w**5/5 - 4*w**4 + 14*w**3 - 18*w**2 + 8275. Factor v(y).
2*y*(y - 3)**2*(y - 2)
Let p(n) be the second derivative of n**7/105 + 3*n**6/20 + 4*n**5/5 + 5*n**4/3 - 117*n**2/2 + n + 34. Let u(w) be the first derivative of p(w). Factor u(j).
2*j*(j + 2)**2*(j + 5)
Suppose -3*a - m + 4 = 0, 0 = -2*a - 5*m + 4748 - 4754. Let l = 35/108 + -2/27. Factor 5/4*y + 0 + y**a - l*y**3.
-y*(y - 5)*(y + 1)/4
Let k(m) = 15106*m - 679768. Let z be k(45). Factor -2*n**z + 24/7 + 80/7*n.
-2*(n - 6)*(7*n + 2)/7
Let p(w) = -w**3 + 5*w**2 + 13*w + 9. Let i be p(7). Suppose -5*f + 22 = -h, 7 = i*h + 1. Find a such that a**2 - 7*a + 0*a**2 - 2 + 3 + f = 0.
1, 6
Factor 195*p**2 - 195 + 5323*p - 14*p**3 + 9*p**3 - 5318*p.
-5*(p - 39)*(p - 1)*(p + 1)
Let j = -21815 - -87273/4. Determine c, given that 5/4*c**4 - 13/4*c**3 - 11/4*c**2 + j*c + 3/2 = 0.
-1, -2/5, 1, 3
Let k = 3074/5257 - 10/751. Factor 3/7*y**2 - 4/7 + 1/7*y**4 - 4/7*y + k*y**3.
(y - 1)*(y + 1)*(y + 2)**2/7
Suppose 5*x - 36 = -11. Let i be (3 - x)*(5 - 6). Factor -3 - 5 + 12*a + 1 - 2 - 3*a**i.
-3*(a - 3)*(a - 1)
Let y be (-36)/135*18/(-4). Suppose -119*b + 114*b = 15, -4*s + 24 = -4*b. Suppose y - 3*n - 3/5*n**s + 12/5*n**2 = 0. Calculate n.
1, 2
Let d = 673 - 671. Factor 2*r + 25 - 12*r**d + 3*r + 7 + 3*r.
-4*(r - 2)*(3*r + 4)
Factor -7780340/11*c**2 - 106580/11*c**3 - 4146143186/11 - 283982410/11*c - 730/11*c**4 - 2/11*c**5.
-2*(c + 73)**5/11
Suppose -66*n = -104*n + 2660. Let m be 11 - n/(-12 - -22). Factor -10/9*g**m - 14/9*g**2 + 2/9*g**5 + 2*g**3 + 0 + 4/9*g.
2*g*(g - 2)*(g - 1)**3/9
Let r(y) = 3*y + 56. Let p be r(-18). Let x**p + 8*x - 9*x - 2*x - 9*x = 0. What is x?
0, 12
Let j(h) be the first derivative of -h**6/30 - 18*h**5/5 - 263*h**4/20 - 58*h**3/5 - 2337. Determine u so that j(u) = 0.
-87, -2, -1, 0
Let y be (2/66)/(3 + -267*1/90). Solve 2/11*z**5 - 4/11*z**2 + 6/11 - 12/11*z**3 - 2/11*z**4 + y*z = 0.
-1, 1, 3
Let k(p) = 382*p - 16421. Let s be k(43). Determine z so that -9/4*z**2 + 1/4*z**3 + 6*z - s = 0.
2, 5
Let s(y) = -6*y**2 + 16*y - 68. Let u(k) = -5*k**2 + 18*k - 69. Let l(x) = 3*s(x) - 4*u(x). Factor l(f).
2*(f - 6)**2
Let y(i) = -100*i**2 + 9004*i - 360. Let n be y(90). Let 8/7*t + 2/7*t**2 + n = 0. What is t?
-4, 0
Let k be ((-325)/(-15))/(2/(-6)). Let j = 72 + k. Find c such that 2*c + 10 + 2*c + 5*c**3 - j*c - 12*c = 0.
-2, 1
Determine g so that -26/7*g**2 + 8/7*g**4 + 40/7 - 23/7*g**3 + 1/7*g**5 + 44/7*g = 0.
-10, -1, 2
Let r(f) be the third derivative of -f**7/70 + 12*f**6/5 - 1199*f**5/10 + 564*f**4 - 2209*f**3/2 - 851*f**2 + 1. Let r(v) = 0. What is v?
1, 47
Let u(a) be the first derivative of -5*a**4/4 + 115*a**3/3 - 280*a**2 + 2083. Let u(d) = 0. What is d?
