9/2*r.
-(r - 7)*(r - 2)/2
Suppose -5*l = 0, 0 = -0*i + 2*i + 2*l - 6. Let f(n) be the third derivative of 1/30*n**5 + 0 + 0*n - 1/4*n**4 + 2/3*n**i + 5*n**2. Suppose f(o) = 0. What is o?
1, 2
Suppose -4*v - 3*y = -24, -4*y - 12 = 5*v - 43. Suppose -a - 2 = v, 2*a + 4 = -3*q. Factor -10*s**q + 7*s**2 + 32*s - 14*s**3 + 8 + 13*s**2.
-2*(s - 2)*(s + 1)*(7*s + 2)
Let b = 2897 + -2894. Let x = 2 - -7. What is d in -x*d - b*d**2 - 1/3*d**3 - 9 = 0?
-3
Factor -5/3*c**3 - 17/9*c**2 - 1/3*c**4 - 2/3*c + 1/9*c**5 + 0.
c*(c - 6)*(c + 1)**3/9
Suppose -1 - 3 = -m. Let d be m/6*(-6 + 15). Determine n, given that -2 - 2*n**3 + 12 - d*n**2 - 2 + 0*n**3 = 0.
-2, 1
Let t(a) = 21*a**3 - 147*a**2 - 150*a - 9. Let k(w) = 5*w**3 - 37*w**2 - 38*w - 2. Let l(z) = 9*k(z) - 2*t(z). Factor l(j).
3*j*(j - 14)*(j + 1)
Find o, given that -4*o**2 - 99*o - 1021 - 579 - 61*o = 0.
-20
Suppose 0 = 2*r + 3*z - 4 - 9, 3*r + 5*z = 21. Let w(b) = 12 + 0*b**r - 13 + b**2. Let h(o) = 8*o**2 - o - 9. Let m(k) = 3*h(k) - 21*w(k). Factor m(g).
3*(g - 2)*(g + 1)
Let m(c) be the second derivative of -c**5/12 - 10*c**4/3 - 160*c**3/3 + 15*c**2/2 - 19*c. Let f(s) be the first derivative of m(s). Factor f(n).
-5*(n + 8)**2
Let i(k) = 4*k**3 + 61*k**2 + 92*k + 5. Let x(d) = 10*d**3 + 156*d**2 + 230*d + 12. Let n(g) = 12*i(g) - 5*x(g). Find t such that n(t) = 0.
-23, -1, 0
Suppose -2*i - 3 = f + 1, 3*f + 3*i = 0. Factor -35*j - j**5 - 4*j**5 - 20 + 10*j**2 - 216*j**4 + 40*j**3 + 434*j**4 - 208*j**f.
-5*(j - 4)*(j - 1)*(j + 1)**3
Let i(s) be the second derivative of 0*s**3 + 0 + 0*s**2 - 7/5*s**5 - 2/15*s**6 + 8/3*s**4 - 33*s. Determine j, given that i(j) = 0.
-8, 0, 1
Suppose 3560*n + 18 = 3569*n. Determine z, given that 3/2*z - 1 - 3/4*z**n + 1/8*z**3 = 0.
2
Suppose -3*r + 4*p = 2*r - 41, -2*p + 2 = 2*r. Factor -5*f + 7*f**3 - 5*f**2 - 17*f**3 + 7*f**3 + r + 8*f**3.
5*(f - 1)**2*(f + 1)
Let c(h) be the third derivative of h**8/2184 - h**7/273 + h**6/195 + 8*h**5/195 - 8*h**4/39 + 16*h**3/39 - 2*h**2 - 214*h. Suppose c(x) = 0. What is x?
-2, 1, 2
Solve -1/5*b**2 - 17/5 - 18/5*b = 0.
-17, -1
Let m(p) be the second derivative of 5*p**4/84 - 2*p**3/21 + 38*p - 2. Let m(x) = 0. Calculate x.
0, 4/5
Suppose -3*s + 10 - 4 = 0. Let b = -13 + 15. Factor 13*p - 5*p + b*p**s + 8 + 0*p**2.
2*(p + 2)**2
Factor 4 - 1/4*o**3 - 7/4*o**2 + 5/2*o.
-(o - 2)*(o + 1)*(o + 8)/4
Suppose 4*y = w + 80, 40 = -6*y + 8*y + 3*w. Factor 13*t - y - 20 + 71*t - 33*t**2 + 4.
-3*(t - 2)*(11*t - 6)
Let i(r) be the third derivative of r**9/272160 + r**8/90720 - 9*r**5/20 - 5*r**2. Let f(b) be the third derivative of i(b). Factor f(m).
2*m**2*(m + 1)/9
Let t(i) = -i**3 + 2*i. Let h(f) = 8*f**3 - 17*f**2 + 62*f - 84. Let d(n) = 2*h(n) + 18*t(n). Factor d(w).
