 a**8/2240 - a**7/840 + a**6/240 + 7*a**4/4 - 13*a. Let b(f) be the third derivative of r(f). Factor b(w).
3*w*(w - 1)**2*(w + 1)
Let v be (-3)/(-9)*3*33/(-3). Let o(b) = -b**2 - 13*b - 22. Let x be o(v). Factor -1/2*f**2 + 0*f - 3/2*f**3 + x.
-f**2*(3*f + 1)/2
Let g(m) be the second derivative of 3*m**5/160 - 3*m**4/8 + 23*m**3/16 + 27*m**2/4 + 802*m. Factor g(o).
3*(o - 9)*(o - 4)*(o + 1)/8
Factor 25/4*m**4 + 65/4*m**3 - 81/4*m - 9/4*m**2 + 0.
m*(m - 1)*(5*m + 9)**2/4
Let o = -48 - 26. Let z = 76 + o. What is u in -3/2*u + 0 - 3/4*u**5 - 3/4*u**z + 3/4*u**4 + 9/4*u**3 = 0?
-1, 0, 1, 2
Let 0 + 2/3*m + 6*m**2 = 0. Calculate m.
-1/9, 0
Factor -2/9*f**3 + 52/9*f - 14/9*f**2 + 16.
-2*(f - 4)*(f + 2)*(f + 9)/9
Let d = -54 + 57. Factor 12*s**3 - 6*s**3 + 12*s - 12*s**2 - d*s**3.
3*s*(s - 2)**2
Find c such that -6/7*c**3 + 18/7*c**2 + 3/7*c - 9/7 + 3/7*c**5 - 9/7*c**4 = 0.
-1, 1, 3
Suppose 0 + 0*g + 2*g**3 + 2/3*g**5 + 2/3*g**2 + 2*g**4 = 0. What is g?
-1, 0
Let g(s) be the first derivative of -s**3/9 - 29*s**2/6 + 10*s - 252. Let g(q) = 0. Calculate q.
-30, 1
Suppose 5*o = -a + 25, -2*o - 110*a = -113*a + 7. Let m(y) be the second derivative of 2*y + 0 + 1/42*y**o + 1/7*y**3 + 0*y**2. Determine g so that m(g) = 0.
-3, 0
Factor -9*j - 18*j**3 - 24*j**2 + 20*j**5 - 6*j**4 + 15*j**4 - 17*j**5 - 9*j**4.
3*j*(j - 3)*(j + 1)**3
Let l(g) be the second derivative of -g**4/6 + 14*g**3/3 - 33*g**2 + 48*g. Determine z so that l(z) = 0.
3, 11
Let d(n) be the second derivative of 1/4*n**4 + 0 + 8*n + 0*n**3 - 3/2*n**2. Solve d(g) = 0.
-1, 1
Let n(q) be the first derivative of -q**6/10 - 51*q**5/25 - 69*q**4/4 - 387*q**3/5 - 972*q**2/5 - 1296*q/5 + 150. Factor n(j).
-3*(j + 3)**3*(j + 4)**2/5
Let w(m) be the third derivative of m**6/60 - 7*m**5/30 + 11*m**4/12 - 5*m**3/3 - 99*m**2. Factor w(x).
2*(x - 5)*(x - 1)**2
Suppose -51*v**2 + 4*v**3 - 4*v**4 + 14*v**3 - 6*v**3 + 351*v**2 - 148*v**2 + 896 - 768*v = 0. Calculate v.
-7, 2, 4
Let f(b) be the third derivative of -b**5/80 - 7*b**4/32 + 770*b**2. Let f(d) = 0. Calculate d.
-7, 0
Solve 2*o - 7*o**4 + 137*o**3 - o**5 - 71*o**3 - 2*o - 8*o - 84*o**3 - 20*o**2 = 0.
-2, -1, 0
Let z(w) = w**2 - 2*w + 2. Let b be z(0). Let d be b/(-7) + (-16)/(-7). Factor -n**2 - n + 3*n**d + n**3 + 2*n.
n*(n + 1)**2
Let b(a) be the first derivative of -a**4/42 - 2*a**3/21 - 11*a + 3. Let l(h) be the first derivative of b(h). Solve l(r) = 0 for r.
-2, 0
Let i be ((-17)/85)/(((-16)/(-18))/(-8)). Suppose 3/5*s**3 + 21/5*s + i + 3*s**2 = 0. What is s?
-3, -1
Let s(t) = 8*t**3 + 3*t**2 + 3*t + 8. Let g(n) = 7*n**3 + 3*n**2 + 3*n + 7. Let a(x) = 7*g(x) - 6*s(x). Factor a(b).
