et k(z) = -z**3 + 4*z**2 - z - 2. Let f = 12 - 9. Let w(l) = -2*l**3 + 5*l**2 - 2*l - 3. Let x(p) = f*k(p) - 2*w(p). Factor x(n).
n*(n + 1)**2
Suppose -4*s = 90 + 754. Let u = s - -214. Factor 3/4*j + 0 + 3/2*j**2 - 3/2*j**4 + 0*j**u - 3/4*j**5.
-3*j*(j - 1)*(j + 1)**3/4
Let z(c) be the third derivative of 32*c**7/735 + 176*c**6/105 + 968*c**5/35 + 5324*c**4/21 + 29282*c**3/21 - 84*c**2 - c. Factor z(r).
4*(2*r + 11)**4/7
Let u(m) be the second derivative of -1/180*m**6 + 14*m - 1/72*m**4 + 1/12*m**3 + 0 - 1/40*m**5 + 1/6*m**2. What is s in u(s) = 0?
-2, -1, 1
Let x(i) be the first derivative of i**4/12 + 2*i**3/3 + i**2/2 - 10*i/3 + 134. Factor x(o).
(o - 1)*(o + 2)*(o + 5)/3
Let y = -1542 - -1546. Let l(p) be the second derivative of 0*p**3 - 1/8*p**y + 0*p**2 + 1/56*p**7 - 3/80*p**5 + p + 0 + 1/20*p**6. Find a, given that l(a) = 0.
-2, -1, 0, 1
Let i(n) be the second derivative of n**5/160 - n**4/96 - 5*n**3/24 - n**2/2 - 31*n - 2. Determine u, given that i(u) = 0.
-2, -1, 4
Let v(h) = h**3 + 5*h**2 + h + 3. Suppose -5*u + 0*u + 15 = 0. Let p(w) = 2*w**3 + 9*w**2 + 2*w + 5. Let b(k) = u*p(k) - 5*v(k). Factor b(f).
f*(f + 1)**2
Let p(j) = 2*j + 1 - 2 - 14*j**2 + 10*j + 15*j**2. Let z be p(-13). Factor u**2 - z*u + 0*u - 6 - 2 - 5*u**2.
-4*(u + 1)*(u + 2)
Let n = 87 + -695/8. Let g(s) be the first derivative of 2 - n*s**2 - 1/12*s**3 + 0*s. Factor g(v).
-v*(v + 1)/4
Suppose 16605 - 16617 = -6*x. Factor 10/17*j**3 - 4/17 - 24/17*j**x + 18/17*j.
2*(j - 1)**2*(5*j - 2)/17
Let p(n) be the second derivative of 0 - 10*n + 4/3*n**3 - 2*n**2 - 1/3*n**4. Solve p(w) = 0.
1
Let d be 22 + 2016/(-105) + 1/5. Determine r, given that 16*r - 8*r**2 + 4/3*r**d - 32/3 = 0.
2
Let o = 177 - 172. Let g(l) be the first derivative of -1/27*l**6 + 8/27*l**3 - 4 - 1/9*l**2 + 1/9*l**4 - 4/9*l - 4/45*l**o. Find w such that g(w) = 0.
-2, -1, 1
Let n(h) be the third derivative of -25*h**2 - 1/210*h**5 + 0*h - 1/420*h**6 + 5/84*h**4 + 0 - 1/7*h**3. What is r in n(r) = 0?
-3, 1
Let x = 56345/204 + -3313/12. Factor 22/17 + 24/17*t + x*t**2.
2*(t + 1)*(t + 11)/17
Let p = 454 + -3177/7. Let y(s) be the first derivative of 0*s**2 + 1/7*s**3 - p*s + 1/14*s**4 - 6. Find h, given that y(h) = 0.
-1, 1/2
Let h(w) = 5*w**3 - w**2. Let r(t) = 14*t**3 - 4*t**2 + t - 1. Let l(v) = 11*h(v) - 4*r(v). Let o be l(4). Factor o*n**2 + 53*n - 53*n - 16.
4*(n - 2)*(n + 2)
Let v(p) be the first derivative of 0*p**3 + 0*p + 21 + 11/2*p**4 + 2/3*p**6 - 4*p**2 + 18/5*p**5. Determine q, given that v(q) = 0.
-2, -1, 0, 1/2
Let h(t) be the third derivative of 0*t**4 + 0 + 5*t**2 - 4/105*t**7 - 1/60*t**6 + 0*t**3 + 1/10*t**5 + 0*t. Let h(c) = 0. What is c?
-1, 0, 3/4
Let k(t) = -2*t**2 - 2*t. Let z(j) = 4*j**2 + 3*j - 1. Let h(d) = -5*k(d) - 2*z(d). Find u such that h(u) = 0.
