**2 + r.
f*(f + 3)
Let z = 2105/13 - 10473/65. Solve 0 + 0*i**3 + z*i**4 + 0*i + 18/5*i**5 + 0*i**2 = 0 for i.
-2/9, 0
Let x(p) be the third derivative of 0*p + 2 - 1/5*p**5 - 1/4*p**4 - 19*p**2 - 1/12*p**6 - 1/6*p**3 - 1/70*p**7. Determine k so that x(k) = 0.
-1, -1/3
Let s = -42 - -44. Let k be s - (-2 + -2 - -3). Factor -10*c**2 + 8*c**3 + 0*c**3 - 5*c**5 + 6*c**k + c**3.
-5*c**2*(c - 1)**2*(c + 2)
Let v(a) be the first derivative of 7*a + 1/12*a**4 - 3/2*a**2 + 1/3*a**3 - 10. Let n(f) be the first derivative of v(f). Let n(l) = 0. Calculate l.
-3, 1
Factor -273*k**2 - 9*k**4 + 26*k - 123*k**3 - 237*k - 78*k**2 - 114 - 134*k + 6*k**4.
-3*(k + 1)**3*(k + 38)
Let b = -449 + 449. Suppose 10*d - 28*d + 1080 = b. Factor 3/5*g**2 - 12*g + d.
3*(g - 10)**2/5
Factor 100*u + 4/5*u**2 + 496/5.
4*(u + 1)*(u + 124)/5
Let z(u) = 2*u**3 + 3*u**2 - 3*u + 1. Let t be z(-2). Suppose 0 = -m - q + 7, 5*q = -t*m + 2 + 21. Determine w so that -3/2*w**3 + m*w**2 + 0 + 0*w = 0.
0, 4
Let k(j) be the second derivative of -83*j - 9/2*j**3 + 0 + 1/4*j**4 + 12*j**2. What is u in k(u) = 0?
1, 8
Suppose 509 = 690*w + 263 - 1134. Factor -4/5 - 1/5*j**3 - j**w - 8/5*j.
-(j + 1)*(j + 2)**2/5
Suppose -21*l = -16*l - 220. Let q be (-3)/(-27) + l/9. Let -15*f + 0*f**4 + 11*f - 12*f**q - 8*f**4 - 7*f**2 + 16*f**3 + 15*f**2 = 0. What is f?
-1, 0, 1/3, 1
Let u(q) be the second derivative of q**5/20 - 3*q**4/4 + 7*q**3/3 - 3401*q + 2. Let u(k) = 0. What is k?
0, 2, 7
Suppose -5*w - 4*v = -4, -4*w + 5*v - 6*v + 12 = 0. Factor -2*b**5 - 105*b**2 + 2*b**5 - 93*b**w + 18*b**4 + 5*b**5 - 490*b + 305*b**3.
5*b*(b - 7)**2*(b - 2)*(b + 1)
Suppose 35 = -173*v + 180*v. Let z(t) be the third derivative of 0*t**v + 0*t - 19*t**2 + 0*t**3 + 1/30*t**6 - 2/3*t**4 + 0. Find s such that z(s) = 0.
-2, 0, 2
Factor 4/3*l**2 + 952/3 - 956/3*l.
4*(l - 238)*(l - 1)/3
Let k(p) be the second derivative of p**5/100 + p**4/8 - 38*p**2 + 32*p - 1. Let t(h) be the first derivative of k(h). Factor t(v).
3*v*(v + 5)/5
Let q(c) be the third derivative of 0 + 0*c**3 + 105*c**2 + 2/33*c**4 - 1/660*c**6 - 1/165*c**5 + 0*c. Factor q(g).
-2*g*(g - 2)*(g + 4)/11
Let c(t) = 17*t**2 + 19*t - 7. Let y(d) = -22*d**2 - 20*d + 8. Let l(r) = 2*c(r) + 3*y(r). What is w in l(w) = 0?
-1, 5/16
Let w be ((-10)/((-720)/486))/((-3)/(-4)). Let q be (-36)/(-162) - 2/w. Suppose -8/5*a**2 - 12/5*a**3 - 8/5*a**4 - 2/5*a - 2/5*a**5 + q = 0. What is a?
-1, 0
Let z(b) be the second derivative of -3/20*b**5 - 298*b + 9*b**3 + 0 + 0*b**2 + 7/4*b**4. Factor z(f).
-3*f*(f - 9)*(f + 2)
Let r(k) = 4*k**2 - 5*k + 6. Let x be r(1). Let d be 19/95 + 2/x. Solve -3/5*m**2 + 0 - d*m = 0 for m.
