115 - 16*g**4/23 - 68*g**3/69 + 32*g**2/23 + 66*g/23 + 358. Determine t so that w(t) = 0.
-1, 1, 33
Let a(q) be the third derivative of 1/36*q**5 + 5/6*q**3 + 35*q**2 - 1/72*q**6 + 0*q + 25/72*q**4 + 0. Factor a(r).
-5*(r - 3)*(r + 1)**2/3
Let w be 12/42 + (-47)/(-7). Factor 18*g**2 + 3*g**2 - 45*g + w*g**3 - 10*g**3 + 27.
-3*(g - 3)**2*(g - 1)
Let l(a) be the first derivative of -a**6/4 + 27*a**5/10 + 9*a**4/8 - 29*a**3/2 + 27*a**2/2 + 98. What is g in l(g) = 0?
-2, 0, 1, 9
Let f = 57 + -511/9. Let l = 143 + -1285/9. Factor 4/9*m**3 + 0 + 0*m - l*m**2 - f*m**4.
-2*m**2*(m - 1)**2/9
Factor 0 - 8*f**4 - 1/3*f**5 - 39*f**3 + 338/3*f**2 + 0*f.
-f**2*(f - 2)*(f + 13)**2/3
Suppose -4*u + 6*u + 300 = 0. Let c = u - -152. Solve 1/2*m**c - 1/4*m**3 + 0 - 1/4*m = 0.
0, 1
Let y(r) be the first derivative of -2*r**5/5 + 9*r**4/2 - 76*r**2 + 192*r + 884. Factor y(g).
-2*(g - 8)*(g - 2)**2*(g + 3)
Suppose 0 = -49*s + 52 + 95. Let y(z) be the first derivative of 1/3*z**6 - z**4 + 4/3*z**s - 2/5*z**5 - 2*z + 9 + z**2. Factor y(f).
2*(f - 1)**3*(f + 1)**2
Let t(i) be the third derivative of 4/3*i**3 + 1/3*i**4 + 0 - 21*i**2 + 0*i + 1/30*i**5. Factor t(l).
2*(l + 2)**2
Let k(d) = 5*d**3 + 2*d**2 - 6*d. Let v(p) = 14*p**3 + 4*p**2 - 17*p. Let j(o) = -17*k(o) + 6*v(o). Solve j(x) = 0.
-10, 0
Let f = -24 - 130. Let d be ((-4)/(-3))/(f/(-21) - 7). Suppose -27/2*u**d + 0 + 21/2*u**5 + 3*u**3 + 0*u + 0*u**2 = 0. Calculate u.
0, 2/7, 1
Let o(d) = 5*d**2 + d. Let u be 1*((-12)/(-4) - -8). Let k(q) = -9*q**2 - 2*q. Let t(h) = u*o(h) + 6*k(h). Find n such that t(n) = 0.
0, 1
Let b(l) be the first derivative of -l**6/9 - 14*l**5/15 - 3*l**4 - 40*l**3/9 - 8*l**2/3 - 425. Factor b(q).
-2*q*(q + 1)*(q + 2)**3/3
Let s(y) be the third derivative of y**6/120 + 17*y**5/300 - y**4/10 + y**2 - 80*y. Factor s(h).
h*(h + 4)*(5*h - 3)/5
Let u(c) be the second derivative of c**4/4 - 17*c**3/2 + 55*c. Factor u(i).
3*i*(i - 17)
Let w = 619 - 6197/10. Let y = 6/5 + w. Factor y*g**2 - 3/4*g + 1/4.
(g - 1)*(2*g - 1)/4
Factor 1/3*y - 1/3*y**3 + 1/3*y**2 - 1/3.
-(y - 1)**2*(y + 1)/3
Let n(p) be the third derivative of 0*p**3 + 0*p - 4/15*p**6 + 0*p**4 - 24*p**2 - 16/15*p**5 - 2/105*p**7 + 0. Determine l, given that n(l) = 0.
-4, 0
Let d(b) be the first derivative of -8*b**5/5 - 9*b**4/2 - 4*b**3/3 - 564. Determine v so that d(v) = 0.
-2, -1/4, 0
Factor 28*y + 1/2*y**2 + 392.
(y + 28)**2/2
Factor 1/2*d**5 + d**2 + 0*d**4 - 3/2*d**3 + 0 + 0*d.
d**2*(d - 1)**2*(d + 2)/2
Let i(y) be the first derivative of -5*y**4/4 + 130*y**3/3 + 425*y**2/2 + 290*y - 130. Factor i(c).
-5*(c - 29)*(c + 1)*(c + 2)
Let t = 1739 - 19112/11. Let h = -1/22 + t. Factor h + 3/2*w**2 + 3*w.
3*(w + 1)**2/2
Let z(f) = 4*f**2 + 6*f. Let o(u) = -23*u**2 - 38*u. Let w(p) = -6*o(p) - 34*z(p). Let w(k) = 0. What is k?
