ch that -1/2*g**d + 7/6*g - 1/3 = 0.
1/3, 2
Find s, given that 1/3*s**5 - 40/3*s**2 + 0 + 2/3*s**4 - 4*s**3 - 32/3*s = 0.
-2, 0, 4
Let t(f) be the third derivative of 0 + 0*f - 2*f**2 - 1/2*f**4 + 2/45*f**6 - 5/3*f**3 + 11/30*f**5. Let h(y) be the first derivative of t(y). Factor h(o).
4*(o + 3)*(4*o - 1)
Let k(a) be the first derivative of a**5/10 - 7*a**4/6 + 8*a**3/3 + 16*a**2 - 5*a - 11. Let m(c) be the first derivative of k(c). Solve m(v) = 0 for v.
-1, 4
Let m(i) be the first derivative of -21/2*i**2 - 5*i**3 - 9*i - 16 - 3/4*i**4. Solve m(h) = 0.
-3, -1
Let a(y) be the first derivative of 4*y**5/5 - 2*y**4 - y**3 + 5*y**2/2 + 2*y - 481. Factor a(o).
(o - 2)*(o - 1)*(2*o + 1)**2
Let -18522/13 - 2646/13*d - 2/13*d**3 - 126/13*d**2 = 0. What is d?
-21
Suppose 2*i = 0, 484*i - 20 = -5*r + 486*i. What is p in -1/2*p**5 - p**r + 0 + p**2 + 1/2*p + 0*p**3 = 0?
-1, 0, 1
Factor 11*k - 17*k**2 + 85*k + 120*k**3 + 16 + 201*k**2 + 25*k**4.
(k + 2)**2*(5*k + 2)**2
Suppose -5*x + 12 = 3*j - 8*x, 0 = -j + 3*x + 8. Solve 4*r - 6*r**3 + 27*r**2 - 10*r - 12*r**j - 3*r**3 = 0 for r.
0, 2/3, 1
Let g be 2176/(-9) - 9/((-54)/(-12)). Let k = g + 244. Factor 2/9 + k*t**2 + 4/9*t.
2*(t + 1)**2/9
Suppose 5 = -2*c + 49. Factor -m - 11*m - 1 + c*m**3 + 26*m**3 - 32*m**4 - 2*m**2 - 1.
-2*(m - 1)**2*(4*m + 1)**2
Factor 69*u**2 - 60*u - 16 - 4*u**3 - 2*u**3 - 107*u**2.
-2*(u + 2)*(u + 4)*(3*u + 1)
Suppose 17 = 6*v - 13. Suppose 0 = -v*m + 3*h + 7, 5*m + h + 4 = 15. Suppose 2/11*j**m + 2/11*j - 4/11 = 0. Calculate j.
-2, 1
Let x = 532/13 - 1051/26. Solve x*p**2 - 1/2 + 0*p = 0 for p.
-1, 1
Let l = 32 - 22. Determine c, given that 16*c**4 - 8*c**3 + l*c - 4*c**4 - 4*c**5 - 10*c = 0.
0, 1, 2
Suppose 37 = -2*k - 23. Let b = -15 - k. Factor -f**3 + 9 + 0*f**2 + 7*f**2 + b*f + 2*f**3.
(f + 1)*(f + 3)**2
Suppose -2*m + 7 = 1. Suppose 3*d - m = -3. Factor 1 + d*s**2 - 3/2*s + 1/2*s**3.
(s - 1)**2*(s + 2)/2
Factor -11/3*p + 10 + 1/3*p**2.
(p - 6)*(p - 5)/3
Let g(s) be the second derivative of 5*s**4/12 + 35*s**3/6 + 30*s**2 - 474*s. Suppose g(d) = 0. Calculate d.
-4, -3
Let m = 5672/9 - 39128/63. Factor -48/7*u**2 - 16/7*u**3 - 32/7 - m*u - 2/7*u**4.
-2*(u + 2)**4/7
Let t(c) be the first derivative of -8*c**4 + 944*c**3/3 - 233*c**2 + 58*c + 107. Factor t(m).
-2*(m - 29)*(4*m - 1)**2
Let r be (-3)/((-6)/7) - 24/16. Suppose 3*y = -4*u + u + 18, 0 = r*u - 8. Find b such that -8/5*b - 12/5 + 4/5*b**y = 0.
-1, 3
Let d(j) be the second derivative of 0 + 5/6*j**4 - 1/30*j**5 - 25/3*j**3 - 16*j + 125/3*j**2. Determine s so that d(s) = 0.
5
Let i be ((-408)/40 + 10)*(-20)/(-16)*-1. Let y = -51/2 - -26. Determine u so that 3/4*u - i*u**2 - y = 0.
