*2*(3*t + 1)/5
Let x(i) be the third derivative of i**9/5040 + i**8/2016 - i**7/210 + i**6/90 + 7*i**5/30 + 18*i**2. Let w(o) be the third derivative of x(o). Factor w(u).
2*(u + 2)*(2*u - 1)*(3*u - 2)
Let t(h) be the first derivative of 3*h**5/10 + 45*h**4/8 + 23*h**3 - 72*h**2 - 192*h + 192. Factor t(y).
3*(y - 2)*(y + 1)*(y + 8)**2/2
Let k be (-1*(-1 + 6))/(-1). Let i be (-4)/(-2)*30/20. Determine u so that -k*u**2 + 3*u**i + 3*u - 3*u - u**2 + 45*u**4 = 0.
-2/5, 0, 1/3
What is a in 0*a**2 + 0*a - 4/9*a**3 + 0 = 0?
0
Let j(a) = 26*a**3 + a**2 + a + 1. Let w be j(-1). Let h = w - -28. Let -h + 50*l + 14 - 5*l**2 - 68 - 68 = 0. What is l?
5
Let c(w) be the second derivative of w**6/60 + w**5/40 - w**4/3 - w**3 - 67*w + 1. Factor c(b).
b*(b - 3)*(b + 2)**2/2
Suppose 0 = 12*r - 5*r - 14. Find w such that -53 - 12*w - 2*w**r - 109 - 9*w - 15*w = 0.
-9
Let v(h) be the second derivative of -5/2*h**2 + 0 + 11*h - 5/12*h**4 + 5/3*h**3. Let v(c) = 0. What is c?
1
Factor 27*j**2 + 38*j**3 - 56*j + 24*j**3 - 4*j**5 - 88*j - 18*j**3 - 8*j**4 + 21*j**2.
-4*j*(j - 2)**2*(j + 3)**2
Factor -16/13*x**3 + 2/13*x**5 - 224/13*x + 128/13*x**2 + 128/13 - 8/13*x**4.
2*(x - 2)**4*(x + 4)/13
What is i in 12*i**3 - 9*i - 3 + 9*i**2 + 18*i**2 - 27*i**2 = 0?
-1/2, 1
Let t(y) = -3*y + 6. Let p be t(1). Let k(s) be the first derivative of 2/11*s**2 - 6 + 0*s + 1/22*s**4 + 2/11*s**p. Solve k(m) = 0.
-2, -1, 0
Let w be (35/20)/1 - 1/(-4). Factor 2*z**2 + 24 + 5*z**2 + 7*z**w + 23*z - 85*z.
2*(z - 4)*(7*z - 3)
Let j(x) be the third derivative of -x**6/720 + 9*x**5/20 - 243*x**4/4 + 4374*x**3 - 2*x**2 - x. Determine d, given that j(d) = 0.
54
Let p(o) be the second derivative of 0 + 0*o**3 - 8*o - 4*o**2 + 1/8*o**4 - 1/20*o**5. Let l(y) be the first derivative of p(y). Factor l(j).
-3*j*(j - 1)
Let i(j) be the second derivative of j**5/50 - j**4/30 - 4*j**3/3 - 273*j. Find m, given that i(m) = 0.
-4, 0, 5
Let i(c) = -9*c**4 - 9*c**3 + 18*c**2 + 30*c - 6. Let y(r) = -19*r**4 - 18*r**3 + 37*r**2 + 59*r - 13. Let j(d) = 13*i(d) - 6*y(d). Factor j(g).
-3*g*(g - 2)*(g + 2)*(g + 3)
Let r(m) be the first derivative of 8*m + 1/30*m**6 + 0*m**2 + 0*m**5 + 1/42*m**7 + 0*m**4 + 0*m**3 - 9. Let d(l) be the first derivative of r(l). Factor d(p).
p**4*(p + 1)
Let q(m) = 10 + 5*m - 4*m - 7 + 3. Let t be q(-4). Factor 8*w + 3*w - 4*w + 16*w**t + 6*w**3 + w.
2*w*(w + 2)*(3*w + 2)
Let h(l) be the third derivative of -l**7/980 + 13*l**6/1260 - l**5/210 - 2*l**4/21 + 5*l**3/6 - 17*l**2. Let v(s) be the first derivative of h(s). Factor v(g).
-2*(g - 4)*(g - 1)*(3*g + 2)/7
Let t(g) be the third derivative of -g**5/45 - 13*g**4/18 - 12*g**2 - 12*g. Factor t(k).
-4*k*(k + 13)/3
Suppose 7*b = 3*b + 16. Solve -5*t**5 + t**2 - 5*t**3 + 556*t**4 + 2*t**5 - 549*t**b = 0 for t.
