k).
-(k - 5)*(k + 2)
Suppose -r - 5*v + 514 = 0, 3*r = 8*v - 4*v + 1466. Let u = r - 1475/3. What is j in 1 - u*j + 5/3*j**2 - 1/3*j**3 = 0?
1, 3
Let w = -310 - -226. Let v be 0/(2/3*w/56). Factor 0*m + v + 1/4*m**3 - 1/4*m**2.
m**2*(m - 1)/4
Let s(t) be the first derivative of 27/2*t**2 + 26*t - 93 + 1/3*t**3. Factor s(o).
(o + 1)*(o + 26)
Let -459 + 156*f - 20*f**2 + 18 + 28*f**2 - 11*f**2 = 0. What is f?
3, 49
Let q(c) be the second derivative of -c**6/150 - 13*c**5/25 - 28*c**4/3 + 1568*c**3/15 - 187*c + 3. Solve q(u) = 0.
-28, 0, 4
Factor -1314*r + 327*r + 385 - 3*r**2 - 384 + 989.
-3*(r - 1)*(r + 330)
Let c(z) be the third derivative of -1/105*z**5 + 0*z**3 + 0 + 5*z - 10/21*z**4 - 5*z**2. Suppose c(m) = 0. Calculate m.
-20, 0
Let q(h) be the first derivative of h**7/4200 + 7*h**6/1800 + 2*h**5/75 + h**4/10 - 74*h**3/3 - 56. Let c(t) be the third derivative of q(t). Factor c(a).
(a + 2)**2*(a + 3)/5
Let b(a) = -2*a**2 + 22*a + 26. Let r be b(14). Let w = r + 408/7. Solve 6/7*k - w - 4/7*k**2 = 0.
1/2, 1
Let p = 4909 - 4906. Let l(x) be the second derivative of 0 + 1/6*x**4 + 2*x**p + 9*x**2 - 10*x. Factor l(r).
2*(r + 3)**2
Suppose 8*r - 123 = -43. Factor -4*n**2 - r*n + 2*n**3 - 8 + 4*n**2 - n**3 - n**2.
(n - 4)*(n + 1)*(n + 2)
Let p(u) be the second derivative of u**6/165 + 326*u**5/55 + 325*u**4/11 + 1948*u**3/33 + 59*u**2 - 300*u - 4. Solve p(j) = 0.
-649, -1
Let j = 8492 - 8490. Let v(z) be the second derivative of 0*z**4 - 1/40*z**5 + 1/12*z**3 + 0 - 20*z + 0*z**j. Factor v(l).
-l*(l - 1)*(l + 1)/2
Let y(w) = -15*w - 4. Suppose 8 = 2*b + 5*a - 5, -3*b - 18 = -5*a. Let c be y(b). Factor -2*r**2 - r**2 + 0 + 1 + c.
-3*(r - 2)*(r + 2)
Suppose -3/2*d**3 - 141/2*d**2 + 0 + 0*d = 0. Calculate d.
-47, 0
Let i = -2 + 14. Suppose -2*n + 29 = 3*x, 5*n - x = i + 69. Factor 3*k**3 - n*k + 8*k**2 + 2*k**3 - k**3 - 5*k**4 + 3*k**4.
-2*k*(k - 2)**2*(k + 2)
Suppose 0 = 192*a - 201*a + 207. Find g, given that 56*g**2 + 271*g**2 + 97*g**2 - 32 - 1040*g**4 - a*g + 68*g**3 + 7*g - 700*g**5 = 0.
-1, -2/7, 2/5
Let l = 1143103 - 1143091. Let -8/3*q**5 + 14/3*q**4 - 28/3*q - 2 - 8/3*q**2 + l*q**3 = 0. What is q?
-1, -1/4, 1, 3
Let j = -278677 - -278680. Factor 0*x**2 + 2/7*x + 0 - 2/7*x**j.
-2*x*(x - 1)*(x + 1)/7
Determine f, given that 118*f + 0*f**3 + 206 + 4*f**3 - 79 + 278*f + 177 + 96*f**2 = 0.
-19, -4, -1
Let -12 - 637/5*x**4 + 3696/5*x**3 + 692/5*x - 2691/5*x**2 = 0. Calculate x.
3/13, 2/7, 5
Let l(o) be the first derivative of -21/5*o**2 - 170 - 1/5*o**3 - 72/5*o. Factor l(b).
-3*(b + 2)*(b + 12)/5
Let t be (3 - 4 - 0)*-4. Let a(y) = -2*y + 8. Let v(d) = -d**2. Let n(s) = t*v(s) + 4*a(s). Suppose n(b) = 0. What is b?
-4, 2
Let c = 191540 + -191538. Let -2/7 + 2/7*d + 2/7*d**c - 2/7*d**3 = 0. Calculate d.