1, 2
Let l = 2/21 + 1/210. Let r(s) be the second derivative of -4*s + 0*s**4 - 3/10*s**5 + 0*s**2 + l*s**6 + 0*s**3 + 0. Factor r(k).
3*k**3*(k - 2)
Suppose -3*l + 8 + 10 = 5*n, 2*l = 3*n - 7. Suppose -2*z = -z - n. Factor -1 + z*r - r**2 + 4*r - r - 4*r.
-(r - 1)**2
Let k(w) be the second derivative of -w**4/3 - 20*w**3/3 - 18*w**2 + 3*w + 13. Suppose k(h) = 0. Calculate h.
-9, -1
Let k(i) be the first derivative of 7*i**4/18 - 22*i**3/9 + 32*i**2/9 + 8*i/3 + 19. Factor k(m).
2*(m - 3)*(m - 2)*(7*m + 2)/9
Let n = -14158/5 + 2841. Let f = -9 + n. Factor -1/5*r**3 + f - 2/5*r**2 + 1/5*r.
-(r - 1)*(r + 1)*(r + 2)/5
Suppose -t + 4*t + 4*a - 24 = 0, t + 4*a = 16. Factor 5*n**3 + 3*n**2 + 0*n**4 + 11*n**t - 2*n**4 + 3*n**5 + 4*n**3.
3*n**2*(n + 1)**3
Let a(k) = -k**3 + 4*k**2 + 5*k + 4. Let u be a(5). Suppose 51*s + 1632*s - 156*s**2 + 96*s - 8788 + u*s**3 + 249*s = 0. Calculate s.
13
Suppose -52 + 76 = 2*n - 4*f, -36 = -5*n - 2*f. Let h(m) be the first derivative of 6 + 8/3*m**3 - n*m - 2*m**2 + m**4. Factor h(j).
4*(j - 1)*(j + 1)*(j + 2)
Let j(c) = c**3 - 37*c**2 - 3*c + 111. Let p be j(37). Let u(l) be the third derivative of -1/240*l**5 + 0*l**3 + 0*l + p - 7*l**2 + 1/48*l**4. Factor u(s).
-s*(s - 2)/4
Let k(p) = -p**2 + 11*p - 7. Let r be k(10). Suppose 4*l**2 - l**5 + 12*l**4 + 5*l**3 - r*l**5 - 2*l**3 - 15*l**3 = 0. Calculate l.
0, 1
Let f(g) = -13*g**2 - 11*g - 3. Let x(h) = 1 + 14*h**2 - 19*h**3 + 20*h**3 + 3*h + 3 + 9*h. Let l(s) = -4*f(s) - 3*x(s). Determine p so that l(p) = 0.
-2/3, 0, 4
Let k(q) be the second derivative of 0 - 1/10*q**5 + 0*q**2 + 14*q + 0*q**3 - 1/30*q**6 - 1/12*q**4. Determine l, given that k(l) = 0.
-1, 0
Let g = -22475/2 - -876323/78. Let p = 1/13 - g. Factor -10/9*i**4 - p*i**3 - 4/9*i + 0 - 2*i**2.
-2*i*(i + 1)**2*(5*i + 2)/9
Factor 106/13 - 8*s - 2/13*s**2.
-2*(s - 1)*(s + 53)/13
Let s = 325 + -323. Suppose 0 = -5*w + 5*m + 40, 8 = -m - m. Factor 3*b**2 + s - w + 0*b**2 - 1.
3*(b - 1)*(b + 1)
Let v(k) be the third derivative of k**5/60 - 11*k**4/24 + 5*k**3 + 2*k**2 - 5. Factor v(p).
(p - 6)*(p - 5)
Let u(x) be the first derivative of 5*x**4/4 + 35*x**3/3 + 55*x**2/2 + 25*x - 20. Solve u(j) = 0.
-5, -1
Suppose l - 9*l = -24. Let h(q) be the third derivative of -3*q**2 - 1/30*q**5 + 0*q + 0*q**l + 1/12*q**4 + 0. Let h(f) = 0. What is f?
0, 1
Let g(i) be the third derivative of -i**7/15 + 113*i**6/30 + 167*i**5/30 - 11*i**4/2 + 1076*i**2. What is v in g(v) = 0?
-1, 0, 2/7, 33
Let j(q) = -15*q**4 - 80*q**3 - 77*q**2 - 17*q - 7. Let k(a) = -15*a**4 - 78*a**3 - 78*a**2 - 18*a - 6. Let w(f) = -6*j(f) + 7*k(f). Solve w(c) = 0.
-2, -2/5, 0
Let z = 18474 - 18471. Determine r, given that 0 - 4/3*r + 2*r**2 - 2/3*r**z = 0.
0, 1, 2
Let j(r) be the second derivative of 10/3*r**3 - 31*r + 0*r**2 + 5/12*r**4 + 0. Let j(l) = 0. What is l?
