3
Suppose 4*k + 18 + 18 = -5*p, -4*k - 2*p = 48. Let m be ((-3)/(-84)*4)/((-7)/k). Factor 2/7*x**2 + 0*x + 0 - 2/7*x**4 + 2/7*x**5 - m*x**3.
2*x**2*(x - 1)**2*(x + 1)/7
Let u be 81/20 + 62 + (-15575)/250. What is p in 25/2 - 5/4*p**2 - u*p = 0?
-5, 2
Let q = 8809/22110 - -7/4422. Suppose 66/5*w - q*w**2 - 2/5*w**3 - 126/5 = 0. Calculate w.
-7, 3
Suppose -5*r = 3*i + 9, -6*r + r - 23 = -4*i. Determine h, given that -35*h + 8*h**2 + 54 - 5*h**2 - 6*h**i - 16*h = 0.
-18, 1
Suppose -70304 - 620/3*v**4 - 35724*v**2 - 4036*v**3 - 382616/3*v - 4*v**5 = 0. Calculate v.
-13, -12, -2/3
Let j = 1806/17 + -37909/357. Let f(q) be the second derivative of -j*q**3 + 0 - 8*q - 2/7*q**2 + 1/14*q**4. Find p such that f(p) = 0.
-2/3, 1
Let s be -3*(-3 - (8 - 12)). Let m be (s/(-2))/((-6)/(-12)). Factor 6/5*y**2 + 0*y + 2/5*y**m - 8/5.
2*(y - 1)*(y + 2)**2/5
Let t be (1/(-2) - 1)/(60/(-80)). Factor 3*i**t - 27*i + 2 - 2 + 13 + 11.
3*(i - 8)*(i - 1)
Let p(d) = -2*d**2 - 24*d - 2. Let t be p(-12). Let r be (-14)/(-3) - t/(-3). Factor r*u + 12 + 14*u**3 - 8*u**2 + 4 - 18*u**3 - 8*u**2.
-4*(u - 1)*(u + 1)*(u + 4)
Let x(g) be the second derivative of 1/30*g**5 + 8/3*g**2 + 4/3*g**3 - g + 111 + 1/3*g**4. Suppose x(q) = 0. What is q?
-2
Let o be 3/((-4)/(12/(-15))). Let p = -46960 + 46960. Solve -1/5*h**5 + p*h - 1/5*h**2 - 3/5*h**3 - o*h**4 + 0 = 0.
-1, 0
Let r(z) = -z**2 + 38*z - 98. Let h be (-18)/(10/((-5)/(-1))). Let w(s) = 3*s**2 - 153*s + 393. Let t(q) = h*r(q) - 2*w(q). Determine x so that t(x) = 0.
4, 8
Let d(u) be the second derivative of 2*u**6/15 - 8*u**5/5 + 19*u**4/3 - 8*u**3 - 1482*u. Factor d(l).
4*l*(l - 4)*(l - 3)*(l - 1)
Find x, given that 0*x**5 - 8*x**4 + 138*x**3 + 17387*x**2 + 2*x**5 - 17245*x**2 - 155*x**4 + 21*x**4 - 140*x = 0.
-1, 0, 1, 70
Let z(j) be the second derivative of j**4/78 + 27*j**3/13 - 340*j**2/13 - 6793*j. Factor z(b).
2*(b - 4)*(b + 85)/13
Suppose -6*j - 3*j + 234 = 0. Suppose j*z = 25*z + 5. Factor -21*n**4 + 16*n**4 + 0*n**5 - 35*n**2 - 20*n**4 + 10*n + 5*n**z + 45*n**3.
5*n*(n - 2)*(n - 1)**3
Let f(v) = 20*v**3 - 187*v**2 - 876*v + 385. Let z(i) = -7*i**3 + 62*i**2 + 313*i - 128. Let c(s) = 6*f(s) + 17*z(s). Factor c(w).
(w - 67)*(w - 2)*(w + 1)
Determine c so that -218/3*c - 2/9*c**2 + 0 = 0.
-327, 0
Let r(t) be the first derivative of 5*t**6/6 + 1899*t**5 + 4521975*t**4/4 + 13509005*t**3/3 + 6745020*t**2 + 4493520*t + 3622. Solve r(h) = 0.
-948, -1
Suppose 81*l - 80*l - 1 = 9, 3*f + 3*l = 36. Factor -1/2*i**4 - 9/2 - 6*i + i**2 + f*i**3.
-(i - 3)**2*(i + 1)**2/2
Let j(u) be the second derivative of -u**7/126 - 2*u**6/15 + 7*u**5/60 + 13*u**4/6 - 4*u**3 + 4142*u. Solve j(k) = 0 for k.
