t -68/9*n**u + 2/9*n**4 - 680/3*n + 200 + 698/9*n**2 = 0. Calculate n.
2, 15
Let d(h) be the first derivative of 28/15*h**5 + 22/3*h**2 + 49/18*h**6 - 32 + 8/3*h - 143/12*h**4 + 14/9*h**3. Find o such that d(o) = 0.
-2, -2/7, 1
Let v(n) be the third derivative of n**6/1800 - 7*n**5/600 - 3*n**4/20 + 45*n**3 - 75*n**2. Let f(q) be the first derivative of v(q). Factor f(i).
(i - 9)*(i + 2)/5
Let p(a) be the first derivative of -a**3/3 + 2*a**2 + 32*a - 4241. Factor p(l).
-(l - 8)*(l + 4)
Factor -39/5*x + 21/5 + 3/5*x**3 + 3*x**2.
3*(x - 1)**2*(x + 7)/5
Factor 337*k**2 + 262579*k - 260871*k - 4*k**3 - 81*k**2 - 1960.
-4*(k - 70)*(k - 1)*(k + 7)
Let f be ((-204)/780 - 23/115)/(-3). Suppose -f*l**2 - 28/13*l - 2 = 0. Calculate l.
-13, -1
Let s(b) = b**3 + 5*b**2 - 8*b - 10. Let d be s(-6). Suppose -2*p - 5*p + d*p = 0. Find v, given that 0*v + p*v - v**2 + 3 + 1 = 0.
-2, 2
Let i(n) be the second derivative of 0 - 97*n - 5/84*n**4 + 9/7*n**2 - 43/42*n**3. Factor i(l).
-(l + 9)*(5*l - 2)/7
Let o = -782/87 + 4519/435. Factor o*h - 1/5*h**2 + 0.
-h*(h - 7)/5
Let b(y) be the first derivative of 24*y**3 + 95 + 3/4*y**4 + 288*y**2 + 1536*y. Factor b(z).
3*(z + 8)**3
Let t(y) be the third derivative of y**8/6720 + y**7/240 + y**6/40 + 13*y**5/20 + 3*y**2 - 2. Let c(u) be the third derivative of t(u). Factor c(x).
3*(x + 1)*(x + 6)
Suppose 0 = 3*w + 3*x - 2*x - 2, -w - 4 = -2*x. Suppose w = -7*v - 0*v + 63. Find m, given that 20*m**3 - 11*m**3 + 7*m**3 - m**4 + v*m**4 + m**5 = 0.
-4, 0
Let g(d) be the second derivative of d**7/8820 - d**6/630 + d**5/140 - 97*d**4/12 + 15*d. Let z(b) be the third derivative of g(b). Factor z(s).
2*(s - 3)*(s - 1)/7
Let h(w) = 8*w**2 - 7*w - 22. Let p(g) = -3*g**2 + 2*g + 7. Let b = -9 + 13. Suppose 4*s = -3*i + 8, i = -s + b - 2. Let x(c) = s*h(c) + 7*p(c). Factor x(d).
-5*(d - 1)*(d + 1)
Let i(u) be the second derivative of u**5/40 - 2*u**4/3 + 4*u**3 + 79*u + 3. Factor i(w).
w*(w - 12)*(w - 4)/2
Let n be (8841/(-2105))/(3/(-4)). Find l such that 2/5*l**3 - 21/5*l**2 + n*l - 9/5 = 0.
1/2, 1, 9
Solve -32/9*a - 1792/3 + 112*a**2 - 18*a**3 - 1/9*a**4 = 0.
-168, -2, 4
Let x = -878610 + 2635850/3. Factor -2/3*f**4 + 0 + 0*f**2 + 0*f + x*f**3.
-2*f**3*(f - 10)/3
Let s be 6/(-16)*206/(-309). Let d(u) be the first derivative of -27 + 2/3*u**2 + 2/3*u**3 + 0*u + 1/30*u**5 + s*u**4. Suppose d(b) = 0. What is b?
-2, 0
Suppose -42*q = 96*q - 690. Let h(j) be the third derivative of 5/6*j**4 + 0 + 10/3*j**3 + 24*j**2 + 1/12*j**q + 0*j. Suppose h(f) = 0. Calculate f.
-2
Let k(p) be the second derivative of -p**4/54 + 104*p**3/27 - 68*p**2/3 - 3*p - 1. Factor k(x).
-2*(x - 102)*(x - 2)/9
Let t(j) be the second derivative of 0*j**3 - 25/8*j**4 - 1/180*j**6 + 0 + 0*j**2 + 14*j + 1/4*j**5. Factor t(n).