-4, 0
Let s(d) be the third derivative of -d**7/525 + d**6/3 - 1199*d**5/75 - 85*d**4 - 867*d**3/5 - 663*d**2. Factor s(z).
-2*(z - 51)**2*(z + 1)**2/5
What is v in -10 - 5 - 5*v**2 - 3 - 9*v + 4*v**2 + 0*v = 0?
-6, -3
Let l be ((-18)/(-8))/(18/(-240)). Let m be ((-24)/l)/(2/5). Let 2*q**3 - 19*q**2 - 3*q + 9 + 11*q**3 + 2*q**3 - m*q**2 = 0. What is q?
-3/5, 1
Let b be (-12)/4 + -103 - -5. Let n = 304/3 + b. Determine v so that 0*v**3 - n*v**5 + 0 - 1/3*v**4 + 0*v + 0*v**2 = 0.
-1, 0
Let q = 142 + -138. Let -2 + 0*y**3 - 4*y**3 - 2 - y + q*y**2 + 5*y = 0. Calculate y.
-1, 1
Factor -3*b + 0 + 3/7*b**2.
3*b*(b - 7)/7
Suppose -2*c + p + 2 + 3 = 0, 5*c - 35 = -2*p. Suppose 5*w - c = 5. Suppose -6*q**5 - 2*q**4 + 0*q**5 - 3*q**2 + 5*q**w - 8*q**4 - 2*q**3 = 0. Calculate q.
-1, 0, 1/3
Suppose t = -5*v + 19, 0*t = v + 3*t - 1. Factor v*z + 2*z + 59 - 59 - 10*z**2.
-2*z*(5*z - 3)
Let m(s) be the third derivative of -1/8*s**4 + 0 + 0*s + 1/40*s**6 - 7*s**2 - 1/20*s**5 + 1/2*s**3. Factor m(p).
3*(p - 1)**2*(p + 1)
Let q(z) be the third derivative of 0*z + 1/84*z**8 - 1/15*z**6 - 8/105*z**7 + 1/6*z**4 - 8/3*z**3 + z**2 + 8/15*z**5 + 0. Find s such that q(s) = 0.
-1, 1, 4
What is v in 10*v**2 - 12*v**3 + 6*v**4 + 660*v - 663*v - v**5 - 1 + 1 = 0?
0, 1, 3
Let k(i) be the first derivative of 7*i**6/4 - 9*i**5/5 - 3*i**4 + 3*i**3 + 3*i**2/4 - 682. Find c, given that k(c) = 0.
-1, -1/7, 0, 1
Suppose 0 = -3*b + g + 2, 3*g = 28*b - 27*b - 6. Let c(p) be the second derivative of 5*p + 0*p**3 - 3/100*p**5 + 0*p**4 + 0 + b*p**2 - 1/50*p**6. Factor c(x).
-3*x**3*(x + 1)/5
Let s(f) be the first derivative of -2/5*f**5 - f**2 + 0*f + 1/2*f**4 + 2/3*f**3 + 12. Solve s(h) = 0.
-1, 0, 1
Let c(m) = 7*m**2 + 29*m + 73. Let p(x) = x**2 - x + 3. Let i(w) = c(w) - 3*p(w). What is h in i(h) = 0?
-4
Let q = -688 + 688. Suppose 0 + 5/6*a**4 + 13/6*a**3 + q*a - a**2 = 0. What is a?
-3, 0, 2/5
Let r(p) be the third derivative of -p**7/2100 - p**6/900 + p**5/150 - p**3/2 + 30*p**2. Let f(b) be the first derivative of r(b). What is q in f(q) = 0?
-2, 0, 1
Let k(l) = l**4 + 3*l**3 - 16*l**2 + 6*l. Let m(p) = -2*p**4 - 7*p**3 + 35*p**2 - 12*p. Let q(z) = 14*k(z) + 6*m(z). Factor q(v).
2*v*(v - 2)*(v - 1)*(v + 3)
Let p(j) be the second derivative of j**7/105 - 13*j**6/75 + 47*j**5/50 - 23*j**4/30 - 16*j**3/5 + 36*j**2/5 + 72*j. Determine t so that p(t) = 0.
-1, 1, 6
Let k be 4908/(-9240) + 12/22. Let j(r) be the second derivative of 3*r + 2/21*r**3 + 1/14*r**2 + 5/84*r**4 + k*r**5 + 0. Factor j(z).
(z + 1)**2*(2*z + 1)/7
Let h(n) = 15*n**3 - 15*n**2 + 12*n - 12. Let t(a) = a**3 - a**2 + a - 1. Let g = 42 + -43. Let u(c) = g*h(c) + 12*t(c). Factor u(x).
-3*x**2*(x - 1)
Let s(p) be the third derivative of p**6/80 - p**5/40 - p**