-12, -3, 0, 1, 2
Let b = 391961/4 - 98546. Let j = 562 + b. Find k, given that -j - 15/4*k - 1/4*k**3 + 9/4*k**2 = 0.
-1, 5
Let r(v) be the first derivative of -4/5*v**5 + 4/3*v**6 + 0*v**2 + 0*v - 3*v**4 + 0*v**3 + 153. Factor r(t).
4*t**3*(t + 1)*(2*t - 3)
Suppose 0 = 3*n - i - 48, n + 25*i - 24*i - 16 = 0. Suppose 0 = -3*g - 3*v - 3, -v = -5*v - n. Factor 8/13*j + 12/13*j**2 + 2/13*j**4 + 8/13*j**g + 2/13.
2*(j + 1)**4/13
Suppose 5*f = 10, 2*w - 3*f - 22 = -14*f. Let n(t) be the third derivative of 0*t - 7*t**2 + 1/9*t**4 - 1/90*t**5 - 1/3*t**3 + w. Factor n(k).
-2*(k - 3)*(k - 1)/3
Let m(r) be the second derivative of r**7/84 + 17*r**6/5 + 81*r**5/8 + 101*r**4/12 + 2441*r - 1. Factor m(y).
y**2*(y + 1)**2*(y + 202)/2
Let p(m) be the third derivative of -m**8/10080 + m**7/840 - 18*m**5/5 - 72*m**2. Let i(u) be the third derivative of p(u). Factor i(n).
-2*n*(n - 3)
Suppose 0 = -29944*c + 29889*c. Factor -3/7*y**2 + c - 15/7*y.
-3*y*(y + 5)/7
Let d = -2561 + 3649. Suppose 1073 = -5*g + d. Let -1/2*o - 1 + 1/2*o**g + o**2 = 0. Calculate o.
-2, -1, 1
Factor -175/2 + 395/2*r + r**4 - 87/2*r**2 - 7/2*r**3.
(r - 5)**2*(r + 7)*(2*r - 1)/2
Let x(l) be the third derivative of 0 + 1/30*l**4 + 1/10*l**3 - 1/150*l**6 - 1/150*l**5 - l**2 + 14*l - 1/1050*l**7. Factor x(c).
-(c - 1)*(c + 1)**2*(c + 3)/5
Let d(c) be the first derivative of 1/195*c**5 + 4/39*c**3 + 0*c - 27 - 3/52*c**4 + 17/2*c**2. Let r(z) be the second derivative of d(z). Factor r(l).
2*(l - 4)*(2*l - 1)/13
Let i = 23 + -23. Let q(w) be the second derivative of 1/39*w**3 + 23/65*w**5 + 0 - 2/13*w**4 + 25/273*w**7 - 4/13*w**6 + i*w**2 + 2*w. Factor q(m).
2*m*(m - 1)**2*(5*m - 1)**2/13
Let p be 640/(-264)*(-1233)/1096. Find a, given that -p*a - 2/11*a**2 + 32/11 = 0.
-16, 1
Let w(l) be the third derivative of -5/8*l**4 + 0*l**3 + 0*l + 7*l**2 + 19/20*l**5 + 19. Solve w(c) = 0.
0, 5/19
Determine p, given that 109*p**3 - 114*p**3 - 74*p**2 - 16*p**2 - 289*p - 71*p = 0.
-12, -6, 0
Let b(n) = 2*n**3 - 836*n**2 - 1700*n - 16. Let v(i) = -7*i**3 + 3342*i**2 + 6802*i + 72. Let p(d) = -9*b(d) - 2*v(d). Factor p(t).
-4*t*(t - 212)*(t + 2)
Let s(k) be the first derivative of 40/9*k**3 - k**4 - 88/9*k**2 + 4/45*k**5 + 32/3*k + 55. Let s(d) = 0. What is d?
2, 3
Let a(l) = 10*l - 8. Let p be a(2). Let g(n) be the second derivative of 1/3*n**3 + 2/9*n**4 + 0 - p*n - 1/30*n**5 - 6*n**2. Factor g(s).
-2*(s - 3)**2*(s + 2)/3
Suppose -28390*l**2 - 4825/3*l**3 - 65/3*l**4 - 72200/3 + 162260/3*l = 0. Calculate l.
-38, 10/13, 1
Suppose 2*k + 2*k = 5*w + 30, k + w = 3. Factor -37 + l**5 - 4*l**4 + 2*l**2 - k*l + 21 + 4*l**3 + 18.
(l - 2)*(l - 1)**3*(l + 1)
Let m(l) be the first derivative of -l**9/16632 - l**8/9240 + l**7/770 + 89*l**3/3 + 68. Let h(v) be the third derivative of m(v). Factor h(w).
-2*w**3*(w - 2)*(w + 3)/11
Solve 218/7*o + 428/7 + 2/7*o**2 = 0.