-n**2*(n - 15)**2/6
What is z in -3*z**3 - 203866*z**2 + 203824*z**2 - 336 + 345*z + 36 = 0?
-20, 1, 5
Let t(q) = q**3 - 27*q**2 + 5*q - 132. Let b be t(27). Let l be (-260)/(-100) - (1 + 0). Find w, given that 12/5*w**b - 4/5*w**4 - l*w**2 + 0 + 0*w = 0.
0, 1, 2
Let y be ((-226)/2)/((-4)/12). Suppose -r + 137 = 2*a, a - y = -4*a + r. Suppose -3*p**3 - 62*p**2 + 3*p**4 + 12*p**3 + a*p**2 = 0. What is p?
-2, -1, 0
Let h(p) = 3*p**2 - 79*p - 135. Let c(r) = 2*r**2 - 78*r - 136. Let k be ((-320)/12)/8*3/2. Let n(d) = k*c(d) + 4*h(d). Determine v so that n(v) = 0.
-35, -2
Factor -2/3*r**2 - 192 + 88/3*r.
-2*(r - 36)*(r - 8)/3
Let f(n) be the second derivative of 4/5*n**2 + 0*n**3 + 0 - 65*n - 1/30*n**4. Factor f(i).
-2*(i - 2)*(i + 2)/5
Let o = 3377 + -10123/3. Let v(m) be the third derivative of 2*m**4 + 0*m + 2/15*m**6 + m**5 - 5*m**2 + 0 - o*m**3. Factor v(t).
4*(t + 2)**2*(4*t - 1)
Let n = -396 - -378. Let j be -1 + 6 + 81/n. Determine z so that j*z**3 - 2*z**2 + 2*z + 0 = 0.
0, 2
Let p be 1080/90 - -3*42/(-11). Let p*u**5 - 14/11*u**4 + 6/11*u**3 + 0 + 6/11*u**2 - 4/11*u = 0. What is u?
-2/3, 0, 1
Factor -2/5*l**3 + 0*l - 366*l**2 + 0.
-2*l**2*(l + 915)/5
Let k(j) = -39*j**3 - 47*j**2 + 15*j. Let z(s) = s**2. Let i(b) = -k(b) + 4*z(b). Let o(y) = 3*y**3 + 4*y**2 - y. Let u(m) = -2*i(m) + 27*o(m). Solve u(g) = 0.
-1, 0
Let g be -8 - -4 - 26/(-2). Suppose -g*y = 160 - 520. Solve 124*w - 14 - 147*w**2 + 2 - y*w = 0.
2/7
Factor -72/7 + 324/7*d + 8*d**2.
4*(d + 6)*(14*d - 3)/7
Let w(f) = 3*f - 24. Let x be w(8). Suppose -u - 1 + 6 = x. Determine t, given that -101*t**5 - 8*t**2 - 16*t**4 + 0*t**2 + 105*t**u + 20*t**3 = 0.
0, 1, 2
Let s(u) = 10*u**2 - 108*u - 1462. Let b(q) = -23*q**2 + 216*q + 2925. Let l(j) = -4*b(j) - 9*s(j). Factor l(g).
2*(g + 27)**2
Let p(l) be the second derivative of l**6/20 - 9*l**5/40 - 255*l**4/8 + 259*l**3/4 + 765*l**2/2 - 9474*l. What is x in p(x) = 0?
-15, -1, 2, 17
Let -206*p - 4*p**4 + 376*p + 508*p**3 - 1004*p**2 + 0*p**4 + 330*p + 0*p**4 = 0. What is p?
0, 1, 125
Let q = 89348 + -89346. Factor -1/5*w**q + 0 - 2*w.
-w*(w + 10)/5
Let c(w) be the first derivative of 2*w**6/105 + 2*w**5/7 + 3*w**4/7 + 7*w - 55. Let m(p) be the first derivative of c(p). Let m(z) = 0. What is z?
-9, -1, 0
Suppose -4*u + 184 = -3*b, 0*u - 2*b = 2*u - 78. Let n = 47 - u. Factor a**2 - 4 + 0*a**2 + 8*a - a**2 - n*a**2.
-4*(a - 1)**2
Let w(d) = -25*d**2 + 1. Let h(c) = -99*c**2 + 20*c - 257. Let g(b) = 5*h(b) - 20*w(b). Factor g(y).
5*(y - 9)*(y + 29)
Let j(n) be the third derivative of n**7/70 - 3*n**6/4 - 3*n**5/20 + 11*n**4 + 30*n**3 + 2*n**2 - 65. Factor j(c).
3*(c - 30)*(c - 2)*(c + 1)**2
Let x be ((-4)/(-7)*-15)/(8/(-84)). Let n be (-9)/(-6)*6*20/x. Solve 2/3*r**4 + 4/3*r**3 + 2 - 8/3*r**n - 4/3*r = 0 for r.
