y. Factor 4*i**2 + 20*i**3 + 25*i**4 - k + 94.
i**2*(5*i + 2)**2
Let z(n) = -5*n**2 + 530*n - 51. Let p(o) = -48*o**2 + 5299*o - 493. Let c(u) = -9*p(u) + 87*z(u). Suppose c(k) = 0. What is k?
-527, 0
Let a(g) be the second derivative of -g**5 + 25/6*g**3 + 215*g - 5/6*g**4 - 5*g**2 + 0 - 5/42*g**7 + 2/3*g**6. Factor a(w).
-5*(w - 2)*(w - 1)**3*(w + 1)
Let j = 99 - 95. Let i be 2/(-3) + -16*j/(-24). What is b in b**2 + b - 7*b**i + 4*b + 11*b**2 = 0?
-1, 0
Let c(b) be the third derivative of -177/20*b**5 + 85*b**2 + 0*b**3 - 1/8*b**6 - 35/4*b**4 + 0 + 0*b. Find w such that c(w) = 0.
-35, -2/5, 0
Let f(r) be the first derivative of -r**4/12 - 4*r**3/3 - 2*r**2 + 80*r/3 + 55. Factor f(k).
-(k - 2)*(k + 4)*(k + 10)/3
Suppose -26522698 + 7024*h**2 - 5480775 - 35009*h**2 + 39172000*h + 5*h**3 - 13942288 + 6801741 = 0. What is h?
1, 2798
Let x(q) = 300*q**2 - 118*q - 3. Let v be x(12). Suppose v + h**2 + 2*h**2 - 5*h**2 + h**2 - 41770 + 10*h = 0. Calculate h.
-1, 11
Let k(q) = -2*q**4 - q**3 - q**2 + q. Let b(d) = -16*d**5 - 340*d**4 - 1399*d**3 + 3230*d**2 + 1865*d + 242. Let f(c) = -b(c) + 6*k(c). Let f(t) = 0. What is t?
-11, -1/4, 2
Suppose -72*l**5 - 103920*l**2 + 186584*l**4 + 23852*l**4 + 474014*l**4 - 96 - 177885*l**5 - 5520*l + 318320*l**3 - 922040*l**3 = 0. Calculate l.
-2/39, 2
What is x in -659/4*x**2 + 1019/4*x**4 - 7/2*x**5 + 57*x**3 + 0 + 73/2*x = 0?
-1, 0, 2/7, 1/2, 73
Suppose -336 = 25*y - 836. Factor 3*s**2 + 3*s**2 - 91*s**4 + y*s**3 - s**3 + 84*s**4.
-s**2*(s - 3)*(7*s + 2)
Suppose 0 = h + 6*h - 14. Let -2*o**h + 2*o**2 + 8*o**3 - 71*o**4 + 75*o**4 = 0. What is o?
-2, 0
Suppose 40*j + 60 = 60*j. Factor -j*r**4 - 45*r**3 - 2*r**4 + 230*r**5 + 45*r**2 - 225*r**5.
5*r**2*(r - 3)*(r - 1)*(r + 3)
Let i(w) be the second derivative of -w**7/3780 - w**6/162 - 23*w**5/540 - 7*w**4/54 - 83*w**3/3 + 89*w. Let r(j) be the second derivative of i(j). Factor r(h).
-2*(h + 1)*(h + 2)*(h + 7)/9
Suppose 1/5*g**3 + 0 + 24*g + 22/5*g**2 = 0. Calculate g.
-12, -10, 0
Suppose -3*h = -s + 17, -2*s = 1 - 5. Let a be (h + 2 + 1 - -2)*-1. Factor -2/9*n**3 + 0*n + 0*n**2 + 2/9*n**4 + a.
2*n**3*(n - 1)/9
Let l(o) be the second derivative of 0 - 1/18*o**6 - 15/2*o**2 + 38*o + 0*o**3 + 0*o**5 + 25/18*o**4. Determine t so that l(t) = 0.
-3, -1, 1, 3
Let x be (-8)/10*75/30. Let f be (5 + x + -16 + 1)/(-10). Factor f*r**3 + 3*r**2 + 9/5*r + 0.
3*r*(r + 1)*(2*r + 3)/5
Suppose 880*a = 884*a. Let u(h) be the first derivative of 0*h + 5 - 3/25*h**5 + 0*h**2 + a*h**3 - 3/20*h**4. Determine m, given that u(m) = 0.
-1, 0
Let l(w) be the second derivative of 3*w**7/1820 - w**6/312 + w**5/390 + 12*w**4 + w + 2. Let x(p) be the third derivative of l(p). Factor x(i).