(b + 1)**3
Let n(u) be the second derivative of u**8/50400 + u**7/4725 + u**6/1350 - 7*u**4/12 - 12*u. Let m(c) be the third derivative of n(c). Find i such that m(i) = 0.
-2, 0
Let s(y) be the first derivative of -4 - 5/3*y**3 + y**5 + 0*y - 5/4*y**4 + 5/2*y**2. Factor s(m).
5*m*(m - 1)**2*(m + 1)
Factor 63*y**2 - 20*y - 52 - 38*y**2 - 66 - 22.
5*(y + 2)*(5*y - 14)
Solve 38/3*k**4 + 460/3*k**3 + 128/3 - 14/3*k**5 + 968/3*k**2 + 688/3*k = 0.
-2, -1, -2/7, 8
Let k = -133 - -141. Suppose 0 = 4*m - u - 10, 0 = 3*u - 14 + k. What is s in -2*s**m + 8/3*s + 0 + 8/3*s**2 = 0?
-2/3, 0, 2
Let g(o) be the second derivative of -o**5/90 + o**4/6 - 8*o**3/9 + 9*o**2/2 + 17*o. Let c(w) be the first derivative of g(w). Factor c(x).
-2*(x - 4)*(x - 2)/3
Let l(h) be the first derivative of -h**7/63 + 2*h**6/45 - h**4/9 + h**3/9 - 14*h + 13. Let c(j) be the first derivative of l(j). Suppose c(x) = 0. Calculate x.
-1, 0, 1
Let l(f) be the second derivative of -11*f**4/60 - 6*f**3/5 - 9*f**2/10 + 295*f. Factor l(b).
-(b + 3)*(11*b + 3)/5
Let w(z) = 375*z + 4125. Let k be w(-11). Factor 49/6*y + 7/3*y**2 + k + 1/6*y**3.
y*(y + 7)**2/6
Let m(l) be the third derivative of -l**5/60 + l**4/6 + 5*l**3/6 - 4*l**2 + 4. Factor m(x).
-(x - 5)*(x + 1)
Let b be (-124)/(-24) - (2 + 3). Let g(j) be the third derivative of 2*j**2 - 1/60*j**5 - b*j**3 + 0*j + 0 + 1/12*j**4. Determine a so that g(a) = 0.
1
Factor 94/5*q - 2/5*q**2 + 60.
-2*(q - 50)*(q + 3)/5
Let g = -749/72 - -85/8. Suppose -2*b = -4*j + 4, -270 = 2*j - 272. Factor g*v**3 + 0*v**2 - 2/9*v + b.
2*v*(v - 1)*(v + 1)/9
Factor -7 - 1/3*d**2 - 22/3*d.
-(d + 1)*(d + 21)/3
Let q(b) = -7*b**3 + 9*b**2 - 60*b + 102. Let w(x) = -15*x**3 + 17*x**2 - 118*x + 203. Let t(g) = 13*q(g) - 6*w(g). Find n, given that t(n) = 0.
3, 6
Let q(y) be the first derivative of -y**5/110 - y**4/66 - 16*y + 17. Let h(d) be the first derivative of q(d). Factor h(m).
-2*m**2*(m + 1)/11
Let n(k) be the third derivative of k**7/5040 - k**6/2160 + 11*k**3/6 + 6*k**2. Let s(x) be the first derivative of n(x). Let s(l) = 0. What is l?
0, 1
Let h(n) = 3*n**3 - 6*n**2 + 12*n - 9. Let v(x) = -x**3 + 2*x**2 - 3*x + 2. Let r(o) = -2*h(o) - 9*v(o). Factor r(a).
3*a*(a - 1)**2
Let m = -6331 + 6335. Determine u, given that -7/9*u**5 + 23/9*u**m + 0*u + 4/9*u**2 - 20/9*u**3 + 0 = 0.
0, 2/7, 1, 2
Let s(b) be the second derivative of b**7/63 + 7*b**6/135 - b**5/90 - 7*b**4/54 - 2*b**3/27 + 6*b + 12. Solve s(w) = 0 for w.
-2, -1, -1/3, 0, 1
Factor 1/2 + c**2 + 5/4*c + 1/4*c**3.
(c + 1)**2*(c + 2)/4
Suppose -3*c + 5*p + 32 = 0, -6*c - 2*p + 13 = -3. Suppose 12*a**4 + c*a**3 - 20/3*a**2 + 4/3*a + 0 = 0. What is a?
-1, 0, 1/3
Let u(q) be the first derivative of -q**7/1050 + 17*q**5/300 - 3*q**4/10 + 2*q**3/3 - q**2 + 49. Let k(s) be the second derivative of u(s). Solve k(o) = 0.