-1
What is l in 3/5*l**5 - 129/5*l**2 + 9/5*l**3 - 84/5*l + 36 + 21/5*l**4 = 0?
-5, -3, -2, 1, 2
Let i = 2764 + -2759. Let h(o) be the first derivative of o**4 - 8 - 2*o - 4/3*o**6 + 16/3*o**3 - 14/5*o**i + 2*o**2. Determine p, given that h(p) = 0.
-1, 1/4, 1
Factor 3405*g - 22945*g**2 + 314*g**3 - 1331*g**2 - 29028*g**3 - 656 - 10309*g - 686*g**4.
-2*(g + 41)*(7*g + 2)**3
Let g(d) = -2*d + 16. Let s be g(5). Suppose s*i - i = 0. Solve -1 - 522*f + i + 524*f - f**2 = 0.
1
Suppose 9*r**4 - 415 + 216*r + 95*r**2 + 114*r**3 + 166*r**2 + 475 = 0. What is r?
-10, -1, -2/3
Let m = 215 - 213. Let w(a) be the second derivative of -2*a**5 + 0*a**m - 2/5*a**6 - 8*a + 0 + 0*a**3 - a**4. Find q such that w(q) = 0.
-3, -1/3, 0
Let z = 1374919/370 + -3716. Let k = 1477/1110 - z. Factor 0 + 0*o + 2/3*o**3 + k*o**2.
2*o**2*(o + 2)/3
Let i(l) be the second derivative of -l**6/2 + 87*l**5/10 - 39*l**4 - 36*l**3 - 2*l - 6. Factor i(h).
-3*h*(h - 6)**2*(5*h + 2)
Let y be -11 - (4625/85)/(-5) - 38/(-34). Solve 17/4*q**2 + y - q**3 - 5*q = 0 for q.
1/4, 2
Let d be (-20)/16*((-159)/30 - -5). Let g(t) be the first derivative of -d*t**4 - 1/6*t**3 - 1 + 1/2*t**2 + 0*t. Factor g(h).
-h*(h + 1)*(3*h - 2)/2
Let c(q) = 6*q**3 - q**2 - 2*q. Let x be c(2). Let t be (-1)/(8/6) + 38/x. Factor 1/5*p**2 - t*p**4 + 0*p - 1/5*p**3 + 1/5*p**5 + 0.
p**2*(p - 1)**2*(p + 1)/5
Let b = 34261159493/4744696115 - 72/3970457. Let u = b - 5/239. Factor 21/5*l**5 + 0 - 6/5*l**2 + u*l**4 + 0*l + 9/5*l**3.
3*l**2*(l + 1)**2*(7*l - 2)/5
Factor 22 - 62 - 55*d**2 + 60*d**2 - 10*d.
5*(d - 4)*(d + 2)
Let y(j) be the first derivative of -7*j**3 + 6*j**2 + 474. Factor y(f).
-3*f*(7*f - 4)
Suppose -3*t = -95 + 77. Let y(u) = 21*u**2 - 46*u + 26. Let s(v) = -62*v**2 + 137*v - 77. Let g(d) = t*s(d) + 17*y(d). Factor g(w).
-5*(w - 2)*(3*w - 2)
Let z(d) be the third derivative of -d**8/224 - d**7/28 - 7*d**6/80 + d**5/40 + d**4/2 + d**3 + d**2 + 172*d. Determine c so that z(c) = 0.
-2, -1, 1
Let p(k) be the second derivative of 1/10*k**6 + 1/2*k**3 + 1/4*k**4 + 0 - 7/20*k**5 + k + 5*k**2. Let w(i) be the first derivative of p(i). Factor w(j).
3*(j - 1)**2*(4*j + 1)
Let w(t) = -2*t**3 - 2*t**2 + 4*t. Let n be w(-3). Let y be (n/20)/((-1)/(-25)). Factor 3 - y*m**5 - 4*m**3 - 3 + 31*m**5.
m**3*(m - 2)*(m + 2)
Factor 172*w + 45 - 3 - 2 - 202*w + 5*w**2.
5*(w - 4)*(w - 2)
Let v(s) be the first derivative of 7*s**4/9 - 152*s**3/27 + 10*s**2/3 - 457. Factor v(u).
4*u*(u - 5)*(7*u - 3)/9
Let p(s) = -s**3 + s**2 + 1. Let i(g) = -2*g**3 - 10*g**2 - 6*g + 77. Let q(j) = i(j) - 5*p(j). Factor q(x).
3*(x - 4)*(x - 3)*(x + 2)
Let v(s) = 2*s**5 + 8*s**4 + 14*s**3 - 10*s**2 + s. Let k(f) = -f**5 - 7*f**4 - 13*f**3 + 11*f**2 - 2*f. Let t(b) = -5*k(b) - 4*v(b). Factor t(x).