2*(3*i - 1)*(9*i - 2)/13
Let f(y) be the third derivative of y**7/840 + y**6/10 + 109*y**5/120 + 5*y**4/4 - 129*y**3/8 - 3480*y**2. Factor f(q).
(q - 1)*(q + 3)**2*(q + 43)/4
Let c be (9 + -7 - 12)*(8/(-64)*-12)/(-6). Factor c - 1/8*z**2 - z.
-(z - 2)*(z + 10)/8
Let b(r) be the first derivative of -2/65*r**5 - 2/13*r**4 + 46 + 108/13*r**2 + 270/13*r + 12/13*r**3. Determine q so that b(q) = 0.
-3, 5
Let z be 19699/42 - -10*11/(-660). Let i = -468 + z. Find q, given that -2/7*q**2 + i*q**3 - 6/7*q + 2/7*q**4 + 0 = 0.
-3, -1, 0, 1
Let y be 9/3*(-2 - -4)*18/(-864)*-4. Factor -1/2*x**3 + 21/2*x + 45/2 - y*x**2.
-(x - 5)*(x + 3)**2/2
Let l(g) be the first derivative of -1/2*g**2 - 58 + 1/3*g**3 - 2*g. Let l(w) = 0. Calculate w.
-1, 2
Suppose 40 = 5*o + 4*t, o + 6 = -0*o + 2*t. Solve 51*r**5 + 3*r**o + 6*r**4 - 21*r**5 - 27*r**5 + 6*r**3 = 0.
-2, -1, 0
Let f(a) be the first derivative of a**3/2 + 27*a**2/2 + 195*a/2 - 505. Factor f(i).
3*(i + 5)*(i + 13)/2
Let f be (1*4594)/(78/351). What is q in -20717*q + 4*q**2 + f*q + 12 + 3*q**2 = 0?
2/7, 6
Let r(h) = h**3 + 5*h**2 - 742*h - 5094. Let c be r(-7). Let i be (-93)/(-54) - 4/18. Determine m so that -5*m**c - 10*m + i*m**4 + 5/2*m**3 - 4 = 0.
-2, -1, -2/3, 2
Let h be ((-22)/6)/((-2)/(-6)). Let z be h/(-6) - ((-45)/10)/(-9). Solve 4/3*r**3 + 0 - 4/3*r + 4/3*r**2 - z*r**4 = 0 for r.
-1, 0, 1
Factor 380/7 - 2/7*h**3 - 286/7*h + 52/7*h**2.
-2*(h - 19)*(h - 5)*(h - 2)/7
Let s = 477778/3 - 159259. Let x be (-7)/(-12) + (-7)/28. Factor s*i**3 + x*i**4 + 0*i + 0 - 1/3*i**2 - 1/3*i**5.
-i**2*(i - 1)**2*(i + 1)/3
Suppose 4*h - 68 = -4*k, -505*h = -3*k - 501*h - 40. Determine d, given that -7/3*d**2 + 6 + 11*d + 5/3*d**k - 17/3*d**3 = 0.
-1, -3/5, 2, 3
Let s(a) be the first derivative of -1/15*a**3 - 32/5*a**2 - 1024/5*a + 85. Factor s(m).
-(m + 32)**2/5
Let n(o) be the second derivative of -o**6/225 + 179*o**5/150 - 341*o**4/3 + 157604*o**3/45 + 1668296*o**2/15 - 11263*o. Factor n(l).
-2*(l - 62)**3*(l + 7)/15
Let i be 5/(-11)*(-158)/395. Let -i*s**4 + 2/11*s**5 + 0 - 6/11*s**3 + 2/11*s**2 + 4/11*s = 0. What is s?
-1, 0, 1, 2
Let q(z) be the third derivative of 0*z + 18 + z**2 + 2/9*z**6 + 46/9*z**3 + 34/9*z**4 - 2/315*z**7 + 22/15*z**5. Factor q(m).
-4*(m - 23)*(m + 1)**3/3
Factor -848/7 + 2/7*q**2 + 90/7*q.
2*(q - 8)*(q + 53)/7
Let w(f) = 2*f + 10. Let k be w(-4). Suppose -3*b + t + 3 = 3*t, -2*t - 12 = -k*b. Factor -180*g**4 + b*g**5 + 88*g**4 + 98*g**4.
3*g**4*(g + 2)
Let y(a) = -8*a - 12 + 14 + a**3 - 7*a**2 + 0*a**2. Let j be y(8). Factor 5*q**2 - 16*q**2 + 20 + 7*q + 9*q + 7*q**j.
-4*(q - 5)*(q + 1)
Suppose -15 = -4*s - 4*j + 17, -4*s = j - 17. Let m(n) be the first derivative of 2/3*n - 1/6*n**2 - 2/9*n**s + 25 + 1/12*n**4. Let m(g) = 0. Calculate g.
