 -4*k - 20. Factor -3*n**2 + o*n**2 + 9 - 6.
-3*(n - 1)*(n + 1)
Factor 0*o + 0*o**3 - 2*o**2 + 0 + 1/2*o**4.
o**2*(o - 2)*(o + 2)/2
Let h(f) be the second derivative of -f**6/30 - 3*f**5/20 + 11*f**4/12 + f**3/2 - 5*f**2 - 27*f. Determine n, given that h(n) = 0.
-5, -1, 1, 2
Suppose 0 = 5*p + h - 337, p - 2*h - 278 = -3*p. Suppose -2*j + 58 = 3*z, 6*z + 5*j - p = 2*z. Factor n**2 - z*n**4 - 2*n**5 + 2*n + 18*n**4 + 3*n**2.
-2*n*(n - 1)*(n + 1)**3
Factor 4*r**4 - 66*r + 4*r**3 - 24*r**2 + 66*r.
4*r**2*(r - 2)*(r + 3)
Let s(m) = -29*m + 1540. Let h be s(53). Factor 3 + 3/2*z - 9/2*z**2 - 3/2*z**h + 3/2*z**4.
3*(z - 2)*(z - 1)*(z + 1)**2/2
Let i(g) = -3*g**3 + 21*g + 12. Let j(n) = -3*n**3 - n**2 + 20*n + 13. Let f(b) = 5*i(b) - 6*j(b). Solve f(l) = 0 for l.
-3, -1, 2
Let y(n) = -4*n - 1. Let r be y(-1). Factor -4*a + 10*a - a**2 + 0*a**2 - r*a - 2.
-(a - 2)*(a - 1)
Suppose -3*y = -r - 13, -r - 3*y - 8 + 25 = 0. Let 0 + 3*v**r - 6/5*v - 9/5*v**3 - 3/5*v**4 + 3/5*v**5 = 0. What is v?
-2, 0, 1
Let k = 3545/4 - 886. Let q(h) be the first derivative of 1/6*h**3 + 0*h - 7 + k*h**2. Suppose q(j) = 0. What is j?
-1, 0
Let i(f) be the first derivative of 2*f**4/9 - 130*f**3/27 - 212*f**2/9 + 38*f/3 + 687. Factor i(d).
2*(d - 19)*(d + 3)*(4*d - 1)/9
Let z(b) be the second derivative of b**8/756 - 2*b**7/315 + b**6/90 - b**5/135 + 3*b**2/2 + 10*b. Let o(c) be the first derivative of z(c). Factor o(f).
4*f**2*(f - 1)**3/9
Suppose -9*t = 4 - 31. Suppose -6*v**2 + 7*v**2 + v + 0*v**2 - t*v + v**3 = 0. What is v?
-2, 0, 1
Let i = 20785/48 - 433. Let f(t) be the third derivative of i*t**4 - 1/120*t**5 + 0 + 0*t**3 - t**2 + 0*t. Determine u so that f(u) = 0.
0, 1
Factor -2/11*c**5 - 74/11*c + 26/11*c**4 + 116/11*c**2 - 84/11*c**3 + 18/11.
-2*(c - 9)*(c - 1)**4/11
Let l(t) = -3*t**2 + 358*t - 10800. Let j(h) = 30*h**2 - 3579*h + 108000. Let s(p) = 2*j(p) + 21*l(p). Factor s(w).
-3*(w - 60)**2
Let d(k) = k**2 + 181*k + 882. Let h be d(-5). Let -4/7*i**3 + 0 - 4/7*i**h + 0*i = 0. What is i?
-1, 0
Let f(l) be the first derivative of -l - 37 + 1/8*l**6 - 7/12*l**3 - 3/2*l**2 + 9/16*l**4 + 11/20*l**5. Solve f(t) = 0 for t.
-2, -1, -2/3, 1
Let m(d) be the third derivative of 0*d**4 + 0 + 0*d**3 + 0*d - 6*d**2 + 0*d**5 - 1/240*d**6 - 1/840*d**7. Let m(a) = 0. What is a?
-2, 0
Factor -z**4 + 980*z**2 + 1235*z + 880*z**3 - 4*z**4 - 345*z + 795*z**2.
-5*z*(z - 178)*(z + 1)**2
Let g(v) be the second derivative of v**7/42 + 7*v**6/30 + v**5/2 - 3*v**4/2 - 9*v**3/2 + 27*v**2/2 + 23*v - 5. Factor g(c).
(c - 1)**2*(c + 3)**3
Let c(z) = -z**2 + 1. Let n be 51/9 - (-2)/6. Let j(l) = 9*l**2 - 6*l + 6. Let o(s) = n*c(s) - j(s). Factor o(v).
-3*v*(5*v - 2)
Let t(s) be the first derivative of -s**4/4 - s**3 - 3*s**2/2 - s + 735. Find i such that t(i) = 0.