-12, 0
Let k be (-12)/(-30)*(4 - -1). Let c = 12/17 - 43/85. Factor c + 0*o - 1/5*o**k.
-(o - 1)*(o + 1)/5
Let z(d) be the first derivative of 0*d - 1/84*d**4 + 0*d**3 + 0*d**5 + 1/420*d**6 + 4 + 3/2*d**2. Let y(p) be the second derivative of z(p). Factor y(v).
2*v*(v - 1)*(v + 1)/7
Let t(g) = -7*g**3 - 16*g**2 - 15*g + 95. Let l(y) = 6*y**3 + 16*y**2 + 14*y - 96. Let h(b) = -5*l(b) - 4*t(b). Factor h(i).
-2*(i - 2)*(i + 5)**2
Let i(j) be the first derivative of j**6/33 + 6*j**5/55 + j**4/11 - 91. Factor i(p).
2*p**3*(p + 1)*(p + 2)/11
Let i be ((-3)/((-9)/40))/(7/21). Let v = i - 79/2. Suppose -1/2*l**3 + 1/2*l + v - 1/2*l**2 = 0. What is l?
-1, 1
Let b(l) = -6*l**4 + 4*l**3 - 4*l**2 + 6*l. Let a(j) = 7*j**4 - 5*j**3 + 5*j**2 - 7*j. Suppose -2*w - w = 18. Let v(h) = w*b(h) - 5*a(h). Factor v(p).
p*(p - 1)*(p + 1)**2
Let 529 + 23*r + 1/4*r**2 = 0. Calculate r.
-46
Factor -416*t**3 - 328*t + 139*t**3 + 141*t**3 + 140*t**3 - 324*t**2.
4*t*(t - 82)*(t + 1)
Let f(c) be the third derivative of c**5/390 - 19*c**4/156 - 20*c**3/39 + 32*c**2. Solve f(n) = 0 for n.
-1, 20
Factor -5/3*k**2 - 105 - 320/3*k.
-5*(k + 1)*(k + 63)/3
Factor 8/3 + 2/9*o**3 - 2/3*o**2 - 8/9*o.
2*(o - 3)*(o - 2)*(o + 2)/9
Let y be 10 + -9 + ((-30)/(-9) - 5/(-15)). Factor -y*i + 4 + 2/3*i**2.
2*(i - 6)*(i - 1)/3
Let a(k) = -2*k**2 + 13*k - 6. Let o be a(6). Let r(w) = -w**2 + 3. Let y be r(o). Factor 6*v**2 - v**4 + 2*v**y - 2*v**2 - v**2.
-v**2*(v - 3)*(v + 1)
Let z(m) be the first derivative of 8/3*m - 13 + 4/3*m**2 + 2/9*m**3. Factor z(w).
2*(w + 2)**2/3
Let z = 61594/115545 - -2/7703. Find v, given that 2/15*v**3 + z*v + 0 + 8/15*v**2 = 0.
-2, 0
Let g = -592 + 594. Suppose 9/4*j**3 + 3/4*j**5 + 0*j - 3/4*j**g + 0 - 9/4*j**4 = 0. What is j?
0, 1
Let x(w) be the first derivative of -2*w**2 - 34*w + 15. Let h be x(-9). Factor 4 - h*u + 1/4*u**2.
(u - 4)**2/4
Let l(d) be the third derivative of 0*d**4 + 0 + 9*d**2 + 0*d**3 + 0*d + 1/336*d**8 + 0*d**6 + 1/210*d**7 + 0*d**5. Solve l(z) = 0 for z.
-1, 0
Suppose q = -c + 5, 2*q + 3*c - 10 = 1. Let s(i) = -i**3 - 9*i**2 - 15*i - 4. Let o be s(-7). Factor 2*v**o + 2*v**3 + q*v**5 - 3*v**5 + 8*v**4 + 3*v**5.
4*v**3*(v + 1)**2
Suppose 24/13*n + 110/13*n**3 + 4*n**4 + 6/13*n**5 + 88/13*n**2 + 0 = 0. What is n?
-6, -1, -2/3, 0
Let m = 119/40 - 71/40. Factor -m*u**2 - 2/5*u + 0 - 4/5*u**3.
-2*u*(u + 1)*(2*u + 1)/5
Suppose j - v + 1 = 0, 5*j - 34 + 7 = -3*v. Let s be 5/(-3) - (67 + -69). Solve -1/3*o**5 + 2/3*o**j - s*o - 2/3*o**2 + 1/3*o**4 + 1/3 = 0 for o.
-1, 1
Let k be (2 - (-20)/8)*-2. Let t(i) = -i - 5. Let b be t(k). Find a, given that 2*a**2 + 7*a + 4*a**2 - 9*a**2 + b + 2 = 0.
