(j) be the third derivative of f(j). Factor p(k).
-3*k**3/5
Let r = -1543 - -1551. Let d(g) be the first derivative of 14/45*g**3 - r + 1/10*g**4 + 0*g**2 - 8/15*g. Factor d(k).
2*(k + 1)*(k + 2)*(3*k - 2)/15
Suppose -604*p = -607*p + 2*n - 10, 4*n - 20 = p. Factor 4/9*u**3 + p + 2/9*u**2 + 0*u.
2*u**2*(2*u + 1)/9
Let u(n) = -13*n**2 - 16*n - 14. Let p(k) = -7*k**2 - 8*k - 7. Let t(g) = -11*p(g) + 6*u(g). Solve t(w) = 0 for w.
-7, -1
Let 8*t + 11341*t**3 - 4*t**2 + 12 + t**4 - 11343*t**3 - 3*t**2 = 0. What is t?
-2, -1, 2, 3
Let k(v) be the first derivative of -2*v**3/33 + 4*v**2/11 + 120*v/11 + 579. Let k(z) = 0. Calculate z.
-6, 10
Factor 3/4*q**2 - 59/4*q + 19/2.
(q - 19)*(3*q - 2)/4
Let p = 3 + -24. Let n = 21 + p. Factor 4*j**3 + 0 + 7*j**4 - 9*j**4 + n.
-2*j**3*(j - 2)
Let h(p) be the first derivative of -p**6/6 - 7*p**5/5 + 17*p**4/2 + 142*p**3/3 - 609*p**2/2 + 441*p + 102. Factor h(j).
-(j - 3)**2*(j - 1)*(j + 7)**2
Suppose -4*j + 35 = -3*j. Suppose -2*i + 5*h = i - j, 2*i - 26 = 2*h. Factor -r**3 + r**2 - i*r + 15*r.
-r**2*(r - 1)
Suppose 4*i - 45*d = -43*d, 3*i = -3*d + 18. Factor -32/9*o**i - 2 - 16/3*o.
-2*(4*o + 3)**2/9
Let c(y) = -4*y**3 - 116*y**2 - 2*y - 56. Let h be c(-29). Let m(b) be the second derivative of -7*b - 1/36*b**4 + 0*b**h - 1/18*b**3 + 0. Factor m(p).
-p*(p + 1)/3
Suppose 3*l + 9 = 6*l. Let o(n) be the second derivative of -1/5*n**6 - 4*n + 1/2*n**4 + 1/14*n**7 + 0*n**2 + 0*n**5 - 1/2*n**l + 0. Let o(z) = 0. Calculate z.
-1, 0, 1
Let w be ((-42)/210)/(72/(-800)). Determine q, given that 2/3*q**3 + 16/9 - w*q**2 + 8/9*q = 0.
-2/3, 2
Let q(s) = -8*s**3 - 4*s**2 + 32*s - 24. Let k(d) = -d**4 - 15*d**3 - 7*d**2 + 63*d - 50. Let j(y) = -4*k(y) + 10*q(y). Factor j(t).
4*(t - 5)*(t - 1)**2*(t + 2)
Let d(t) be the third derivative of -1/390*t**5 + 2/39*t**3 - 1/156*t**4 + 5*t**2 + 0 + 0*t. Factor d(b).
-2*(b - 1)*(b + 2)/13
Suppose 11*w = -3 + 25. Factor 1116*f + 4 - 12*f**w - 1112*f - 4*f**3 + 8.
-4*(f - 1)*(f + 1)*(f + 3)
Find b such that 6/11 + 42/11*b**2 - 6/11*b**3 - 34/11*b - 8/11*b**4 = 0.
-3, 1/4, 1
Let h(o) be the first derivative of -2*o**5/75 + 11*o**4/15 + 310. Let h(l) = 0. Calculate l.
0, 22
Let g(v) be the second derivative of -11*v**4/3 + 64*v**3/3 + 6*v**2 - 565*v. Factor g(r).
-4*(r - 3)*(11*r + 1)
Let n(r) be the first derivative of -2*r - 1/9*r**4 - 21 + 22/27*r**3 - 4/3*r**2. Factor n(j).
-2*(j - 3)**2*(2*j + 1)/9
Let r = 94109/39 + -2413. Let u(w) be the first derivative of 4/13*w - 3/13*w**2 + 7 + r*w**3. Suppose u(t) = 0. Calculate t.
1, 2
Let s(v) be the third derivative of -v**7/112 + 3*v**6/40 - 7*v**5/32 + 3*v**4/16 + v**3/4 - 2*v**2 + 39. Solve s(w) = 0.
-1/5, 1, 2
Let v(o) be the second derivative of o**4/6 + 3*o**3 + 8*o**2 - 155*o. What is k in v(k) = 0?