-1
Let w = 45/92 - -6/23. Let d(j) be the second derivative of 0 + 3/2*j**3 + j**2 - 3*j - 1/20*j**5 - 1/10*j**6 + w*j**4. Let d(i) = 0. What is i?
-1, -1/3, 2
Solve 0 + 13/8*c**2 + 1/8*c**4 - 3/4*c - c**3 = 0.
0, 1, 6
Let w(l) be the third derivative of -l**7/7560 + l**6/720 + l**4/12 - 27*l**2. Let t(o) be the second derivative of w(o). Factor t(m).
-m*(m - 3)/3
Let r be (-110)/(-30) + -14 - -12. Factor -r - 1/3*c**2 + 2*c.
-(c - 5)*(c - 1)/3
Let i(h) be the second derivative of -3/40*h**5 + 0*h**4 + 0 + 0*h**2 + 13*h + 1/4*h**3. Find w, given that i(w) = 0.
-1, 0, 1
Find a such that -2/7*a**3 + 0*a**2 + 2*a - 12/7 = 0.
-3, 1, 2
Let o be 0/5 + 4 + 8. Factor o*w**4 - 3*w**3 - 5*w**3 + 4*w**2 + 8*w - 16*w**4.
-4*w*(w - 1)*(w + 1)*(w + 2)
Let b = -11 - -13. Suppose b*c = -5*j + 21, c - 2*j - 6 = -3*c. Find v such that 0*v**5 + 7*v**3 - 6*v**4 + 3*v**5 + 2*v**c - 6*v**5 = 0.
-3, 0, 1
Let l(z) be the first derivative of -z**5/5 - 4*z**4 - 46*z**3/3 + 72*z**2 - 81*z - 40. Factor l(c).
-(c - 1)**2*(c + 9)**2
Let l be ((-14)/(-3))/(12/18). Suppose x - l = -1. Factor -x*u**2 - 16*u**4 + 12*u**2 + 24*u**3 - 7*u**2 - 1 - 6*u.
-(u - 1)**2*(4*u + 1)**2
Suppose -10*r + 108 = 2*r. Suppose -r = -3*h, -9*n - h - 1 = -11*n. Factor -3*b**3 - 3/2*b + 13/4*b**n + 1/4 + b**4.
(b - 1)**2*(2*b - 1)**2/4
Let x(g) = 8*g**4 - 144*g**3 + 151*g**2 - 5*g. Let q(n) = -4*n**4 + 72*n**3 - 77*n**2 + 3*n. Let p(l) = -5*q(l) - 3*x(l). Solve p(s) = 0 for s.
0, 1, 17
Let x(z) be the third derivative of 0*z**5 - 1/42*z**7 - 6*z**2 + 0*z - 1/12*z**6 + 0 + 5/12*z**4 + 5/6*z**3. Let x(h) = 0. What is h?
-1, 1
Suppose -62*k - 12*k**2 - 16*k**3 - 3*k**5 + 11*k**5 + 12*k**4 + 70*k = 0. What is k?
-2, -1, 0, 1/2, 1
Suppose j + 68 = 2*j. Let n be (-20)/(-90) - j/(-18). Suppose -6*l**n - 23 + 2*l**2 + 4*l + 23 - 8*l**3 = 0. Calculate l.
-1, 0, 2/3
Let k(h) be the third derivative of 2/255*h**5 - 1/2856*h**8 - 6*h**2 - 2/255*h**6 + 0*h + 0*h**4 + 0*h**3 + 1/357*h**7 + 0. Factor k(j).
-2*j**2*(j - 2)**2*(j - 1)/17
Factor 6*z - 3/2*z**3 + 0 - 9/2*z**2.
-3*z*(z - 1)*(z + 4)/2
Suppose 3*f = c + 3*c + 143, f - 133 = 4*c. Let r = c + 34. Factor -4/9*b - 2/9*b**3 + 0 - 2/3*b**r.
-2*b*(b + 1)*(b + 2)/9
Factor 1031*f**2 + 8748*f - 86*f**3 + 43*f**3 + 160*f**2 + 151*f**3 + 267*f**2 + 3*f**4 + 19683.
3*(f + 9)**4
Suppose 5*b - 2*s - 2 = 17, 3*b + s = 18. Determine x, given that 4*x**3 - 4*x**2 - b*x**3 + 1 - 5*x - 3 = 0.
-2, -1
Let o(u) be the first derivative of -u**5/50 + u**4/3 - 5*u**3/3 - 38*u + 8. Let f(b) be the first derivative of o(b). Factor f(w).
-2*w*(w - 5)**2/5
Let m be 61 + -53 + 39/(-6). Suppose -m*u - 7/4*u**2 - 1/4*u**3 + 0 = 0. Calculate u.
