b) = -3*b**3 - b. Let c be o(-1). Let t(y) = y**2 + y + 2. Let v(q) = 8*q + 8. Let a(m) = c*t(m) - v(m). Find p such that a(p) = 0.
0, 1
Let z be 644*(1920/(-630) + (10 - 6)). What is r in -3178/3*r**2 + z*r - 98/3*r**3 - 88 = 0?
-33, 2/7
Let w be (3 + (-90)/20)*(-16969)/1131. Let f = -2/377 + w. Factor -1 - 7/2*v + f*v**3 + 6*v**2.
(3*v + 1)**2*(5*v - 2)/2
Let f be (85/19635)/(36/(-21) - -2). Let w(s) be the second derivative of -f*s**4 + 7*s + 0 + 4/11*s**2 - 1/11*s**3. What is k in w(k) = 0?
-4, 1
Let o(z) = 3*z**2 + 85*z + 500. Let q be (2 - 78/9) + 2/(-6). Let x(s) = s**2 + 28*s + 167. Let p(r) = q*x(r) + 2*o(r). Let p(h) = 0. What is h?
-13
Determine v, given that 50/21*v**2 + 170/21*v**4 + 8/3*v**5 + 170/21*v**3 - 10/21*v - 4/21 = 0.
-1, -2/7, 1/4
Let p(w) be the second derivative of w**5/50 - 5*w**4/3 - 72*w**3/5 + 4*w + 349. Factor p(d).
2*d*(d - 54)*(d + 4)/5
Determine g, given that -384 - 1768/3*g**2 + 4/3*g**5 + 188*g**3 + 2432/3*g - 80/3*g**4 = 0.
1, 2, 4, 9
Let i(s) be the third derivative of 169*s**6/120 + 13*s**5/10 + s**4/2 + 4*s**3/3 + 83*s**2. Let j(f) be the first derivative of i(f). Factor j(d).
3*(13*d + 2)**2
Let g be 2*(482/4 + -2). Let -69*l**2 - g*l - 363 - 3*l**3 - 89*l - 103*l = 0. Calculate l.
-11, -1
Let a be 0 + 3 + 72 + (1 - 1). Let g be 3/4 - (-9)/4. Find v such that 12 - 90*v**g + 26*v - 33*v**2 + 3*v + a*v**4 + 7*v = 0.
-2/5, 1
Let l(d) = -984*d**2 - 260*d - 22. Let w(v) = -4*v**2 + v - 1. Let r = -582 + 581. Let o(i) = r*l(i) + 4*w(i). Find z, given that o(z) = 0.
-3/22
Let q(k) be the first derivative of -7*k**5/10 - 23*k**4 - 395*k**3/6 - 133*k**2/2 - 24*k + 2641. Suppose q(f) = 0. Calculate f.
-24, -1, -2/7
Let w(g) = -2*g**2 - 8*g + 4. Let m be w(-4). Let j be (-1)/(-2)*(-3 + (m - 1)). Factor -2*x + 10 - 3*x + j + 0*x - 5*x**2.
-5*(x - 1)*(x + 2)
Let 335/2*w**3 + 1/2*w**5 - 168*w + 0 + 31*w**4 - 31*w**2 = 0. What is w?
-56, -6, -1, 0, 1
Let d(q) be the third derivative of -7*q**5/10 + 13*q**4/6 + 11*q**3/3 - 6298*q**2. Let d(v) = 0. Calculate v.
-1/3, 11/7
Let u(b) be the second derivative of -b**6/105 - 122*b**5/35 - 121*b**4/7 - 724*b**3/21 - 241*b**2/7 + 146*b + 2. Factor u(c).
-2*(c + 1)**3*(c + 241)/7
Suppose 0 = -v - 2, 2*v - v + 17 = 5*c. Suppose -c*a = 4*a - 35. Let -9*f**3 - a*f**5 + 8*f**5 + 2*f**4 - 4*f - 5*f**2 - 7*f**2 = 0. What is f?
-1, -2/3, 0, 2
Suppose -2*k + 0 = -6. Let i be (-11)/(-7) + (-12)/(-28). Factor -i*u**3 - 2 + 6 - 12*u + 0*u**3 - 4*u**2 + 14*u**k.