0, 7, 16
Suppose -45 + 395 = 50*s. Let u(t) be the third derivative of -5/132*t**4 + 1/1155*t**s + 0 + 1/30*t**5 + 0*t - 7/660*t**6 - 27*t**2 + 0*t**3. Factor u(n).
2*n*(n - 5)*(n - 1)**2/11
Solve 0 + 3/2*y**4 + 18*y**2 + 9*y**3 + 12*y = 0.
-2, 0
Suppose 0 = -2*l - 4, -5*b + 117*l + 18 = 118*l. Let z(q) be the first derivative of -2*q**3 + 1/12*q**6 - 3/5*q**5 + 19 + 13/8*q**b + 0*q + q**2. Factor z(c).
c*(c - 2)**2*(c - 1)**2/2
What is k in -620/3*k + 2*k**4 - 64 + 92/3*k**3 - 34*k**2 = 0?
-16, -2, -1/3, 3
Let a(w) be the second derivative of -13/2*w**2 + 0*w**4 - 1/120*w**5 + 1/3*w**3 + 0 + 11*w. Let b(d) be the first derivative of a(d). Factor b(h).
-(h - 2)*(h + 2)/2
Let m(y) = 10*y**4 + 28*y**3 - 108*y**2 + 112*y + 250. Let a(o) = -o + 19. Let k be a(7). Let t(q) = -q**4 - q**2 - q. Let w(b) = k*t(b) + m(b). Factor w(v).
-2*(v - 5)**3*(v + 1)
Let f(u) = -61*u - 427. Let b be f(-7). Let w(x) be the first derivative of b*x**3 - 2/3*x**6 + 3 - 4/5*x**5 + 0*x**4 + 0*x**2 + 0*x. Factor w(s).
-4*s**4*(s + 1)
Suppose 2*j + 153 - 1441 = -4*p, 0 = -j + 2. Suppose -2 = -322*c + p*c. Factor 1/2*g**3 + 1/4*g**c + 0 - 1/4*g.
g*(g + 1)*(2*g - 1)/4
Let z(o) be the second derivative of o**7/630 - 4*o**6/45 + 32*o**5/15 - 61*o**4/12 - 104*o. Let m(b) be the third derivative of z(b). Factor m(k).
4*(k - 8)**2
Let l(z) be the second derivative of -3*z**7/13 + 9*z**6/65 + 209*z**5/65 + 106*z**4/39 - 8*z**3/13 - 2940*z. Find q such that l(q) = 0.
-2, -2/3, 0, 2/21, 3
Let s be (18/6)/(6/40). Suppose 0 = -u - 2*w + s, 5*w - 8*w + 12 = 0. Factor -7*g**3 + u*g**3 - 3*g**3 - g**2 - 6*g - g**3.
g*(g - 3)*(g + 2)
Suppose 2 = 2*x, 2*c - 13 = -3*c + 2*x. Let -4*g**4 - 44*g**5 - 11*g**c + 45*g**5 - 9*g**2 + 3*g**2 = 0. What is g?
-1, 0, 6
Determine x, given that -1632/5 - 228/5*x - 3/5*x**2 = 0.
-68, -8
Let z(n) be the second derivative of -n**6/1980 + 13*n**5/660 - n**4/11 + n**3/3 + 29*n**2/2 - 141*n. Let r(q) be the second derivative of z(q). Factor r(f).
-2*(f - 12)*(f - 1)/11
Let s = 70890 + -70890. Let 0*q**2 - 4/21*q**3 + 2/21*q + 2/21*q**5 + s + 0*q**4 = 0. Calculate q.
-1, 0, 1
Let k(m) be the first derivative of -m**5/20 + 7*m**4/2 - 467*m**3/6 + 525*m**2 - 5625*m/4 - 3409. Let k(x) = 0. What is x?
3, 25
Let k(h) be the second derivative of -1/108*h**4 + 1/9*h**2 - 71 - 2*h + 1/54*h**3. Suppose k(j) = 0. Calculate j.
-1, 2
Suppose 9*h = 7*h + 62. Let k = h - 26. Solve -6 + 0*t**5 + 21*t**4 + 5*t**5 - 15*t**2 + 15*t**3 - 21*t + t**k = 0 for t.
-2, -1, -1/2, 1
Let m(n) be the second derivative of 7*n**6/360 + n**5/20 + n**4/36 - 43*n**2 + 4*n - 2. Let v(c) be the first derivative of m(c). Factor v(b).
b*(b + 1)*(7*b + 2)/3
Factor -1/5*b**4 - 6084/5 - 5773/5*b**2 - 154/5*b**3 + 12012/5*b.
