(s) + 7*w(s). Factor v(a).
5*a*(a + 1)*(a + 30)
Let q(c) = -7*c**2 - 60*c + 27. Let l be q(-9). Let s(y) be the second derivative of 4/7*y**3 + 4/21*y**2 + 9/14*y**4 + l - 2*y. Factor s(b).
2*(9*b + 2)**2/21
Let t be 3459/10*(9 + (-1820)/204). Let l = t + -366/17. What is z in 98/5 + 2/5*z**2 - l*z = 0?
7
Solve 272/5*s + 172/5*s**2 - 68/5*s**4 - 8*s**3 - 16/5*s**5 + 112/5 = 0 for s.
-2, -1, 7/4
Let t(f) be the first derivative of 6*f**2 - 22/3*f**3 - 7/20*f**5 + 31 + 0*f - 53/16*f**4. Determine r so that t(r) = 0.
-4, 0, 3/7
Let m(k) be the second derivative of k**4/12 - 19*k**3/3 + 37*k**2/2 - 18*k - 13. Factor m(u).
(u - 37)*(u - 1)
Let q = 158737 - 634947/4. Let 2*s**3 + 0 + 0*s + 5*s**2 - q*s**4 = 0. Calculate s.
-2, 0, 10
Determine l so that 2/5*l**3 + 58/5*l**2 - 24 - 64/5*l = 0.
-30, -1, 2
Let z(o) be the second derivative of 18*o**3 - 6*o**2 + 6/5*o**5 - o + 7 - 33/4*o**4. Find b, given that z(b) = 0.
1/8, 2
Let s(t) = -3*t**2 + 2*t**2 - 3 - 15*t + 2 + 17*t. Let y(a) = a**2 - a. Let o(r) = -2*s(r) - 4*y(r). Factor o(g).
-2*(g - 1)*(g + 1)
Let j(o) be the first derivative of -100*o - 1/3*o**3 + 10*o**2 + 86. Let j(s) = 0. Calculate s.
10
Suppose 7*c + 5*n + 55 = 12*c, -n + 13 = 3*c. Suppose -4*s + 2 = -5*q, -3*s - c*q = -31 + 10. Factor -8*u**2 - 6*u + 8/3*u**4 + 0 - 2/3*u**5 + 4/3*u**s.
-2*u*(u - 3)**2*(u + 1)**2/3
Let q(r) be the third derivative of 0*r**3 + 0*r**4 - 1/10*r**6 + 0*r - 1/112*r**8 - 2/35*r**7 + 0*r**5 - 73*r**2 + 0. Find u, given that q(u) = 0.
-2, 0
Let y(a) = 6*a**2 + 49*a + 74. Let x be y(-2). Let r(h) be the second derivative of x*h**2 + 0 - 15*h + 7/72*h**4 + 1/30*h**5 - 1/18*h**3. Factor r(k).
k*(k + 2)*(4*k - 1)/6
Let a = 99983/7 + -14283. Solve 26/7*u - 4 + a*u**2 = 0.
-14, 1
Let x(u) be the first derivative of u**5/100 + 113*u**2/2 - 82. Let q(c) be the second derivative of x(c). Let q(v) = 0. What is v?
0
Let r(v) be the first derivative of 5*v**4/3 - 95*v**3/6 + 75*v**2/2 - 21*v + 102. Let o(g) be the first derivative of r(g). Factor o(s).
5*(s - 1)*(4*s - 15)
Let r be (5/6)/((-15)/(-4)*245/2205). Determine c so that -2/5*c**r - 28 + 74/5*c = 0.
2, 35
Let d(n) be the second derivative of n**7/14 - 9*n**6/10 - 303*n**5/10 + 456*n**4 + 1008*n**3 + 76*n + 20. Solve d(m) = 0 for m.
-14, -1, 0, 12
Let u(o) be the third derivative of -o**5/360 + 8*o**4/3 - 1024*o**3 + 7*o**2 - o. Solve u(l) = 0.
192
Let p(q) be the first derivative of -q**4/12 - 917*q**3/9 - 1831*q**2/6 - 305*q + 6403. Factor p(v).
-(v + 1)**2*(v + 915)/3
Let x = 17 + -2. Suppose -3*i - x = -8*i. Solve 4*k**2 - 2*k**2 + i*k**2 - 2*k**2 + 6 + 9*k = 0.
-2, -1
Let n(i) be the first derivative of 2/15*i**6 + 4/25*i**5 + 63 + 162*i**2 - 38/5*i**4 + 24/5*i**3 - 540*i. Factor n(z).