-5, 1, 2
Let m be (-6 - -2) + 10 + 2 + -4. Let 0*x**5 - 6*x**2 - 21*x**4 + 9*x**m - 21*x**3 + 12*x**5 = 0. What is x?
-1/2, 0, 2
Let o(v) be the first derivative of -v**5/80 + v**3/24 - v - 3. Let g(x) be the first derivative of o(x). Suppose g(n) = 0. Calculate n.
-1, 0, 1
Let s(y) be the second derivative of -y**6/15 + y**5/2 + y**4 - 46*y. Suppose s(f) = 0. What is f?
-1, 0, 6
Suppose 5*b = -c - 2*c + 45, -2*b = c - 17. Find f such that 5*f**4 - 20*f**2 + b*f**5 + 3*f**3 + 40*f + 0*f**4 - 33*f**3 - f**5 = 0.
-2, 0, 1, 2
Let p(h) = h - 2. Let o be p(0). Let y be 0/(o + 3 + -2 + -1). Factor 0 + 2*k**4 + y*k + 4/9*k**2 - 22/9*k**3.
2*k**2*(k - 1)*(9*k - 2)/9
Let l(r) = 13*r**5 + 8*r**4 + 5*r**3 - 5*r**2 - 5. Let y(d) = 6*d**5 + 4*d**4 + 2*d**3 - 2*d**2 - 2. Let u = -24 + 22. Let v(b) = u*l(b) + 5*y(b). Factor v(h).
4*h**4*(h + 1)
Let n = 7415 - 7411. Determine x, given that 0 - 1/3*x**n + 1/3*x - x**2 + x**3 = 0.
0, 1
Let k(l) = 11*l**4 + 42*l**3 + 67*l**2 - 19*l - 96. Let d(i) = 5*i**4 + 21*i**3 + 34*i**2 - 10*i - 48. Let r(w) = 5*d(w) - 2*k(w). Factor r(n).
3*(n - 1)*(n + 2)**2*(n + 4)
Let f = 29 + -6. Suppose -f = -4*c + 2*r + 169, 0 = -3*r. Determine u so that 16 + 16*u**3 + 23 - 60*u**2 - 23 + c*u = 0.
-1/4, 2
Let h be ((-6)/45)/((-6)/72). Find f, given that -124/5*f - 1809/5*f**3 - 1944/5*f**4 - h - 142*f**2 - 729/5*f**5 = 0.
-1, -2/9
Let m = -4944 - -24842/5. Let b = m + -24. Factor -1/5*g**2 - b*g + 0.
-g*(g + 2)/5
Let s(b) = 33*b**3 - 2*b**2 - 38*b - 13. Let h(d) = d**3 - 2*d**2 - 2*d - 1. Let w(p) = 5*h(p) - s(p). Factor w(m).
-4*(m - 1)*(m + 1)*(7*m + 2)
Let u(b) be the second derivative of 16*b**6/135 + 28*b**5/45 + 19*b**4/18 + 19*b**3/27 + 2*b**2/9 - 35*b. Suppose u(f) = 0. What is f?
-2, -1, -1/4
Let a(h) = h**2 - 10*h + 7. Let s be a(10). Let y(o) = o**2 - 6*o - 7. Let n be y(s). Factor n - 2/3*l**2 + 0*l.
-2*l**2/3
Let m = 13344/55 + -1174/5. Find n such that 14/11*n**4 - 48/11*n - 60/11*n**3 + 8/11 + m*n**2 = 0.
2/7, 1, 2
Let k(d) be the third derivative of d**7/210 - d**6/15 + d**5/12 + 19*d**4/12 + 4*d**3 + 459*d**2. Factor k(m).
(m - 6)*(m - 4)*(m + 1)**2
Let b(y) be the first derivative of 2*y**6/15 - 8*y**5/25 - y**4/5 + 8*y**3/15 + 85. Suppose b(p) = 0. Calculate p.
-1, 0, 1, 2
Let c(n) be the second derivative of 0 + 0*n**2 + 2/15*n**5 - 5/18*n**4 + 18*n + 4/27*n**3 + 4/135*n**6. Solve c(v) = 0.
-4, 0, 1/2
Let s(l) be the first derivative of l**5/90 + l**4/18 - 4*l**2/9 - 14*l - 16. Let t(c) be the first derivative of s(c). Factor t(g).
2*(g - 1)*(g + 2)**2/9
Let r(x) be the third derivative of x**6/90 + x**5/30 - 5*x**3/6 + 7*x**2. Let l(u) be the first derivative of r(u). Factor l(h).
4*h*(h + 1)
Let n(l) be the third derivative of 0*l - 1/4*l**4 + 1/105*l**7 - l**2 + 1/20*l**6 + 1/30*