-1, 1
Determine l so that 0 - 98*l + 1/4*l**2 = 0.
0, 392
Let g(w) = -3*w**3 + w**2 - w - 1. Let s be g(-1). Suppose -31 - 17 = -s*a. Factor -3*i - 2 + 3*i - 10*i**2 + a*i**2.
2*(i - 1)*(i + 1)
Let y = 2/2155 + 2149/6465. Let g(z) be the second derivative of 0*z**2 + 0*z**3 - 15*z + 0 + y*z**4 - 1/5*z**5. Factor g(x).
-4*x**2*(x - 1)
Let n = 123308 - 123304. Factor 24/7*r**3 + 36/7*r**2 + 0 + 3/7*r**n + 0*r.
3*r**2*(r + 2)*(r + 6)/7
Let u be 2784/88 - (-450)/(-275). Factor -3*i**2 - u*i - 36 + 3/2*i**3.
3*(i - 6)*(i + 2)**2/2
Let b(q) be the second derivative of 31/28*q**4 + 675/14*q**2 + 0 + 255/14*q**3 + 3/140*q**5 + 23*q. Factor b(d).
3*(d + 1)*(d + 15)**2/7
Let t be 18/(-1600)*-445 + -5. Let n(y) be the third derivative of -15*y**2 - 1/16*y**3 + 0*y**4 + 0 + 0*y + t*y**5. Let n(f) = 0. What is f?
-1, 1
Let u be 0 - -7 - (-1 - -6)/5. Suppose -17 - 37 = -u*p. Factor -12*q**4 - 33*q**4 - 10*q - 70*q**2 + p*q**2 - 100*q**3 - 4*q**2.
-5*q*(q + 1)**2*(9*q + 2)
Let d be 3*9/12 + (-6183)/108 + 57. Factor 14/3*i**d + 2/3*i**3 + 28/3*i + 16/3.
2*(i + 1)*(i + 2)*(i + 4)/3
Let p(c) be the first derivative of -2*c**3 + 0*c + 55 - 3/4*c**4 - 3/2*c**2. Suppose p(a) = 0. Calculate a.
-1, 0
Let -3099/4*d**3 + 51/4*d**5 + 2937/4*d**2 - 183*d + 975/4*d**4 - 33 = 0. Calculate d.
-22, -2/17, 1
Let n be ((-4687)/(-129) - 39)*(54/(-4))/(8 - -2). Factor -n*b - 3/5*b**2 - 24/5.
-3*(b + 2)*(b + 4)/5
Let y(a) = -10*a - 125. Let s be y(-14). Let b(j) = 17*j. Let x be b(1). Factor -15*p**3 - 36*p - 26*p**2 + 7 - 13*p**2 + x - s*p**2.
-3*(p + 2)**2*(5*p - 2)
Let l = 1023/796 + 192/199. What is j in l*j + 3/2 - 3/4*j**3 + 0*j**2 = 0?
-1, 2
Let w be 104/39*-1*(-3 + 0). Let z(j) be the first derivative of -2/3*j**3 + 0*j**2 + 31 + w*j. Determine h, given that z(h) = 0.
-2, 2
Let f be (-15)/35 + (-2495)/(-5985). Let c = 376/2907 + f. Factor 0*z**2 - 2/17*z**3 + 0*z - c*z**4 + 0.
-2*z**3*(z + 1)/17
Let b = 1102 + -1093. Let s = 9 - b. Determine z, given that -4/5*z + 8/5*z**2 + 1/5*z**4 - z**3 + s = 0.
0, 1, 2
Let n(a) be the second derivative of a**5/16 + 1085*a**4/12 + 2165*a**3/6 - 5873*a. Factor n(y).
5*y*(y + 2)*(y + 866)/4
Let w(r) = 4*r - 153. Let x be w(40). Determine v, given that 15 - 29*v**5 + 15*v**4 - 30*v**2 + 10*v**5 - 5*v + x*v**5 + 7*v**5 + 10*v**3 = 0.
-1, 1, 3
Let f(o) be the second derivative of 2*o**6/15 - 11*o**5/5 - 25*o**4/3 - 26*o**3/3 + 716*o + 3. Factor f(z).
4*z*(z - 13)*(z + 1)**2
Let 3/5*b**2 - 378/5*b - 2376/5 = 0. What is b?
-6, 132
Let b(d) = -159*d**2 - 2*d + 5 - 4*d**3 + 0*d + 153*d**2. Let q be b(-5). Factor -10*i**2 - 4*i - 351*i**3 + 2 + q*i**3 - 2.
2*i*(i - 1)*(7*i + 2)
Let d = 21 + -7. Solve 0*r + r + 3*r + r**2 - d + 4*r - r**3 + 2 = 0 for r.
-3, 2
Let l(m) = 24*m**2 + 1654*m - 3257. Let n(c) = 17*c**2 + 1103*c - 2169. Let u(z) = -5*l(z) + 7*n(z). Suppose u(r) = 0. Calculate r.