-2/3, 3
Let x = -65 - -67. Let f = -36/11 + 296/77. Let 0*z**x + 0 + 0*z - f*z**4 - 8/7*z**3 = 0. What is z?
-2, 0
Let z(f) = -3*f**2 - 9*f. Let y(m) = m**2 + m. Let v(k) = -6*y(k) - 3*z(k). Factor v(p).
3*p*(p + 7)
Factor 42/5*x + 2/5*x**3 - 36/5 - 16/5*x**2.
2*(x - 3)**2*(x - 2)/5
Let t(q) be the second derivative of -q**7/8820 - q**6/1260 - q**5/420 + 5*q**4/12 + 4*q. Let f(p) be the third derivative of t(p). Factor f(z).
-2*(z + 1)**2/7
Let t be 30/8*(-40)/(-30). Let m(r) be the first derivative of 1/15*r**3 + 9/5*r + 3/5*r**2 + t. Factor m(x).
(x + 3)**2/5
Find v, given that -7*v**2 - 1800*v**3 - 92*v - 43*v**2 + 1798*v**3 = 0.
-23, -2, 0
Let r(c) = c**2 + 5*c. Let f be r(-5). Let j be 14 + (9 - 6 - 14). Solve f + 0*i - 1/3*i**2 + 2/3*i**j - 1/3*i**4 = 0 for i.
0, 1
Let q(c) be the first derivative of -4/9*c**2 + 2/27*c**3 + 8/9*c - 1. Let q(p) = 0. Calculate p.
2
Let n(q) be the second derivative of -q**6/30 + 9*q**5/20 + 143*q. What is v in n(v) = 0?
0, 9
Determine p, given that 8*p - 2/3*p**3 + 0 + 8/3*p**2 = 0.
-2, 0, 6
Let o(i) be the third derivative of i**5/120 - 7*i**4/6 + 196*i**3/3 - 81*i**2. Find l such that o(l) = 0.
28
Let s(k) = -720*k**4 - 120*k**3 + 95*k**2 - 5*k. Let m(w) = -1080*w**4 - 180*w**3 + 142*w**2 - 7*w. Let g(f) = -5*m(f) + 8*s(f). Suppose g(b) = 0. What is b?
-1/2, 0, 1/6
Suppose 0*b - 5*b - 2791 = -3*w, -2*w = -5*b - 2789. Let i = 3905/7 + b. Factor 2/7 + 2/7*p**3 + i*p + 6/7*p**2.
2*(p + 1)**3/7
Suppose 29 = 5*i - 2*f - 0*f, -8 = -2*i - f. Let m(k) be the second derivative of 1/30*k**6 + 0 - k + 0*k**3 - 1/12*k**4 + 0*k**2 + 0*k**i. Factor m(g).
g**2*(g - 1)*(g + 1)
Let y be 0 + 6 + (1 - 4). Suppose -z - 8 = i - 3*i, i + y*z + 3 = 0. Let -45*v**2 - 16*v - 8*v + 0 - 25*v**i - 1 - 3 = 0. What is v?
-1, -2/5
Suppose -r - 14 = -3*w + w, -3*w - 4*r = 1. Suppose -w*u + 5 = 5*c, 5 = -5*c - 0*c + 5*u. Let -5*i**2 + c*i**4 + 3*i**4 - i**4 + 3*i**4 = 0. What is i?
-1, 0, 1
Let s be (7 - 7)/(2 + -5). Factor s*q**2 - 1/6*q**4 - 1/3*q**3 + 0*q + 0 + 1/6*q**5.
q**3*(q - 2)*(q + 1)/6
Let y(h) = -h**2 - 3*h + 7. Let i(b) = -b**2 - 5*b + 10. Let g(z) = -3*i(z) + 4*y(z). Find f, given that g(f) = 0.
1, 2
Suppose -h + 4*l = -10, 4*h - 2*l - 30 = h. Suppose 0 = s + 4 - h. Let -3*w**3 - 9*w**2 + s*w**2 + 15*w**2 - 15*w + 6 = 0. What is w?
1, 2
Factor -16/3 - 4/9*b**2 + 38/9*b.
-2*(b - 8)*(2*b - 3)/9
Determine p, given that -8/5 - 1/5*p**2 + 9/5*p = 0.
1, 8
Let k(i) be the second derivative of -i**4/8 - 5*i**3/2 - 129*i. Factor k(q).
-3*q*(q + 10)/2
Let g(s) be the first derivative of s**7/42 + s**6/8 - s**5/12 - 5*s**4/8 + 5*s**2/2 + 18. Let p(w) be the second derivative of g(w). Let p(v) = 0. What is v?
-3, -1, 0, 1
Let w(i) = -3*i**3 + 183*i**2 - 3975*i + 27789. Let a(c) = 3*c**3 - 184*c**2 + 3974*c - 27788.