-1, 0
Let r(h) be the third derivative of -h**6/900 + 251*h**5/225 - 12397*h**4/36 - 256036*h**3/45 + 10209*h**2. Factor r(f).
-2*(f - 253)**2*(f + 4)/15
Let r(n) be the first derivative of 5*n**4/4 - 2675*n**3/3 + 1330*n**2 + 5340*n + 3734. Find l such that r(l) = 0.
-1, 2, 534
Let g be 30/45*(180 - 3). Factor -24 - g*p + 25/2*p**3 - 140*p**2.
(p - 12)*(5*p + 2)**2/2
Let t(o) be the third derivative of 19*o**5/80 - 9*o**4/8 - o**3/2 + 93*o**2. Suppose t(l) = 0. Calculate l.
-2/19, 2
Let i(m) be the third derivative of -m**7/1260 + m**6/720 + 7*m**5/120 - 41*m**4/144 + 5*m**3/9 - 476*m**2 - 1. Factor i(x).
-(x - 4)*(x - 1)**2*(x + 5)/6
Suppose 11*l = 7*l + 4*n + 4, 0 = 3*l + 4*n - 17. Let -1441*h**3 + 1444*h**l + 52*h**2 - 10*h**2 + 99*h = 0. Calculate h.
-11, -3, 0
Let n(l) = -4*l**2 - 862*l - 48398. Let h(i) = 4*i**2 + 853*i + 48397. Let k(r) = 2*h(r) + 3*n(r). Determine s, given that k(s) = 0.
-110
Let s = 241/790 + 15/158. Let d(c) = c + 2. Let f be d(-2). Find l such that 0 + 0*l + 8/5*l**4 - s*l**5 - 8/5*l**3 + f*l**2 = 0.
0, 2
Let g(r) = -r**4 + 2*r**2 - r + 1. Let d(n) = -2*n**5 + 2*n**4 + 20*n**3 + 12*n**2 - 14*n - 22. Let y(f) = -d(f) - 4*g(f). Find x, given that y(x) = 0.
-3, -1, 1, 3
Suppose 5 = -t + 36. Let x(g) = 29*g**2 - 44 - 13 + t + 66*g. Let y(j) = -j**2 + j - 1. Let r(k) = -x(k) + 6*y(k). Factor r(h).
-5*(h + 2)*(7*h - 2)
Let f be (20/(-70))/((-426)/21 - 3). Let g = f - -300/2119. Factor g*u**3 + 50/13*u + 0 - 20/13*u**2.
2*u*(u - 5)**2/13
Let l(i) be the second derivative of -2/15*i**5 + 0*i**2 + 0 + 1/3*i**3 - 1/9*i**4 + 131*i + 2/45*i**6 + 1/63*i**7. Determine j so that l(j) = 0.
-3, -1, 0, 1
Suppose -13553*j + 13373*j = -360. Factor -2/3*g**4 + 2*g + 2/3*g**3 + 0 + 10/3*g**j.
-2*g*(g - 3)*(g + 1)**2/3
Suppose 2344 + 293/2*a**4 + 4*a**3 - 8*a - 1172*a**2 - 1/2*a**5 = 0. Calculate a.
-2, 2, 293
Factor 20*r**4 - 2182 + 1097 - 25*r**2 + 30*r - 35*r**3 + 1085.
5*r*(r - 2)*(r + 1)*(4*r - 3)
Determine o so that 9/5*o**2 + 4/5 - 1/5*o**4 - 11/5*o - 1/5*o**3 = 0.
-4, 1
Let u = 121481/91113 - -1/30371. What is f in 10/21*f - u + 2/21*f**2 = 0?
-7, 2
Let h(q) be the first derivative of 8*q**3 + 111*q**2/2 + 87*q - 3500. Determine i so that h(i) = 0.
-29/8, -1
Let n(w) be the third derivative of -w**8/168 + 26*w**7/105 - 4*w**6/5 - w**5/15 + 49*w**4/12 - 8*w**3 + w**2 - 56*w - 13. Let n(y) = 0. Calculate y.
-1, 1, 24
Let h(o) be the first derivative of o**6/720 + o**5/30 + o**4/4 - 196*o**3/3 - 56. Let k(s) be the third derivative of h(s). Factor k(j).
(j + 2)*(j + 6)/2
What is t in 21/5*t**3 - 1/5*t**2 + 6/5 - 17/5*t**4 - 13/5*t + 4/5*t**5 = 0?
-3/4, 1, 2
Let r = 11179/9270 - 11/1854. Factor 14/5*c + r + 4/3*c**2 - 4/5*c**3 + 2/15*c**5 - 2/5*c**4.