-2*(w - 2)**2*(w + 21)
Let p(i) = 141*i**4 - 399*i**3 - 573*i**2 + 1335*i - 594. Let r(o) = -71*o**4 + 199*o**3 + 286*o**2 - 668*o + 296. Let b(w) = -4*p(w) - 9*r(w). Factor b(h).
3*(h - 3)*(h + 2)*(5*h - 4)**2
Let a(x) = 5*x**3 + 45*x**2 + 41*x + 8. Let l be a(-8). Factor l - 1/3*i**2 + i.
-i*(i - 3)/3
Let w be (48/(-32))/((3/10)/(-1)). Suppose -6*v - w + 29 = 0. Factor 1/4*b + 0 - 3/4*b**3 - 1/2*b**5 + 1/4*b**2 - 5/4*b**v.
-b*(b + 1)**3*(2*b - 1)/4
Let m(h) be the second derivative of 0*h**2 + 1/10*h**3 + 0*h**4 - 3/100*h**5 + 13*h + 0. Solve m(c) = 0 for c.
-1, 0, 1
Suppose 63*m - 522 = 69*m. Let b = -84 - m. Determine d, given that 1/4*d**b + 1/4*d**2 - d - 1 = 0.
-2, -1, 2
Let k be 10/(-4)*12/(-10). Let d(w) be the second derivative of -1/6*w**k - 1/24*w**4 + 0 - 4*w - 1/4*w**2. Find m, given that d(m) = 0.
-1
Let j(z) be the third derivative of z**7/1050 - z**6/120 - 7*z**5/300 + z**4/24 + z**3/5 - 10*z**2 - 4. Factor j(s).
(s - 6)*(s - 1)*(s + 1)**2/5
Suppose 184/11 + 2/11*c**2 + 186/11*c = 0. Calculate c.
-92, -1
Factor -2255/3*a**2 + 10/3*a**3 + 63845/3 + 126560/3*a.
5*(a - 113)**2*(2*a + 1)/3
Let r(o) = -2*o + 11. Let n be r(4). Solve -n*z**4 - 36*z + 36*z + 12*z**3 - 9*z**2 = 0 for z.
0, 1, 3
Let o(n) be the third derivative of n**5/240 + 73*n**4/96 + 733*n**2. Let o(b) = 0. Calculate b.
-73, 0
Suppose -5*q + 5 = -4*q. Suppose 6*c - 3*c - 2*v = 14, q*v = -c - 18. Factor 2*x**5 - 2*x**3 + 1 + 8*x**4 - 6*x**4 - c*x**2 - 1.
2*x**2*(x - 1)*(x + 1)**2
Find x, given that 9*x + 0 + 1/2*x**3 - 19/2*x**2 = 0.
0, 1, 18
Let d(c) be the first derivative of c**7/105 - c**6/15 + c**5/10 - 39*c**2/2 + 33. Let a(t) be the second derivative of d(t). Determine n, given that a(n) = 0.
0, 1, 3
Suppose -6 = 7136*q - 7138*q + 4. Factor q*h - 25 - 1/4*h**2.
-(h - 10)**2/4
Let h be (-4 - 114/3) + 2. Let x be h/6*(-9)/5. Factor 3*z**4 + 11*z**4 + z**4 + 4*z - 4 - 46*z**3 + x*z**3 + 19*z**2.
(z - 1)**2*(3*z - 2)*(5*z + 2)
Let r(s) = -9*s**3 + 48*s**2 - 132*s + 78. Let a(y) = -16*y**3 + 96*y**2 - 261*y + 156. Let t(l) = -3*a(l) + 5*r(l). Factor t(n).
3*(n - 13)*(n - 2)*(n - 1)
Let w be 0/(-1) + 6/72. Let u(t) be the second derivative of 1/6*t**3 + w*t**4 + 0 - t**2 + t. Factor u(y).
(y - 1)*(y + 2)
Let u(z) be the third derivative of z**8/168 + 2*z**7/35 + 11*z**6/60 + z**5/15 - z**4 - 8*z**3/3 - 162*z**2. Suppose u(r) = 0. What is r?
-2, -1, 1
Let t(x) be the second derivative of -2*x - 22 - 1/84*x**7 + 1/30*x**6 + 9/20*x**5 + 3/2*x**2 + 4/3*x**4 + 23/12*x**3. Factor t(h).
-(h - 6)*(h + 1)**4/2
Suppose -96*g + 95*g = 4*o - 21, 0 = -o + 5*g - 21. Let 0 - 34/11*s**3 + 2/11*s**2 + 4/11*s + 28/11*s**o = 0. What is s?
-2/7, 0, 1/2, 1
Let q(y) be the first derivative of 2*y**3/9 - 4*y**2 + 164. Find a such that q(a) = 0.