-(b - 1)**2*(b + 78)**2/5
Suppose 52 = -4*f + 24702*i - 24697*i, i = 12. Factor -7/3*l**f - 6*l + 0 + 1/3*l**3.
l*(l - 9)*(l + 2)/3
Factor -382347/4*c + 1071/4*c**2 + 45499293/4 - 1/4*c**3.
-(c - 357)**3/4
Let f(a) be the third derivative of -1/135*a**6 + 2/315*a**7 + 5/108*a**4 + 0*a**3 + 2*a**2 + 0 - 1/45*a**5 + 27*a - 1/1512*a**8. Determine i so that f(i) = 0.
-1, 0, 1, 5
Let b(s) be the first derivative of 15/38*s**4 + 0*s + 1/57*s**6 - 23 - 16/57*s**3 - 16/19*s**2 + 16/95*s**5. Let b(z) = 0. Calculate z.
-4, -1, 0, 1
Let x be (-1)/((-15)/(-9) + -2). Suppose -8 = 2*k - 5*v + 11, -2*k = -v - 1. Find n, given that -4 + 6*n**2 - x*n - 3*n**k + 4 = 0.
0, 1
Let w be (-97)/(-76) - ((-67)/(-100) + (-426)/(-5325)). Find k such that -2/19*k**4 + 8/19*k + 48/19*k**2 + w*k**3 - 64/19 = 0.
-2, 1, 8
Let r = -6091460/2191 + 471/313. Let a = -2773 - r. Determine n so that 100/7 - a*n + 4/7*n**2 = 0.
5
Let f(h) = 9*h**3 + 3*h**2 - h - 1. Let v(b) = 220*b**3 + 55*b**2 - 30*b + 5. Let a(d) = 25*f(d) - v(d). Suppose a(o) = 0. What is o?
-3, -2, 1
Let z(c) = -4*c**3 + 13*c**2 + 53*c - 16. Let v(l) = 4*l**2 - l + 1. Let r(x) = 6*v(x) + 3*z(x). Let r(p) = 0. Calculate p.
-2, 1/4, 7
Determine f so that -70*f**2 + 1080 + 246*f - 24453*f**3 + 174*f + 24448*f**3 = 0.
-18, -2, 6
Let c(t) be the second derivative of t**5/4 - 85*t**4/12 + 155*t**3/6 - 75*t**2/2 - 704*t. Suppose c(i) = 0. Calculate i.
1, 15
Suppose 196/13*s + 240/13 + 42/13*s**2 + 2/13*s**3 = 0. What is s?
-15, -4, -2
Let j(n) be the first derivative of 2*n**3/3 + 4*n**2 + 5*n - 6. Let b be j(-4). Factor b*i - 4*i + 7*i + i - 9*i**3 - 6*i**2 + 6.
-3*(i - 1)*(i + 1)*(3*i + 2)
Suppose 0*j + 148 = -5*k + j, -k - 2*j = 34. Let h = -27 - k. Suppose -53*w**3 - 17*w**h + 30*w + 38*w**2 - 2*w**2 + 4 = 0. What is w?
-2/7, -1/5, 1
Let a(p) be the first derivative of -p**4/4 - 227*p**3/12 + 57*p**2/8 - 182. Factor a(t).
-t*(t + 57)*(4*t - 1)/4
Let j(c) be the second derivative of 5*c**7/28 + 6*c**6/5 - 3*c**5 - 69*c**4/4 + 179*c**3/4 - 45*c**2/2 - c + 15. Solve j(u) = 0.
-5, -3, 1/5, 1, 2
Factor -42*c**2 - 11 + 26 - 15 + 40*c**2 - 1772*c.
-2*c*(c + 886)
Let g be -53 + 58 + (-2)/6 + 16/(-15). Determine m, given that -66/5*m**2 - 58/5*m**3 - g*m**4 - 4/5 - 6*m = 0.
-1, -2/9
Let u be 2 - 13/(-26)*16*-60. Let n = -2382/5 - u. Suppose -6/5*m**4 + 26/15*m**2 - n*m + 38/15*m**3 - 14/15*m**5 - 8/15 = 0. Calculate m.
-2, -1, -2/7, 1
Factor -252/11 + 2/11*s**2 - 78/11*s.
2*(s - 42)*(s + 3)/11
Let u be (6 - 8 - -2)/(6 - 5). Let c(f) be the second derivative of -7*f - f**4 - 1/10*f**5 + u - 4*f**2 - 3*f**3. Find t such that c(t) = 0.
-4, -1
Let q = -19030 + 742048/39. Let n = q + 45/13. Find j, given that 4/3 + 2*j**2 + n*j**3 + 3*j = 0.
-4, -1
Let p(b) = -133*b - 10773. Let t be p(-81). Suppose -2/13*q**3 - 10/13*q**2 + 2/13*q**4 +