-6, -1, 0
Let f(s) be the third derivative of -7/780*s**6 - 11/156*s**4 + 0*s - 6*s**2 - 8/195*s**5 + 0 - 2/39*s**3. Find z, given that f(z) = 0.
-1, -2/7
Let i(h) = 25*h**4 + 35*h**3 - 40*h**2 - 5*h - 15. Let n = 47 + -43. Let v(p) = -6*p**4 - 9*p**3 + 10*p**2 + p + 4. Let q(t) = n*i(t) + 15*v(t). Factor q(x).
5*x*(x - 1)*(x + 1)*(2*x + 1)
Let r(b) be the first derivative of -40*b**6/3 - 100*b**5 - 4325*b**4/16 - 1775*b**3/6 - 175*b**2/2 - 10*b + 74. Factor r(q).
-5*(q + 2)**3*(8*q + 1)**2/4
Let l(s) be the third derivative of s**5/150 + s**4/2 + 29*s**3/15 + 16*s**2 - 5*s. Determine t, given that l(t) = 0.
-29, -1
Let p(r) be the second derivative of 0*r**2 + 3/4*r**3 + 1/16*r**4 + 0 - 19*r. Factor p(c).
3*c*(c + 6)/4
Let g(d) = 2*d**2 + 2*d - 2. Let w be g(-2). Factor -5*t + 7*t**5 - 9*t**3 - 11*t**w - 17*t**5 - t**4 + t + 11*t**5.
t*(t - 4)*(t + 1)**3
Factor 2*f**4 + 20*f**4 - 19*f**4 + 24*f**2 - 18*f**3.
3*f**2*(f - 4)*(f - 2)
Solve -36/7*j**2 - 12*j + 0 + 3/7*j**3 = 0 for j.
-2, 0, 14
Let w(u) = 3*u**3 - 6*u**2 - 6*u. Let o = 30 - 13. Let n(g) = o*g**2 - 8*g**3 + 9*g - g + 9*g. Let y(k) = -6*n(k) - 17*w(k). Factor y(v).
-3*v**3
Find k such that -722/7 - 2/7*k**2 - 76/7*k = 0.
-19
Let q(i) be the third derivative of i**6/30 - 2*i**5/5 + 5*i**4/6 - 3*i**2 + 11. Factor q(a).
4*a*(a - 5)*(a - 1)
Let n(u) be the second derivative of u**5/10 - 5*u**4/2 + 56*u**3/3 - 60*u**2 - 666*u. Suppose n(x) = 0. What is x?
2, 3, 10
Let z(v) be the third derivative of -v**8/1344 + v**7/168 + v**6/144 - v**5/8 - 19*v**4/24 - 16*v**2. Let j(w) be the second derivative of z(w). Solve j(t) = 0.
-1, 1, 3
Let p(r) be the second derivative of -20*r**7/21 - 23*r**6/10 + 6*r**5/5 + r**4/3 + 3*r - 54. Let p(y) = 0. What is y?
-2, -1/8, 0, 2/5
Let 54*f - 72 + 31*f**2 - 28 - 8 + 24*f**2 - f**2 + 2*f**3 - 2*f**4 = 0. What is f?
-3, 1, 6
Let x = -67 - -71. Let z(u) = 45*u**4 + 10*u**3 - 35*u + 35. Let a(t) = -5*t**4 - t**3 + 4*t - 4. Let h(c) = x*z(c) + 35*a(c). Factor h(f).
5*f**3*(f + 1)
Let y(i) be the third derivative of -i**8/1680 + i**7/280 - i**6/120 + i**5/120 + 19*i**3/3 + 44*i**2. Let a(q) be the first derivative of y(q). Factor a(x).
-x*(x - 1)**3
Suppose -4 = -m + j, -2*j - 1 = m - 4*j. Suppose -m*i + 12 = -3*i. Solve 0 - 3/2*l + 1/2*l**i = 0 for l.
0, 3
Let l(r) be the third derivative of 3*r**7/350 - r**6/50 + r**5/75 + 22*r**2. Factor l(j).
j**2*(3*j - 2)**2/5
Let z(w) be the first derivative of w**3/15 - 7*w**2/10 + 12*w/5 - 13. Factor z(u).
(u - 4)*(u - 3)/5
Let a(m) = m + 1 + 9*m + m**3 + 18*m**2 + 8*m. Let h(t) = -834*t - 45*t**2 + 0 + 789*t - 3*t**3 - 3. Let c(i) = -12*a(i) - 5*h(i). Factor c(g).
3*(g + 1)**3
Let h(v) = -4*v**3 + 168*v**2 + 4*v + 8. Let x(d) = 12*d**3 - 506*d**2 - 11*d - 22. Let q(a) = 11*h(a) + 4*x(a). Factor q(u).
4*u