4*(u - 1)*(u + 1)*(3*u - 1)
Let r be (180/144)/(2 + 7/(-4)). Suppose -170 = -5*p - 2*d, -3*d + 64 = -4*p + 223. Suppose r*q + 8 + p*q**2 - 20*q**3 + 4*q**4 - 20*q - 13*q = 0. What is q?
1, 2
Suppose -2*u + 21 = 5*l, -4*u = -2*l - 17 + 11. Find g such that -5 + 4 - 6 - 2 - 3 + 9*g + l*g**2 = 0.
-4, 1
Let h be (-16)/(-28)*(-7)/(-2). Suppose -24 + h = -2*v + l, -3*v + 33 = -2*l. Factor 12*j - v*j - j + 5*j**2.
5*j**2
Factor -2/11*g**3 - 60/11 + 4/11*g**2 + 58/11*g.
-2*(g - 6)*(g - 1)*(g + 5)/11
Let v(b) = 235*b**3 + 2156*b**2 + 7459*b - 494. Let r(d) = 490*d**3 + 4311*d**2 + 14919*d - 989. Let k(j) = -4*r(j) + 9*v(j). Factor k(t).
5*(t + 7)**2*(31*t - 2)
Let f be (-1)/(-10) - ((-1729)/(-130) - 14). Let w = 1148/5 - 229. Determine j so that 4/5*j**3 - f*j - 1/5*j**4 - 2/5*j**2 + w = 0.
-1, 1, 3
Let t = 16 + -14. Let i = -999 - -999. Determine w so that i*w + 1/3*w**t - 1/3 = 0.
-1, 1
Let 0*v**4 + 0*v**2 + 0*v - 1/5*v**5 + 0 + 1/5*v**3 = 0. What is v?
-1, 0, 1
Let z = -4737 + 4737. Let t(d) be the first derivative of 7 + z*d - 1/2*d**3 + 1/8*d**4 + 1/2*d**2. Find s, given that t(s) = 0.
0, 1, 2
What is q in -2/5*q**4 + 206/5*q**3 - 5196/5*q**2 - 5824/5*q + 10816/5 = 0?
-2, 1, 52
Let c(p) = 48 - p**3 - p**3 + 252*p + 54*p**2 + 154. Suppose -102*i + 111*i - 9 = 0. Let s(q) = q**3 + q**2 - 1. Let z(l) = i*c(l) + 6*s(l). Factor z(u).
4*(u + 1)*(u + 7)**2
Let m(q) be the third derivative of 1/60*q**5 + 48*q + q**2 + 0*q**3 + 0 + 0*q**4 + 1/16*q**6 + 1/60*q**7. Let m(x) = 0. What is x?
-2, -1/7, 0
Let y(t) = -3*t**2 - 59*t - 4. Let b(h) = -10*h**2 - 177*h - 14. Let g(p) = 4*b(p) - 14*y(p). Factor g(a).
2*a*(a + 59)
Let x(v) be the first derivative of 10*v + 16/11*v**2 - 28/11*v**3 + 20/11*v**4 - 5/22*v**5 + 16. Let h(b) be the first derivative of x(b). Factor h(u).
-2*(u - 4)*(5*u - 2)**2/11
Let c be ((6*-1)/2 + -2)/(1850/(-1110)). Let g(w) be the second derivative of -33/20*w**5 + c*w + 3/2*w**2 - 17/4*w**3 + 0 + 37/8*w**4. What is h in g(h) = 0?
2/11, 1/2, 1
Factor -5262436/3 + 4588/3*q - 1/3*q**2.
-(q - 2294)**2/3
Let z(b) be the third derivative of 5*b**5/36 - 485*b**4/12 + 580*b**3/9 - 563*b**2 - b - 2. Factor z(f).
5*(f - 116)*(5*f - 2)/3
Let d = 515/46 + -108/23. Let s(h) be the first derivative of 11 - 13/3*h**3 + 3/4*h**4 + d*h**2 - 3*h. Suppose s(w) = 0. Calculate w.
1/3, 1, 3
Suppose 0*f - f = c + 7, 3*c = f - 21. Let y(n) be the second derivative of 1/70*n**5 + f*n**2 + 0 + 0*n**4 - 1/21*n**3 + 7*n. Factor y(w).
2*w*(w - 1)*(w + 1)/7
Let j(a) be the third derivative of -a**5/20 - 197*a**4/8 - 195*a**3 + a**2 + a - 517. Let j(s) = 0. What is s?