-107, -2
Let w(i) = i**2 + 13*i + 62. Let c be w(-5). Solve 6*x**4 - c*x - x**4 + 22*x - 70*x**3 = 0 for x.
0, 14
Let j(m) be the second derivative of -5/42*m**7 - 70/3*m**3 + 2*m + 29/4*m**5 + 17 - 7/6*m**6 + 50*m**2 - 65/12*m**4. Determine s, given that j(s) = 0.
-10, -1, 1, 2
Let i(t) be the third derivative of 0 - t**5 + 0*t + 1/2*t**4 + 9/70*t**7 - 186*t**2 + 7/40*t**6 + 0*t**3. Factor i(w).
3*w*(w - 1)*(w + 2)*(9*w - 2)
Let n(t) be the second derivative of t**7/336 - t**6/10 - t**5/4 - t**4/6 - 5*t**3/6 - 3*t - 6. Let z(x) be the third derivative of n(x). Factor z(q).
3*(q - 10)*(5*q + 2)/2
Factor 5 + a - a**3 - 11/4*a**2.
-(a + 2)**2*(4*a - 5)/4
Let k(w) be the first derivative of w**6/2 + 12*w**5 + 102*w**4 + 326*w**3 + 21*w**2/2 - 1470*w + 915. Suppose k(b) = 0. Calculate b.
-7, -5, -2, 1
Suppose -419/8 - 629/4*c - 211/4*c**3 - 315/2*c**2 - 1/8*c**4 = 0. What is c?
-419, -1
Let f = 54/3287 - -6196/23009. Factor 24/7 + 26/7*a + f*a**2.
2*(a + 1)*(a + 12)/7
Let m(t) be the second derivative of -63/80*t**5 - 19/2*t**3 - 3*t**2 - 209*t + 0 + 41/8*t**4. Solve m(q) = 0.
-2/21, 2
Suppose 15*m = 5*m + 130. Suppose d = -m*d + 42. Factor 0*b**4 + 15*b**4 + 39*b**3 + 16*b**d + 30*b**2.
5*b**2*(b + 3)*(3*b + 2)
Suppose 6*o = -c + 7*o - 4704, 0 = -3*c + 5*o - 14120. Let v = 32960/7 + c. Factor -120/7*l**4 - v*l - 160/7*l**2 - 4*l**5 - 200/7*l**3 - 8/7.
-4*(l + 1)**4*(7*l + 2)/7
Let d(p) be the first derivative of p**6/12 - 23*p**5/10 - 105*p**4/8 - 85*p**3/6 + 26*p**2 + 54*p + 1643. Suppose d(n) = 0. Calculate n.
-2, -1, 1, 27
Let s(k) be the first derivative of -2*k**3/3 + 18*k**2 - 76*k - 183. Let m(h) = 2*h**2 - 37*h + 76. Let w(d) = -6*m(d) - 5*s(d). Factor w(x).
-2*(x - 19)*(x - 2)
Let x(p) = 2*p**2 - 59*p + 90. Let t be x(28). Suppose 47 = -t*h + 65. Let 6*v**2 - 2*v + 0 - 5/2*v**h = 0. What is v?
0, 2/5, 2
Factor 1952/9 + 260/9*y + 2/9*y**2.
2*(y + 8)*(y + 122)/9
Let k(s) be the third derivative of 1/240*s**6 + 1/120*s**5 + 0*s + 44*s**2 + 0 + 0*s**4 + 0*s**3. Find c, given that k(c) = 0.
-1, 0
Let r be (5/(-11))/((-162)/(2 + 1780)). Let 49/2*b**2 - 63/2*b**3 - 1/2*b**r + 15/2*b**4 + 0 + 0*b = 0. Calculate b.
0, 1, 7
Let -69*t - 10*t**2 + 40 - 25*t**3 - 3*t + 43*t**3 = 0. Calculate t.
-2, 5/9, 2
Suppose -a - 15 = 2*n - 12, 3 = -3*a - 4*n. Factor -1/4*c - 1/4*c**2 + 0 + 1/4*c**4 + 1/4*c**a.
c*(c - 1)*(c + 1)**2/4
Let n be 65 + -78 + 1*16. Let q(u) be the first derivative of -17/8*u**2 + 3/2*u + 5/4*u**n - 1/20*u**5 - 3/16*u**4 - 24. Solve q(l) = 0 for l.
-6, 1
Let r(v) be the first derivative of -361/9*v**3 - 1/18*v**6 - 48*v - 96 - 68*v**2 + 7/5*v**5 - 25/4*v**4. Factor r(n).
-(n - 12)**2*(n + 1)**3/3
Determine b, given that 2/7*b - 120/7 + 1/7*b**2