4*(z - 3)**3*(z + 5)**2/5
Let h(f) be the second derivative of f**6/30 - f**5/2 + 7*f**4/3 - f**3 - 45*f**2/2 + 9*f - 50. Suppose h(o) = 0. Calculate o.
-1, 3, 5
Let n(s) be the first derivative of 81/4*s**4 - 75*s**3 - 64*s - 55 + 104*s**2. Factor n(g).
(g - 1)*(9*g - 8)**2
Let w = -36725/6 - -12243/2. Factor -w*n**5 + 0*n**2 - 4/3*n**3 + 0*n + 2*n**4 + 0.
-2*n**3*(n - 2)*(n - 1)/3
Let g(o) be the second derivative of o**4/8 - 79*o**3/2 - 3465*o**2/4 - 16377*o. What is v in g(v) = 0?
-7, 165
Let o(x) be the third derivative of -x**6/360 - 5*x**5/36 - 11*x**4/9 - 14*x**3/3 + 534*x**2. Factor o(v).
-(v + 2)**2*(v + 21)/3
Let c(t) be the third derivative of -t**6/80 + 17*t**5/40 + 3*t**4/2 - 27*t**3 + 161*t**2 - 4. Factor c(v).
-3*(v - 18)*(v - 2)*(v + 3)/2
Factor 470701 - 1573986 + x**2 - 3016545 + 289981 - 5*x**2 - 7828*x.
-(2*x + 1957)**2
Suppose 12*y - 25 = 11. Determine f, given that 3*f**5 + 2*f**3 - 2*f**y - 4*f - 6*f**3 + 7*f = 0.
-1, 0, 1
Let k be (4/7)/(34/119). Let 24 + 11387*a**k - 11390*a**2 - 10*a - 11*a = 0. What is a?
-8, 1
Let r be (16 + -22)*(5 - (-17)/((-255)/80)). Determine g, given that 2/7*g**4 - 36/7*g**r + 24/7*g**3 - 648/7*g + 1458/7 = 0.
-9, 3
Let m(r) be the third derivative of -1/90*r**6 + 1/945*r**7 - 2*r - 4/9*r**3 + 0 + 1/27*r**4 + 1/30*r**5 + 10*r**2. Let m(c) = 0. What is c?
-1, 2, 3
Suppose 31*g + 16*g = 376. Let h(b) = 10*b**3 - 102*b**2 + 116*b. Let c(o) = -4*o**3 + 34*o**2 - 39*o. Let s(v) = g*c(v) + 3*h(v). Solve s(a) = 0 for a.
-18, 0, 1
Suppose -9*s = -10*s + 20. Find r, given that -7*r - r**2 - 17 + 5 + s = 0.
-8, 1
Let b(c) be the second derivative of 5*c**4/12 + 1505*c**3/3 + 453005*c**2/2 - 1352*c. Determine m so that b(m) = 0.
-301
Determine r so that 4/3*r + 16 - 10/3*r**2 = 0.
-2, 12/5
Let v(p) = -33*p**2 - 515*p. Let l(i) = -16*i**2 - 254*i. Let y(k) = -17*l(k) + 8*v(k). Factor y(a).
2*a*(4*a + 99)
Let i = 8 + -5. Let w(s) = -s**3 - 3*s**2 - 73*s - 306. Let u be w(-4). Factor 0 + 0*a - 1/2*a**4 - 1/2*a**5 + 0*a**u + 0*a**i.
-a**4*(a + 1)/2
Let f be (1 - (-15)/(-20))/(52/416). Let i(b) be the second derivative of 0 + 3/20*b**4 - 7/30*b**3 + 1/5*b**f - 1/20*b**5 + 20*b + 1/150*b**6. Factor i(p).
(p - 2)*(p - 1)**3/5
Let y be -5 - -4 - (-2)/1. Suppose a - 5*n = 17, 8*a - 6*a - y = -n. Factor -a*d**4 + d**3 - 8*d**2 + 17*d**2 - 9*d**2 + d**5.
d**3*(d - 1)**2
Let y be 12 + -18 - 68/(-10). Let j = 20732 + -20727. Solve 4/5*f - 3/5*f**3 - 4/5*f**2 + 0 - 1/5*f**j + y*f**4 = 0.
-1, 0, 1, 2
Factor -889/5*u + 888/5 + 1/5*u**2.
(u - 888)*(u - 1)/5
Suppose 21 = 2*y + 5*c - 2*c, -5*y = -4*c + 5. Factor 7*z - 2275*z**2 + z**y + 32 - 5*z**3 + 17*z + 2263*z**2.
-4*(z - 2)*(z + 1)*(z + 4)
Let t(o) be the first derivative of 1960*o**2 + 11*o**4 - 1/5*o**5 - 5488*o - 224*o**3 - 161. Factor t(c).