-8, -1
Factor 9800/3 + 280/3*f + 2/3*f**2.
2*(f + 70)**2/3
Let o(f) be the second derivative of -f + 0*f**3 + 0*f**2 + 0 + 1/66*f**4. Solve o(h) = 0 for h.
0
Factor 2/5*n**2 - 4/5 + 2/5*n.
2*(n - 1)*(n + 2)/5
Let m(d) = -2*d**2 + d. Let p(r) = -10*r**2 + 22*r + 44. Let g(u) = 4*m(u) - p(u). What is j in g(j) = 0?
-2, 11
Let t(d) be the second derivative of 4/7*d**2 - 10/21*d**3 + 4/21*d**4 + 21*d - 1/35*d**5 + 0. Suppose t(o) = 0. Calculate o.
1, 2
Let s(d) be the second derivative of d**9/4536 - d**8/2520 - 17*d**3/3 - 35*d. Let g(c) be the second derivative of s(c). Let g(p) = 0. What is p?
0, 1
Let d = -1142 + 1142. Suppose d + 0*i**2 + 0*i + 2/9*i**4 + 2/9*i**3 = 0. What is i?
-1, 0
Let g(l) be the first derivative of 3*l**4/16 + 3*l**3/4 + 109. Factor g(v).
3*v**2*(v + 3)/4
Factor 32*y**2 - 9*y**4 - 96*y - 82*y**5 + 44*y**5 + 39*y**5 + 18*y**3.
y*(y - 4)**2*(y - 3)*(y + 2)
Suppose -4/5 + 28/5*g**4 + 24/5*g**2 + 2/5*g - 44/5*g**3 - 6/5*g**5 = 0. Calculate g.
-1/3, 1, 2
Let t = 22030 + -66089/3. Let 0*r**3 - 4/3*r**2 + t*r**5 + r**4 + 0*r + 0 = 0. What is r?
-2, 0, 1
Let v be 2/((-6)/(-15))*(-20)/25. Let g(i) = 2*i**4 - 12*i**3 - 2*i**2. Let s(f) = -f**4 + f**3 - f**2. Let w(x) = v*s(x) - g(x). Factor w(t).
2*t**2*(t + 1)*(t + 3)
Let q(i) = -i**4 - 2*i**3 - i**2. Let m be 6/15*(5 + 0). Suppose 3*v = -m*v - 55. Let b(s) = 5*s**4 + 10*s**3 + 5*s**2. Let u(k) = v*q(k) - 2*b(k). Factor u(t).
t**2*(t + 1)**2
Let n(w) = -w + 14. Let q(x) = 14. Let m(s) = 3*n(s) - 4*q(s). Let z be m(-6). Factor 0*y**3 - 1/3*y**z + 0*y - 1/3 + 2/3*y**2.
-(y - 1)**2*(y + 1)**2/3
Let p(z) = -6*z**2 + 60*z - 396. Let j(g) = -g**2 + g - 1. Let r(i) = 4*j(i) - p(i). Solve r(v) = 0.
14
Find j, given that 224*j**2 + 5*j + 1399*j**5 + 144*j**3 + 123*j + 40*j**4 - 1395*j**5 = 0.
-4, -2, 0
Let -112/9*o + 109/3*o**2 + 4/3 - 16/9*o**5 - 313/9*o**3 + 40/3*o**4 = 0. What is o?
1/4, 2, 3
Let w(f) = 6*f**2 + 138*f + 134. Let h be w(-22). Factor 6/11 - 4/11*t - 2/11*t**h.
-2*(t - 1)*(t + 3)/11
Let v(m) be the first derivative of m**4/20 + m**3 + 27*m**2/10 + 13*m/5 - 72. Factor v(s).
(s + 1)**2*(s + 13)/5
Suppose -5*m = -4*f - 16, -1017*f - 14 = -5*m - 1011*f. Factor 0 - 3/4*l**2 + 3/4*l**3 - 1/4*l**m + 1/4*l.
-l*(l - 1)**3/4
Let m(j) be the first derivative of 135*j**4/16 + j**3/2 - 3*j**2 - 1. Determine v, given that m(v) = 0.
-4/9, 0, 2/5
Let n = -12 - -17. Suppose 4*l - 17 = i, -l = n*i + 11 + 11. Suppose 7*k**2 - 4*k**2 + l - 3 - 2*k - k**4 = 0. What is k?
-2, 0, 1
Let m be 1 + (-2 - (2 - 2)). Let f be (-1)/(-1)*(12 - m). Factor -4 - w**4 + 9*w - 10*w - 6*w**3 - f*w**2 - 11*w.
-(w + 1)**2*(w + 2)**2
Suppose 3*a + 36 = 12. Let t be -1 + -1 - a/((-6)/(-3)). Let 4/3*g + 4/3 + 1/3*g**t = 0. What is g?