-3, -1, 1
Let r(l) be the third derivative of l**6/40 + 211*l**5/80 - 269*l**4/32 + 27*l**3/4 - 813*l**2. Determine p so that r(p) = 0.
-54, 1/4, 1
Solve d**3 + d**3 - 4*d**3 - 2*d**3 - 800*d - d**3 - 3840 + 145*d**2 = 0 for d.
-3, 16
Let y be ((-146)/(-30) - 4) + 1/(-5). Let k(n) be the third derivative of 0*n + 1/4*n**4 + y*n**3 + 1/30*n**5 + 0 - n**2. Determine o, given that k(o) = 0.
-2, -1
Let l(t) be the third derivative of -t**6/450 - 2*t**5/75 + 2*t**4/5 + t**3/3 - 68*t**2. Let g(y) be the first derivative of l(y). Determine z so that g(z) = 0.
-6, 2
Let 1506*z**3 - 21*z**4 + 133*z**2 - 237*z + 675*z + 1832*z**2 - 1 + 1 = 0. Calculate z.
-1, -2/7, 0, 73
Let r(v) be the first derivative of 0*v + 38/11*v**3 + 37 - 9/11*v**2 - 24/11*v**4. Suppose r(i) = 0. Calculate i.
0, 3/16, 1
Let f(p) be the third derivative of 0*p + 0*p**5 + 0*p**4 - 117*p**2 + 0*p**3 + 0 + 1/84*p**8 + 2/15*p**6 - 2/21*p**7. Suppose f(d) = 0. What is d?
0, 1, 4
Let j be 202/303 - (-30)/36. Let -6 + j*p**2 + 0*p = 0. Calculate p.
-2, 2
Let x(v) = v**3 + 8*v**2 - v - 6. Let m be x(1). Let -10/11*a**m + 0 - 4/11*a**3 + 2/11*a**4 + 12/11*a = 0. Calculate a.
-2, 0, 1, 3
Let n(q) be the second derivative of -2*q**6/15 + 3*q**5/5 + 4*q**4/3 + 508*q. Factor n(u).
-4*u**2*(u - 4)*(u + 1)
Let y(c) = 2*c**2 - 2*c - 17. Suppose -209 + 205 = -w. Let l be y(w). Solve 0*z**3 - 11 - l + 2*z**3 + 28 + 14*z**2 + 22*z = 0.
-5, -1
Determine j, given that 2*j**5 + 7*j**3 - 81*j**2 - 92*j**2 - 7*j**5 + 103*j**2 - 10*j**4 + 53*j**3 + 25*j = 0.
-5, 0, 1
Let y = -85679 - -85681. Let w = -669/4 + 168. Let 2*a - 2*a**3 - w*a**4 - 3/4 + 3/2*a**y = 0. What is a?
-3, -1, 1/3, 1
Let n(f) be the third derivative of f**8/588 - 2*f**7/105 - 6*f**6/35 + 32*f**5/105 + 128*f**4/21 + 160*f**3/7 - 165*f**2 + 3*f. Find p such that n(p) = 0.
-2, 3, 10
Factor 4051*p + 7*p**2 - 2*p**3 - 26 - 4030*p + p**3 - 1.
-(p - 9)*(p - 1)*(p + 3)
Let c(x) = -2*x**2 + 1600*x + 6434. Let f be c(-4). Find n such that 1/8*n**3 + 1/2*n**f + 1/2*n + 0 = 0.
-2, 0
Let i be (24*(-75)/(-1140))/3. Let -44/19*t**2 - 18/19*t**3 + i*t**4 + 16/19 + 72/19*t = 0. What is t?
-2, -1/5, 2
Let n(o) be the second derivative of 4*o**4/3 + 962*o**3 - 722*o**2 - 12044*o. Factor n(z).
4*(z + 361)*(4*z - 1)
Let k(z) be the first derivative of 8*z**5 + 165*z**4/4 + 220*z**3/3 + 105*z**2/2 + 10*z - 912. Factor k(x).
5*(x + 1)**2*(x + 2)*(8*x + 1)
Let f(x) = -2*x**3 + 183*x**2 - 1111*x + 1335. Let v(l) = l**3 - 94*l**2 + 555*l - 666. Let u(g) = -8*f(g) - 18*v(g). Determine w so that u(w) = 0.
2, 3, 109
Let h(b) be the first derivative of -62/3*b**2 - 66 + 0*b + 2/9*b**3. Factor h(p).
2*p*(p - 62)/3
Let t(h) = 10*h**4 + 302*h**3 + 24