-1, 1, 2
Let h(u) be the first derivative of u**4 + 748*u**3/3 + 5600*u**2 + 43776*u - 6569. Let h(n) = 0. Calculate n.
-171, -8
Let l(k) be the third derivative of -k**7/1575 + k**6/50 - k**5/10 - 37*k**4/45 - 28*k**3/15 - 3*k**2 - 343*k. Find y such that l(y) = 0.
-1, 6, 14
Let p be (1554/1890 + ((-165)/25 - -6))*24. Find z, given that -20/3*z - 1/3*z**3 + 8/3*z**2 + p = 0.
2, 4
Find r such that 1798 - 3*r**2 - 3759 + 1880 + 36*r = 0.
3, 9
Let s(x) = 12*x - 106. Let i be s(9). Determine y so that -10*y - 33 - 3*y**2 + 7*y**i + 9 + 30*y = 0.
-6, 1
Suppose 2*n - 3*z - 31 = -18, 0 = -9*z - 27. Let x(f) be the first derivative of -6/7*f**n + 0*f + 3/28*f**4 - 3/7*f**3 - 27. Let x(d) = 0. Calculate d.
-1, 0, 4
Let c(q) be the third derivative of -3/32*q**6 + 0*q**3 + q - 9*q**2 + 2*q**4 + 0 - 3/5*q**5 - 1/280*q**7. Factor c(p).
-3*p*(p - 1)*(p + 8)**2/4
Let h(o) be the third derivative of -o**6/30 + 2*o**5/5 + o**4/6 - 4*o**3 - 21*o**2 + 3*o + 1. Factor h(d).
-4*(d - 6)*(d - 1)*(d + 1)
Determine h, given that -1/6*h**2 - 63/2*h - 94/3 = 0.
-188, -1
Let w(j) = 43*j + 422. Let u be w(-10). Let d(x) = -4*x + 2*x**2 + 8*x - 2 + 2*x. Let i(t) = -5*t**2 - 17*t + 6. Let k(c) = u*d(c) - 3*i(c). Factor k(o).
-(o - 2)*(o - 1)
Let z(i) be the third derivative of i**5/330 + 2441*i**4/66 + 5958481*i**3/33 + 12282*i**2. Factor z(j).
2*(j + 2441)**2/11
Let h(t) = 7*t**2 - 13*t + 7. Let i(s) = 3*s**2 - 6*s + 3. Suppose 0 = -18*a + 124 + 38. Let j(v) = a*i(v) - 4*h(v). Factor j(l).
-(l + 1)**2
Let c(l) be the first derivative of 123*l**5/5 + 3*l**4/4 - 41*l**3 - 3*l**2/2 + 5052. Factor c(d).
3*d*(d - 1)*(d + 1)*(41*d + 1)
Let d(u) = u**2 + 8*u + 25. Let r be d(-4). Factor -1 - r*i**4 + 12*i**3 + 361*i**5 - 364*i**5 + 1.
-3*i**3*(i - 1)*(i + 4)
Let x(q) = -4*q**3 + 66*q**2 - 60*q - 2. Let m(z) = -22*z - z - z**3 + 13*z**2 + 11*z. Let h(b) = -11*m(b) + 2*x(b). Factor h(l).
(l - 2)*(l - 1)*(3*l - 2)
Suppose 0 = 4*j + 5*c - 68, 3*c = -0*j - 2*j + 36. Let i be -3*8/j + 4. Solve 4 - 10*g + 36*g**i - 17*g + 3*g = 0 for g.
1/3
Let r(b) be the second derivative of b**5/90 + 23*b**4/54 - 26*b**3/27 - 16*b**2/3 - 4232*b. Determine o so that r(o) = 0.
-24, -1, 2
Let y(v) be the second derivative of -v**5/4 + 233*v**4/24 + 57*v**3/4 - 18*v**2 - 2224*v. Factor y(p).
-(p - 24)*(p + 1)*(10*p - 3)/2
Let n be (3 + (4 - 3))*(-3)/(-4). Suppose x + 2*x = 441. Factor 139 - x - 6*d - n*d - d**2.
-(d + 1)*(d + 8)
Let k(a) be the second derivative of a**5/5 - 55*a**4/9 - 76*a**3/9 - 3197*a. Factor k(s).
4*s*(s - 19)*(3*s + 2)/3
Let n(y) be the second derivative of 0 - 4/3*y**3 - 8*y**2 - 1/15*y**6 + 53*y + 1/10*y**5 + y**4. Factor n(i).
-2*(i - 2)**2*(i + 1)*(i + 2)
Let z = 8148/31 - 32561/124. Factor 0*t + z*t**3 + t**2 + 0.
t**2*(t + 4)/4
Let x(f) = 5*f**2 - 1