-2
Let n be (10/(-6))/((-15)/36). Find x such that 0*x - 3/4*x**3 + 0*x**2 + 0 - 3/4*x**n = 0.
-1, 0
Let n(l) be the third derivative of -l**8/1344 + l**7/60 - 61*l**6/480 + 7*l**5/20 - 3*l**4/8 - 227*l**2. Solve n(a) = 0 for a.
0, 1, 6
Let s(i) be the second derivative of 0*i**5 - 1/2*i**3 + 1/14*i**7 - 1/5*i**6 + 0 + 1/2*i**4 + 20*i + 0*i**2. Determine m, given that s(m) = 0.
-1, 0, 1
Let z(m) = -145*m**3 + 225*m**2 + 945*m - 765. Let x(g) = 9*g**3 - 14*g**2 - 59*g + 48. Let q(n) = 65*x(n) + 4*z(n). Factor q(h).
5*(h - 4)*(h - 1)*(h + 3)
Let p(o) = -14*o**3 - 36*o**2 + 12*o - 4. Let c(m) = -42*m**3 - 107*m**2 + 36*m - 14. Let q(b) = 4*c(b) - 14*p(b). Find v such that q(v) = 0.
-3, 0, 2/7
Let q(k) be the third derivative of 1/80*k**5 - 1/16*k**4 - 3/8*k**3 + 7*k**2 + 0*k + 0. Determine h, given that q(h) = 0.
-1, 3
Let s = 198682 - 17086327/86. Let h = s + -12/43. Factor 5/2*c**3 + 0*c - c**2 + 0 + h*c**4.
c**2*(c + 1)*(7*c - 2)/2
Let o(j) be the second derivative of j**6/30 - 3*j**5/20 - 5*j**4/6 - 147*j. Factor o(a).
a**2*(a - 5)*(a + 2)
Let u = 3450 - 3448. Solve -2/5 - 2/5*t**3 + 2/5*t**u + 2/5*t = 0.
-1, 1
Suppose -6*z - z + 392 = 0. Factor 10*q**3 + z*q + 4 + q**4 - 5*q**2 + 7 + 21 + 41*q**2.
(q + 2)**3*(q + 4)
Let q = 2/66721 + 9007307/934094. Let g = -64/7 + q. Factor -1/4*f**2 + 0 - g*f + 1/4*f**3.
f*(f - 2)*(f + 1)/4
Factor 1156/5 + 136/5*s + 4/5*s**2.
4*(s + 17)**2/5
Let n be (12/(-14))/(1/((-105)/30)). Let t(w) be the first derivative of -2/7*w - 5/14*w**2 + 4 - 4/21*w**n - 1/28*w**4. Solve t(f) = 0.
-2, -1
Let m(v) be the first derivative of -1/10*v**4 + 8 + 432/5*v - 108/5*v**2 + 12/5*v**3. Factor m(q).
-2*(q - 6)**3/5
Let n(y) = -y**3 + 3*y**2 + 12*y - 6. Let w be n(5). Factor -180*q + 5 + 300*q**2 - 5 - 65*q**3 + 7*q**5 - 12*q**5 - 50*q**w.
-5*q*(q - 1)**2*(q + 6)**2
Let c(a) be the second derivative of 0*a**4 - 1/210*a**6 + a - 3/140*a**5 - 1 + 0*a**3 + 0*a**2. Suppose c(z) = 0. What is z?
-3, 0
Let x(z) be the first derivative of 0*z**5 - 1/360*z**6 + 0*z**2 + 0*z**4 - z**3 + 0*z - 2 + 1/840*z**7. Let g(o) be the third derivative of x(o). Factor g(m).
m**2*(m - 1)
Let y(u) be the first derivative of -u**5 + 15*u**3 - 10*u**2 - 60*u - 140. Factor y(w).
-5*(w - 2)**2*(w + 1)*(w + 3)
Suppose -87*s = -33*s - 37*s. Factor s + 6/5*f + 2/15*f**2.
2*f*(f + 9)/15
Let y(o) be the second derivative of 1/42*o**7 - o - 1/30*o**6 + 0*o**3 + 1/12*o**4 + 0*o**2 - 1/20*o**5 + 0. Factor y(p).
p**2*(p - 1)**2*(p + 1)
Suppose 0 = 4*z + x - 4*x - 423, -4*z - 2*x + 438 = 0. Factor -58 + 2*f**2 + 150 + 50*f + z - 10*f.
2*(f + 10)**2
Let l = -2/2285 - -4576/6855. Let p(n) be the second derivative of -1/21*n**7 - 1/3*n**3 - 3/5*n**5 - 4/15*n**6 + 7*n + 0*n**2 + 0 - l*n**4. Factor 