0, 12
Let w(d) be the second derivative of d**8/33600 - d**7/12600 - d**6/720 - d**5/200 + 5*d**4/2 + 2*d. Let g(b) be the third derivative of w(b). Factor g(i).
(i - 3)*(i + 1)**2/5
Let i(o) be the first derivative of 8*o**5/5 - 11*o**4 + 20*o**3/3 - 122. Factor i(r).
4*r**2*(r - 5)*(2*r - 1)
Suppose 4*w + 3*b + 0 = -4, 0 = 3*b + 12. Let m be (w + 56/(-36))/((-10)/(-6)). Factor 0*r**4 - m*r**3 + 0*r**2 + 2/15*r + 0 + 2/15*r**5.
2*r*(r - 1)**2*(r + 1)**2/15
Let i(f) = -9 + 0*f + f**2 + f**4 + 10 + f. Let x(o) = -3*o - o**5 - 54*o**4 + 2*o**3 - 6*o**2 + 54*o**4. Let g(m) = -2*i(m) - x(m). Find p such that g(p) = 0.
-1, 1, 2
Let 172*u**2 + u**3 - 28*u**2 + 3*u**3 = 0. What is u?
-36, 0
Let g(u) be the second derivative of 0 + 2/11*u**2 - 1/66*u**4 - 1/33*u**3 + 8*u. Let g(w) = 0. What is w?
-2, 1
Find j such that -8/7*j - 3/7*j**2 + 1/7*j**4 + 2/7*j**3 - 4/7 = 0.
-2, -1, 2
Let l(u) = 184*u - 14. Let x be l(-1). Let v = -198 - x. Let -4/11*f - 6/11*f**2 + v = 0. Calculate f.
-2/3, 0
Let d = 1 - -1. Suppose -9*c = -4*c - 10. Factor p**c - 5*p + 1 + p**d + p + p.
(p - 1)*(2*p - 1)
Let x(d) be the second derivative of -d**4/12 + 20*d**3/3 + 156*d - 2. Factor x(t).
-t*(t - 40)
Suppose -576*f + 12*f**3 + 107*f**2 + 62*f**2 - 28*f**2 + 135 = 0. What is f?
-15, 1/4, 3
Let s(j) = j**3 - 6*j**2 - 4*j + 4. Let t be s(4). Let h = t - -221/5. Factor -7/5*m + 3/5 + m**2 - h*m**3.
-(m - 3)*(m - 1)**2/5
Let m(b) be the third derivative of 1/2*b**3 + 0 + 1/20*b**5 + 0*b - 34*b**2 - 5/16*b**4. Factor m(j).
3*(j - 2)*(2*j - 1)/2
Let u(q) be the second derivative of 1/30*q**6 - 24*q - 1/6*q**2 + 1/126*q**7 + 0 - 1/6*q**3 + 1/30*q**5 - 1/18*q**4. Find o, given that u(o) = 0.
-1, 1
Let r(o) = -o**3 - 3*o**2 + 4*o + 1. Let n be r(-6). Let s = n + -46. What is v in s*v**2 + 6*v + v**5 + 20*v**5 + 69*v**4 + 23*v**3 + 58*v**3 = 0?
-1, -2/7, 0
Let u(p) = -7*p**4 - 55*p**3 + 58*p**2 - 61*p + 13. Let b(o) = -3*o**4 - 27*o**3 + 30*o**2 - 30*o + 6. Let i(n) = -13*b(n) + 6*u(n). Factor i(h).
-3*h*(h - 4)*(h - 2)*(h - 1)
Let y be (-23)/(-40) - 1/2. Let u(w) be the second derivative of 1/4*w**4 - 2*w + 0 + y*w**5 + 0*w**2 - 1/20*w**6 + 0*w**3. Factor u(h).
-3*h**2*(h - 2)*(h + 1)/2
Determine w, given that -24*w**2 + 4/11*w**3 + 4*w**4 + 310/11*w + 6/11*w**5 - 100/11 = 0.
-5, 2/3, 1
Suppose 3*g = -131*u + 126*u + 7, -4*u - 4*g = -4. Factor -64/5*i - 48/5 + 12/5*i**u.
4*(i - 6)*(3*i + 2)/5
Factor -12*y - 1/5*y**2 - 180.
-(y + 30)**2/5
Let z(i) = 2*i + 14. Let y be z(-7). Let b be (-1)/(3/(-9) + y). Solve 0 - 1/3*o**2 - 1/3*o**b + 0*o = 0.
-1, 0
Factor -23*r**4 + 23*r**4 + 27*r**3 + 9*r**4 - 3*r**5 + 15*r**2.
-3*r**2*(r - 5)*(r + 1)**2
Suppose -s + 6*s = 5*r + 15, 0 = -5*r + 2*s. Let p be 4*(-4)/24*-3*r. Determine