-(c - 14)**3*(c - 2)
Let c(o) be the second derivative of o**6/540 - 16*o**5/135 + 64*o**4/27 + 88*o**2 - 193*o. Let p(k) be the first derivative of c(k). Factor p(r).
2*r*(r - 16)**2/9
Let a = 17143 - 17141. Factor 4*j + 16/5 - 6/5*j**a.
-2*(j - 4)*(3*j + 2)/5
Let s(d) be the third derivative of d**7/112 + d**6/20 + 9*d**5/80 + d**4/8 - 43*d**3/6 - 172*d**2. Let z(o) be the first derivative of s(o). Factor z(w).
3*(w + 1)**2*(5*w + 2)/2
Suppose 2*b - 3 = -s + 3*b, -5*s = -b - 3. Find w, given that 6*w**4 + w**4 - 30*w**2 - 25*w**3 + 6*w**4 - 3*w**4 + s*w**5 + 5*w**5 = 0.
-3, -1, 0, 2
Let j(a) be the second derivative of a**4/6 - 91*a**3/27 - 100*a**2/9 - 5*a + 23. Suppose j(g) = 0. What is g?
-1, 100/9
Let r(a) be the second derivative of 3/8*a**4 + 2*a - 23/12*a**3 - 1/40*a**5 + 15/4*a**2 + 35. Factor r(m).
-(m - 5)*(m - 3)*(m - 1)/2
Let z(d) be the third derivative of -5/84*d**4 + 0*d - 2/7*d**3 + 0 + 1/210*d**5 + 294*d**2. Factor z(i).
2*(i - 6)*(i + 1)/7
Let v(o) be the second derivative of 54*o + 3/20*o**5 + 0*o**2 - 1/4*o**4 + 0 + 0*o**3. Determine u so that v(u) = 0.
0, 1
Suppose -m + 2*x - 3*x = -160, -4*m + 2*x + 640 = 0. Let k be 1*6 + (5 - 1744/m). Find w, given that 5/2 + w + k*w**2 = 0.
-5
Let h = 474 - 468. Let v be 9/(-12) + (-10)/(-80)*h. Solve v - 2/9*l**2 + 2/3*l = 0.
0, 3
Find f such that -469*f**4 + 359*f**3 + 4*f**5 + 1428*f**2 + 653*f**3 - 2312*f + 337*f**4 = 0.
-2, 0, 1, 17
Factor -3*t - 1/3*t**3 - 4*t**2 + 22/3.
-(t - 1)*(t + 2)*(t + 11)/3
Let k(y) = -y + 3*y + y**2 - 876 + 878. Let z be k(0). Determine r, given that 10/3*r**z - 4/3*r + 0 = 0.
0, 2/5
Let l = -8504 + 136065/16. Let v(r) be the second derivative of -l*r**4 - 22*r + 3/8*r**2 + 3/16*r**3 + 0. Factor v(x).
-3*(x - 2)*(2*x + 1)/8
Let o be (10/30)/((-1)/3). Let i be (48/132)/(o/(-11)). Find a, given that -a**2 - 3*a**3 + 1/2 + 3/2*a + 3/2*a**5 + 1/2*a**i = 0.
-1, -1/3, 1
Factor -35 + 108*c**2 - 62*c - 11*c + 46 + 81 - 105*c**2.
(c - 23)*(3*c - 4)
Let q = 2188 - 2185. Let z(g) be the third derivative of g**q - 13*g**2 - 1/8*g**4 + 0*g - 1/20*g**5 + 0. Find a, given that z(a) = 0.
-2, 1
Let k(s) = s**3 + 2*s**2 - 4*s - 3. Let d be k(-2). Suppose d*r + z - 2*z - 41 = 0, r + 3*z = 21. Factor r + 3*x**3 + x - 10 - x**2 - 4*x + 2*x**4.
(x - 1)*(x + 1)**2*(2*x + 1)
Let i(p) be the first derivative of p**5/35 - 23*p**4/14 - 85*p**3/7 - 5446. Factor i(q).
q**2*(q - 51)*(q + 5)/7
Suppose 0 = 4*f - 2*f - 24. Let j be 1/(40/f - 3). Solve -3*h**3 - 3*h**4 + 3*h**j - 2*h**3 + 5*h**4 = 0.
0, 1
Let g(m) be the first derivative of m**5/10 + m**4/4 - 2*m**3 + 7*m**2/2 - 5*m/2 + 299. Factor g(v).
(v - 1)**3*(v + 5)/2
Let h(c) be the first derivative of 2*c**7/21 + 2*c**6/5 + c**5/5 - c**4 -