0, 1/3, 1
Let t(k) = -4*k**2 + 22*k. Let u(h) = -9*h**2 + 44*h. Let x(v) = -5*t(v) + 2*u(v). Determine b, given that x(b) = 0.
0, 11
Let 39/4*b**2 + 15/4*b + 0 = 0. Calculate b.
-5/13, 0
Let a(t) = -t**3 + 10*t**2 - 4*t + 6. Let o be a(9). Let s = o - 34. Determine c so that 12*c**2 - 21*c - 6*c**3 + 6 - 18*c**4 + 10*c**3 + s*c**3 = 0.
-1, 1/2, 2/3, 1
Let y(v) be the first derivative of 3*v**5/5 + 3*v**4 - 6*v**3 - 6*v**2 + 15*v - 89. Determine d so that y(d) = 0.
-5, -1, 1
Suppose -6*p + 10 = -20. Suppose -p*a = -5*n + 20, 5*n - a - 11 = -5*a. Let 2/15*u**4 + 0 + 2/15*u**n + 0*u - 4/15*u**2 = 0. What is u?
-2, 0, 1
Let j be (0 + 0 - 1)*0/(-38). Let k(l) be the third derivative of j + l**3 + 0*l - 1/10*l**5 + 1/60*l**6 + l**2 - 1/12*l**4. Factor k(t).
2*(t - 3)*(t - 1)*(t + 1)
Let v be (55/825)/(((-9)/(-10))/9). Factor 0*x + v*x**2 - 4*x**3 - 25/6*x**5 + 15/2*x**4 + 0.
-x**2*(x - 1)*(5*x - 2)**2/6
Let s(h) be the first derivative of -10 + 2/7*h**3 + 1/14*h**4 + 0*h**2 - 8/7*h. Factor s(y).
2*(y - 1)*(y + 2)**2/7
Let v(h) be the first derivative of -3/8*h**4 + 27 + 3/4*h**2 + 0*h + 0*h**3. Solve v(o) = 0 for o.
-1, 0, 1
Factor 14 - 12*i**3 - 35*i + 17*i**3 + 12*i**2 + 4 - 2*i**2 + 2.
5*(i - 1)**2*(i + 4)
Let i = 2399/70 - 3/140. Let d = -34 + i. Suppose -1/4*t**2 + 1/4*t - d*t**3 + 1/4 = 0. What is t?
-1, 1
Let m(n) = 11*n**3 + 19*n**2 + 4*n - 19. Let t(c) = 16*c**3 + 29*c**2 + 5*c - 29. Let l(q) = 7*m(q) - 5*t(q). Factor l(o).
-3*(o - 1)*(o + 1)*(o + 4)
Let f(g) be the second derivative of g**5/100 + g**4/15 - g**3/10 - 9*g**2/5 + 3*g. Let f(x) = 0. What is x?
-3, 2
Factor -36*u**2 + 32 + 7 - 6*u**2 + 36*u**3 + 3*u**4 - 27*u - 9*u.
3*(u - 1)**2*(u + 1)*(u + 13)
Suppose 4 + 6 = -m. Let l(d) = 2*d + 8 + 0*d - 845*d**2 + 837*d**2. Let o(p) = p**2 - p. Let n(g) = m*o(g) - l(g). Find h, given that n(h) = 0.
2
Let o(j) = -20*j - 82. Let r be o(-5). Let t be (-3)/(r/60)*1/(-5). Find u such that -4/9*u + 2/9*u**t + 2/9 = 0.
1
Factor -121/2 + 11/2*w - 1/8*w**2.
-(w - 22)**2/8
Let g(m) be the second derivative of -m**6/30 - 3*m**5/20 + 2*m**3/3 + m - 359. Factor g(r).
-r*(r - 1)*(r + 2)**2
Let q(h) be the first derivative of 4*h**3/3 - 6*h**2 - 16*h - 16. Find l, given that q(l) = 0.
-1, 4
Let f(i) = 2*i**5 - 18*i**4 + 40*i**3 + 80*i**2 - 36*i - 68. Let o(l) = l**5 + l**4 - 2. Let d(x) = f(x) - 6*o(x). Determine r so that d(r) = 0.
-7, -1, 1, 2
Let l(f) be the first derivative of -f**6/24 + 9*f**5/4 - 85*f**4/8 + 125*f**3/6 - 165*f**2/8 + 41*f/4 + 80. Factor l(m).
-(m - 41)*(m - 1)**4/4
Let i(d) be the second derivative of d**6/540 - 2*d**5/135 + d**4/27 + 25*d**2/2 + 13*d. Let v(s) be the first derivative of i(s). Let v(z) = 0. Calculate z.