-551, 2
What is a in 140*a**3 - 5061*a**4 + 4948*a - 448*a - 1500*a**2 + 5057*a**4 = 0?
0, 5, 15
Let b(i) be the first derivative of 2/9*i**6 + 0*i**2 + 0*i + 6*i**3 - 5/3*i**5 + 125/24*i**4 - 4. Let u(z) be the third derivative of b(z). Factor u(s).
5*(4*s - 5)**2
Let g(x) = -3*x**4 - 59*x**3 + 233*x**2 - 317*x + 126. Let a(n) = 80*n**4 + 1600*n**3 - 6290*n**2 + 8560*n - 3400. Let v(f) = 2*a(f) + 55*g(f). Factor v(z).
-5*(z - 2)*(z - 1)**2*(z + 13)
Let s be (-1)/(5/(-2)) + (-492)/(-20). Suppose 3*z - 26 - s = 0. Solve 7*g**3 - 20*g - g**2 - 9*g**3 + 21*g**2 + z*g**3 = 0.
-2, 0, 2/3
Let x be -8*5/(-18)*(-6)/(-4) - (-44)/(-66). Suppose x + 1/6*b**2 + 17/6*b = 0. What is b?
-16, -1
Let p(c) be the third derivative of -2*c + 0 - 1/40*c**6 + 1/10*c**5 + 0*c**4 + 34*c**2 + 0*c**3. Factor p(w).
-3*w**2*(w - 2)
Let g(w) = w**3 - 8*w**2 + 2*w - 11. Suppose -k + 3 = -5. Let f be g(k). Factor 2*n**4 - n**3 + 2 + f*n**3 - 2 + 2*n**2.
2*n**2*(n + 1)**2
Suppose i - 3*i = -4*f + 6, 3*i + 4*f + 29 = 0. Let b be (-12)/(-18) - i/3. Suppose -256/5 - 1/5*w**4 + 256/5*w + 16/5*w**b - 96/5*w**2 = 0. Calculate w.
4
Let r(q) = q**4 + q**3 - 14*q**2 - 4*q + 4. Let m(i) = -17*i**2 - 2 + 2*i**2 - 5*i + 0 + 7. Let a = 6 + -2. Let l(f) = a*m(f) - 5*r(f). Solve l(k) = 0.
-2, 0, 1
What is u in 13/5*u**2 + 44/5*u + 1/5*u**3 + 32/5 = 0?
-8, -4, -1
Let v(q) be the first derivative of q**6/21 - 51*q**4/14 - 452*q**3/21 - 372*q**2/7 - 432*q/7 - 1295. What is a in v(a) = 0?
-3, -2, 9
Let s = -43/2568 - -899/2568. Factor -4/3*v + 8 + s*v**3 - 10/3*v**2 + 1/3*v**4.
(v - 2)**2*(v + 2)*(v + 3)/3
Suppose -18 = -25*r + 16*r. Determine n, given that -2*n - n**4 - r*n**2 + 3*n**2 - 2322*n**3 + 2324*n**3 = 0.
-1, 0, 1, 2
Suppose -4*a = -2*g + g - 4, 2*g - 1 = -a. Let t(n) be the third derivative of g*n + 1/3*n**4 - 1/15*n**5 - 5*n**2 + 0*n**3 + 0. Factor t(y).
-4*y*(y - 2)
Suppose 83 = 9*g - 79. Let c be 9/g*(-12)/(-2). Factor c*x**2 + 19*x**2 - 19*x + 8*x**3 - 19*x + 8.
2*(x - 1)*(x + 4)*(4*x - 1)
Solve 62/19*y**3 + 8/19*y**4 + 8*y**2 + 102/19*y - 36/19 = 0.
-3, -2, 1/4
Suppose -766 = -14*p + 88. Suppose -4*i = l - 43, 2*l + 3*l = 3*i - p. Factor 24/7*a**3 + 36/7 + 3/7*a**4 + i*a + 69/7*a**2.
3*(a + 1)*(a + 2)**2*(a + 3)/7
Factor 0 + 24/7*b**2 - 9/7*b**3 + 1/7*b**4 - 16/7*b.
b*(b - 4)**2*(b - 1)/7
Let i(m) = 1. Let h(n) = 3*n - 32. Let z(p) = -h(p) + 4*i(p). Let y be z(11). Factor -307 + 307 - 8*s**2 - 12*s + 4*s**y.
4*s*(s - 3)*(s + 1)
Let c(x) = -x**3 - 3*x**2 + 12*x + 34. Let a be c(-4). Factor 23*s + 11*s**3 - 24*s**a + 3*s - 10*s**3 - 3*s.
s*(s - 23)*(s - 1)
Let r(x) be the first derivative of 31 