-195, -2
Find g such that -120*g - 315 - 226 - 130 - 127 + 42 - 4*g**2 = 0.
-21, -9
Let u(y) = 3632*y + 29058. Let f be u(-8). Factor -f*a**2 - 1/3*a**3 - 3*a - 4/3.
-(a + 1)**2*(a + 4)/3
Let c(g) be the third derivative of -5*g**8/336 + 25*g**7/14 - 145*g**6/12 + 215*g**5/6 - 475*g**4/8 + 355*g**3/6 - 6*g**2 + 38. What is y in c(y) = 0?
1, 71
Let r(w) be the second derivative of -w**6/90 + 5*w**5/12 - 11*w**4/18 - 8*w**3/3 - 2965*w. Factor r(k).
-k*(k - 24)*(k - 2)*(k + 1)/3
Let j(v) = v - 3. Let r be j(5). Find h such that -14*h + 94*h**2 + 4*h + 96*h**2 + 21 - 286*h**r + 97*h**2 = 0.
3, 7
Let i(s) be the second derivative of s**5/5 + 104*s**4/3 - 856*s**3/3 + 864*s**2 + 1401*s. Let i(x) = 0. Calculate x.
-108, 2
Let r be 74/111*((-60)/24 - (-5 + (-1)/2)). Solve 6*p**r - 3/2*p - 9 - 3/2*p**3 = 0.
-1, 2, 3
Let w(k) be the first derivative of 0*k - 26/7*k**3 + 1/14*k**4 - 26 + 0*k**2. Factor w(x).
2*x**2*(x - 39)/7
Let q(f) = 3*f - 12. Let k be q(16). Factor k - 4*y**2 - 4*y**3 + 61*y - 23*y - 2*y.
-4*(y - 3)*(y + 1)*(y + 3)
Solve -231*l**3 - 1035*l**2 - 1593*l - 832*l**4 - 486 + 400*l**4 + 417*l**4 = 0 for l.
-9, -3, -2/5
Let z be 24/11 + -2 + 57/(-66)*(-1582)/565. Factor -b**2 + 1/5*b**3 - 7/5 - z*b.
(b - 7)*(b + 1)**2/5
Let f(s) be the second derivative of -s**7/42 + s**6/24 + s**5 + 5*s**4/6 - 40*s**3/3 + 45*s**2 - 105*s. Let r(n) be the first derivative of f(n). Factor r(l).
-5*(l - 4)*(l - 1)*(l + 2)**2
Suppose -2*h = -118*z + 122*z, -4*h - z + 7 = 0. Factor -122*y**3 + 240*y**h - 198*y**3 + 3674*y - 3719*y.
-5*y*(8*y - 3)**2
Let u(z) = -29*z**2 - 56*z + 22. Let w(n) = -51*n**2 - 114*n + 42. Let l(y) = -5*u(y) + 3*w(y). Suppose l(i) = 0. What is i?
-8, 1/4
Let l(k) be the third derivative of k**5/420 + k**4/14 - 135*k**3/14 + 13*k**2 + k - 53. Solve l(r) = 0.
-27, 15
Let i(g) be the second derivative of g**4/12 + 8*g**3/3 - 27*g**2/2 + 28*g. Let a be i(-18). Factor 7*d**3 - a*d**4 + d**3 + 13*d**4 - 4*d**5.
-4*d**3*(d - 2)*(d + 1)
Determine d so that -335/6*d - 1/6*d**2 + 56 = 0.
-336, 1
Suppose 2*v + 34 = 3*f, 11*v = -5*f + 10*v + 35. Factor 20*y**4 + 92*y**2 + f*y - 62*y**2 - 8*y**3 - 50*y**2.
4*y*(y - 1)*(y + 1)*(5*y - 2)
Let i be (-6)/((-792)/1606) - 12. Determine g, given that -1/2*g**3 + 1/3*g + i*g**2 + 1/6*g**5 - 1/6*g**4 + 0 = 0.
-1, 0, 1, 2
Let n(k) be the third derivative of k**5/60 + 17*k**4/8 + 24*k**3 - 1745*k**2. Factor n(w).
(w + 3)*(w + 48)
Determine l so that -15696*l + 6352*l**2 + 4*l**4 - 324*l**3 + 2