0, 2
Let y be (-1)/(15/33)*-5. Let h = y - 8. Solve h*s + 3 + 3*s**5 - 5*s**3 - s**2 - 2*s**2 + 3*s**4 - s**3 - 3*s**2 = 0 for s.
-1, 1
Suppose 0 = -125*w + 47*w - 108*w + 372. Let 32/21 - 16/21*q + 2/21*q**w = 0. Calculate q.
4
Let g(w) be the third derivative of 0 + 1/6*w**3 - 9*w**2 + 0*w**4 - 1/70*w**7 - 1/15*w**6 - 1/10*w**5 + 0*w. Factor g(d).
-(d + 1)**3*(3*d - 1)
Suppose -h + 4 = y, -208 = 3*h - 5*y - 188. Factor 0*i + 1/6*i**4 + 5/6*i**3 + h + 2/3*i**2.
i**2*(i + 1)*(i + 4)/6
Let z = -97/6 + 293/18. Let u(a) be the third derivative of z*a**4 + 0*a + 6*a**2 + 0 - 1/6*a**3 - 1/30*a**5 + 0*a**6 + 1/630*a**7. Factor u(t).
(t - 1)**3*(t + 3)/3
Find c, given that -4*c**3 - 4*c**2 + 2 - 3*c + 11 + 7*c - 9 = 0.
-1, 1
Let g(y) be the third derivative of y**8/15120 + y**7/2520 + y**6/1620 - 29*y**3/6 + 27*y**2. Let t(s) be the first derivative of g(s). Let t(v) = 0. What is v?
-2, -1, 0
Factor l**2 + 3*l + 4*l**2 + l + 5 + 6*l.
5*(l + 1)**2
Let s(h) be the third derivative of 0*h + 2/3*h**3 + 2/3*h**4 - 7/90*h**6 + 0 - 2/5*h**5 + 7*h**2. Let t(k) be the first derivative of s(k). Factor t(v).
-4*(v + 2)*(7*v - 2)
Let c(q) be the second derivative of 1/80*q**5 + 0 + 1/4*q**2 - 1/8*q**3 + 0*q**4 - 8*q. Suppose c(k) = 0. Calculate k.
-2, 1
Let a(r) = -r**3 - 5*r**2 + 4*r + 8. Let w(t) = t**3 + 4*t**2 - 5*t - 8. Let m be ((-28)/(-8))/(-7) - (-14)/(-4). Let c(x) = m*a(x) - 3*w(x). Factor c(l).
(l - 1)*(l + 1)*(l + 8)
Let q(d) be the first derivative of -8/7*d + 0*d**2 + 2/21*d**3 - 26. Find w such that q(w) = 0.
-2, 2
Let i(v) be the second derivative of 1/45*v**4 + 9*v + 1/315*v**7 + 0 - 1/75*v**5 - 1/15*v**2 - 1/225*v**6 + 1/45*v**3. Factor i(r).
2*(r - 1)**3*(r + 1)**2/15
Determine v, given that -2685*v + 14*v**2 + 2*v**4 - 12*v**3 + v**5 + 0*v**5 + 2680*v = 0.
-5, 0, 1
Let h be (-3)/3 - (-1 + -2). Suppose -4*u + 5*p = -33, 4*u - 8*p + 12*p + 12 = 0. Factor 0 + 2*i**h - 6 + 2*i**3 - u*i + 4.
2*(i - 1)*(i + 1)**2
Let y(i) = 12*i**3 - 48*i**2 + 36*i - 17. Let m(f) = 4*f**3 - 16*f**2 + 12*f - 6. Let j(x) = -17*m(x) + 6*y(x). Find q, given that j(q) = 0.
0, 1, 3
Factor 12*g + 32 + 32*g**2 - 75*g**2 + 44*g**2.
(g + 4)*(g + 8)
Let p be ((-6)/4)/(2*8/(-32)). Let m(n) be the first derivative of 1/8*n**2 + 0*n**3 - 1/16*n**4 + 0*n - p. Suppose m(j) = 0. What is j?
-1, 0, 1
Let w(b) be the first derivative of -3*b**5/40 - 3*b**4/16 - b**3/8 + 43. Find m such that w(m) = 0.
-1, 0
Let i = -253112/9 + 28124. Suppose 0*f - 20/9*f**2 - i*f**3 + 0 = 0. What is f?
-5, 0
Let m = 184 + -182. Let j(w) be the first derivative of -4/7*w + 1/7*w**m - 2 + 2/21*w**3. Find b such that j(b) = 0.
-2, 1
Suppose -3*d - 7 = 4*q - 3, -6 = q + 2*d. Let j be ((-2)/(-6) + 0)*(22 - 16). Let 0*a**2 + 2*a**2 + j*a**3 + 6*a**q + 4*a + 2*a**