2*(c - 3)**2*(c + 1)**3/15
Let m be 35/5 - (3 + -1). Factor 2 + 187*i**3 + i**m - 7*i**4 - 204*i**3 - i**2 - 8*i**2 - 2.
i**2*(i - 9)*(i + 1)**2
Let y(o) be the second derivative of 2*o**5/45 - 1655*o**4/54 + 18998*o**3/3 + 4761*o**2 + 1852*o. Factor y(s).
2*(s - 207)**2*(4*s + 1)/9
Factor -4253*z + 10818 + 240*z**2 + 6274 + 404 + 8465*z + 4*z**3.
4*(z + 6)*(z + 27)**2
Let l = -1 + 7. Suppose -32 = -l*z + 4*z. Factor -387*q**2 + z*q - 32 + q**3 + q**3 + 401*q**2.
2*(q - 1)*(q + 4)**2
Suppose 204 + 97 = 7*c. Suppose c*m + 16 = 47*m. Factor 0*k - 3/4*k**2 + 0*k**3 + 3/4*k**m + 0.
3*k**2*(k - 1)*(k + 1)/4
Let n(u) be the second derivative of u**5/420 - u**4/56 - 2*u**3/21 + 129*u**2/2 + 175*u. Let s(h) be the first derivative of n(h). Find t such that s(t) = 0.
-1, 4
Let q(w) be the first derivative of -1/6*w**4 + 14 + 4/3*w**2 + 2/9*w**3 - 8/3*w. Solve q(s) = 0.
-2, 1, 2
Determine o, given that -5*o**2 - 240689*o**3 + 26*o + 240688*o**3 - 6*o**2 = 0.
-13, 0, 2
Let y(a) be the first derivative of 48*a + 16*a**2 - 64 - 2/3*a**6 - 52/3*a**3 + 4*a**5 - 3*a**4. Let y(r) = 0. Calculate r.
-1, 2, 3
Let u(g) be the first derivative of g**6/24 - 19*g**5/12 + 175*g**4/24 - 85*g**3/6 + 22*g**2 + 7. Let z(j) be the second derivative of u(j). Factor z(x).
5*(x - 17)*(x - 1)**2
Factor -1124*b**2 + 467*b + 921*b + 292*b**3 - 552 + 27613*b**4 - 27617*b**4.
-4*(b - 69)*(b - 2)*(b - 1)**2
Let i(d) be the second derivative of d**4/42 + 113*d**3/21 + 16*d**2 + 165*d - 5. What is r in i(r) = 0?
-112, -1
Suppose 4 - 238 = -6*d. Let r = d + -36. Factor -q - r*q**3 + 2*q**2 + q**3 - 9*q + 20*q + 6.
-2*(q - 3)*(q + 1)**2
Suppose -136*g + 1069 = 176 + 349. Factor 24/5*x**g + 2/5*x**5 + 24*x**2 + 0 + 10*x + 92/5*x**3.
2*x*(x + 1)**2*(x + 5)**2/5
Let r(z) = 2*z**3 - 2*z**2 - 3*z + 2. Let a be r(2). Let g(o) be the first derivative of -7*o**4 + 3*o**a + o**4 - 36 + 2*o**4. Let g(b) = 0. What is b?
0
Let n(l) be the second derivative of -l**4/54 - 628*l**3/27 - 447*l - 4. Solve n(h) = 0 for h.
-628, 0
Factor -2/7*h**4 + 2/7*h**2 + 2/7*h - 2/7*h**3 + 0.
-2*h*(h - 1)*(h + 1)**2/7
Let b = -22 + 25. What is r in 2*r**3 - 25*r**2 - r**b + 4*r**3 + 181*r - 35 - 246*r = 0?
-1, 7
Let o(f) be the second derivative of f**4/6 - 442*f**3 - 1327*f**2 - 884*f. What is j in o(j) = 0?
-1, 1327
Let a(k) be the first derivative of k**4/4 + 61*k**3/3 + 77. Let u be a(-61). Factor -1/7 - 81/7*x**4 + u*x + 18/7*x**2 + 0*x**3.
-(3*x - 1)**2*(3*x + 1)**2/7
Let j(l) be the first derivative of -33*l**5/5 - 663*l**4/2 + 371*l**3 + 123*l**2 - 7786. Let j(p) = 0. Calculate p.
-41, -2/11, 0, 1
Let v(r) = 0*r**3 - r**2 + 43*r - 7 - 14*r**2 + r**3 - 18*r. Let t(b) = b - 3. Let j(o) = 4*t(o) + 2*v(o). Determine f, given that j(f) = 0.
1, 13
Suppose -11 = -2*i - 2*t + 7*t, -3*t = -5*i - 1. Let a be i*1/4*-22. Find p such that a*p - 64*p + 1 + 24 - 17*p - 15*p**2 =