-3*x*(x - 1)**3*(x + 2)
Let r = 2 - -2. Let w = -1425 + 1425. Factor -2/7*p**3 + 0*p + 1/7*p**2 + w + 1/7*p**r.
p**2*(p - 1)**2/7
Solve 0*w**2 + 1/4*w**3 + 0*w + 0 - 1/4*w**4 = 0 for w.
0, 1
Let b be (13 - 3/(-3)) + 3 + -1. Suppose -4*g**5 + 0*g**5 + 4*g**4 + 13*g**3 - b*g**3 - 4*g**2 + 4*g + 3*g**5 = 0. What is g?
-1, 0, 1, 2
Factor 8*j + 42957 + 3*j**2 + 32*j - 42944.
(j + 13)*(3*j + 1)
Let n = 1607 + -1597. Let f(b) be the second derivative of -n*b + 0 - 1/12*b**4 + 0*b**2 + 1/3*b**3. Suppose f(y) = 0. Calculate y.
0, 2
Let u(b) = 8*b**5 - 11*b**3 + 3*b - 5. Let x(p) = -18*p**5 - 6*p**5 + 9*p**5 + 9 - 6*p + 21*p**3. Let t = 5 + -10. Let h(g) = t*x(g) - 9*u(g). Factor h(w).
3*w*(w - 1)**2*(w + 1)**2
Let i be (260/(-728))/(2/(-7)). Let c(j) be the first derivative of 10/3*j**3 + 5/2*j**2 + i*j**4 - 8 + 0*j. Solve c(z) = 0.
-1, 0
Let i(a) be the third derivative of a**7/210 + a**6/20 + a**5/5 + a**4/3 + 29*a**2 - 8*a. Solve i(t) = 0 for t.
-2, 0
Let u be 0 - (4 - 3)*-2. Factor -2/11 + 10/11*f**u - 6/11*f**3 - 2/11*f.
-2*(f - 1)**2*(3*f + 1)/11
Suppose 18 = 2*f - 6*w + w, -4*w - 48 = -4*f. Suppose 0 = f*k - 27*k + 39. Factor -4/5*b**k + 8/5 + 2/5*b**4 + 8/5*b - 6/5*b**2.
2*(b - 2)**2*(b + 1)**2/5
Determine p, given that 1/2*p**4 - 5/6*p**5 + 7/6*p**3 + 0 - 1/3*p - 1/2*p**2 = 0.
-1, -2/5, 0, 1
Find v such that 5/3*v**3 + 215*v + 0 - 650/3*v**2 = 0.
0, 1, 129
Let g be (-1)/(-75)*((-243)/(-18) + -12). Let s(d) be the second derivative of -g*d**6 - 1/20*d**4 + 0*d**3 + 0*d**2 + 3/50*d**5 + 0 - d. Factor s(u).
-3*u**2*(u - 1)**2/5
Let a = 1386 - 24947/18. Let q(m) be the third derivative of -1/72*m**5 + m**2 + 0*m + 1/48*m**4 + a*m**3 + 0. What is k in q(k) = 0?
-2/5, 1
Suppose -2/3*d**2 - 35378/3 - 532/3*d = 0. What is d?
-133
Let u(n) be the first derivative of -3*n + n**3 + 1/4*n**4 - 3 + 3/2*n**2. Let w(g) be the first derivative of u(g). Suppose w(s) = 0. What is s?
-1
Suppose -3*l + 12*l - 63 = 0. Determine w, given that 2*w**2 + l*w**2 - 4*w - 13*w**2 = 0.
-1, 0
Factor 9/10*q**2 + 0 - 1/10*q**3 - 2*q.
-q*(q - 5)*(q - 4)/10
Let i(l) = -l**2 - 84*l + 93. Let n(t) = 4*t**2 + 251*t - 277. Let d(j) = 11*i(j) + 4*n(j). Find p, given that d(p) = 0.
-17, 1
Let r = 4 + -25. Let t be (-2)/(-7) + (-162)/r. Find d, given that -t + 378*d**4 + 48*d + 17*d**2 - 530*d**3 + 6*d**2 + 7*d**2 + 0*d + 882*d**5 = 0.
-1, -1/3, 2/7, 1/3
Let d = 263 + -256. Let m(w) be the third derivative of 2/105*w**d + 0 + 0*w**4 + 0*w**5 + 0*w - 1/60*w**6 + 0*w**3 + w**2. Factor m(a).
2*a**3*(2*a - 1)
Factor 98/13 + 0*t - 2/13*t**2.
-2*(t - 7)*(t + 7)/13
Let n(l) = 153*l + 15916. Let t be n(-104). Factor -4/7 - 110/7*m**3 - 26/7*m + 38/7*m**t + 102/7*m**2.
2*(m - 1)**3*(