tive of -u**5/100 + u**4/30 + u**3/30 - u**2/5 - 22*u. Factor v(w).
-(w - 2)*(w - 1)*(w + 1)/5
Let t = -4/887 - -7140/9757. What is b in -30/11*b**2 - 4/11*b**3 + 10/11*b**4 - t + 32/11*b = 0?
-2, 2/5, 1
Let r be 100/(-250) - 6/(-5). Factor -r*w + 6/5*w**2 + 0.
2*w*(3*w - 2)/5
Let g(s) be the second derivative of -s**7/840 + s**6/120 + 5*s**4/6 + 10*s. Let i(h) be the third derivative of g(h). Determine p, given that i(p) = 0.
0, 2
Let o(u) be the third derivative of -u**5/96 + 199*u**4/96 + 10*u**3/3 - 4*u**2. Determine l, given that o(l) = 0.
-2/5, 80
Let j(t) be the second derivative of 1/78*t**4 + 1/13*t**3 + 8*t + 0 + 0*t**2. Find o, given that j(o) = 0.
-3, 0
Let d(n) = 31*n**2 + 23*n - 14. Let b(s) = -154*s**2 - 114*s + 68. Let m(h) = -3*b(h) - 14*d(h). What is c in m(c) = 0?
-1, 2/7
Let q(v) be the second derivative of 16/27*v**3 - 4/9*v**4 - 1/135*v**6 - 8*v + 0 + 0*v**2 + 1/10*v**5. Factor q(m).
-2*m*(m - 4)**2*(m - 1)/9
Find y, given that -11/2*y + 0 + 1/2*y**2 = 0.
0, 11
Let z = -3 + 1. Let n(u) = -4*u + 1. Let y be n(z). Let -y*w**2 - 5*w**3 + 0 + 0 + 2*w**3 = 0. What is w?
-3, 0
Let t be (72/(-90))/((-4)/10). Suppose b**t + b**2 - 4*b**4 + 2*b**4 - 3*b**5 + b**3 + 2*b**5 = 0. What is b?
-2, -1, 0, 1
Let u be (-24)/(-15)*(325/(-52) - -7). What is h in 0 + 3/5*h**2 + u*h = 0?
-2, 0
Let l(a) be the first derivative of a**5/20 + 9*a**4/16 + 3*a**3/2 - a**2/2 - 6*a + 587. Let l(x) = 0. What is x?
-6, -2, 1
Suppose -30*q + 25*q = -20. Suppose -h = -q*h + 6. Factor -9*v + 9*v**4 + 3*v**5 - 3 + 8*v**3 + 0*v**3 - 6*v**h - 2*v**3.
3*(v - 1)*(v + 1)**4
Let j(l) be the first derivative of 5*l**4/26 - 4*l**3/39 - l**2 - 12*l/13 + 92. Factor j(t).
2*(t - 2)*(t + 1)*(5*t + 3)/13
Let x(k) = 13*k**3 - k**2 + 9*k. Let y(q) = 7*q**3 + 5*q. Let d(m) = -4*x(m) + 7*y(m). Factor d(u).
-u*(u - 1)*(3*u - 1)
Let r(v) = v**3 - 16*v**2 + 15*v - 6. Let z be r(15). Let j be z - -8 - 20/14. Factor 2/7 - j*q + 2/7*q**2.
2*(q - 1)**2/7
Factor -624*p - 24625*p**3 - 8676*p**2 - 16 - 29301*p**3 - 104976*p**4 + 3382*p**3.
-4*(6*p + 1)**2*(27*p + 2)**2
Let k be 1 - (4/(-2) + 0). Suppose -n**3 - 6*n - 9*n**2 - n**k - n**3 = 0. Calculate n.
-2, -1, 0
Let b(z) be the second derivative of z**7/14 + 2*z**6/5 + 3*z**5/5 + 131*z. Factor b(x).
3*x**3*(x + 2)**2
Suppose 1 + 5 = i. Suppose -i = 3*l - 2*z - z, 3*l - z = 4. Suppose 99/2*p**l - 33*p**2 + 6*p - 111/4*p**4 + 21/4*p**5 + 0 = 0. Calculate p.
0, 2/7, 1, 2
Let j be (-20)/(-6) + 2/3. Suppose 7*x = -f + 4*x + 15, -3*f - 7 = -4*x. Determine m so that 0*m + 0 + 0*m**2 - 1/3*m**j - 1/3*m**f = 0.
-1, 0
Let x(c) be the third derivative of -c**6/240 + 31*c**5/240 - 55*c**4/48 - 21*c**3/8 - 35*c**2 - 3*c. Let x(s) = 0. What is s?
-1/2, 7, 9
Suppose -10 = -8*m + 30. Factor -4*q**5 + 4*q**4 + 4*q**3 - 8*q**m + 13*q**5.
q**3*(q + 2)**2
Let n be ((-28)/784)/((-18)/21). Let r(o) be the third derivative of n*o**4 - 4*o**2 + 0*o**3 + 0*o + 0 + 1/60*o**5. Determine m, given that r(m) = 0.
-1, 0
Let s(t) = -t**3 - 103*t**2 - 69*t. Let l(j) = 20*j**2 + 14*j. Let a(f) = -22*l(f) - 4*s(f). Determine z so that a(z) = 0.
-1, 0, 8
Let p(v) be the first derivative of -21*v**3/2 - 33*v**2 - 6*v - 735. What is z in p(z) = 0?
-2, -2/21
Let f(u) be the second derivative of -2*u**6/3 - 37*u**5/5 - 44*u**4/3 - 8*u**3 - 152*u. Factor f(g).
-4*g*(g + 1)*(g + 6)*(5*g + 2)
Let l be 5*4*7/28. Let p(f) be the second derivative of 0 + 0*f**3 - 3/35*f**7 + 0*f**2 + 1/15*f**4 - 1/10*f**l - 16/75*f**6 - 3*f. Suppose p(g) = 0. What is g?
-1, 0, 2/9
Let q(z) be the first derivative of 0*z**4 - 3 + 0*z - 1/240*z**5 + 2/3*z**3 - 1/720*z**6 + 0*z**2. Let s(p) be the third derivative of q(p). Factor s(x).
-x*(x + 1)/2
What is o in 1/10*o**2 - 1/2*o - 12/5 = 0?
-3, 8
Let v = -57 - -343/6. Let d(l) = l**3 + 89*l**2 - 167*l + 1365. Let z be d(-91). Suppose -v*j**3 + 1/6*j**2 + z + 1/3*j = 0. Calculate j.
-1, 0, 2
Suppose 27 = 2*b - o + 11, -22 = -b + 4*o. Suppose 2*p = 44 - 44. Factor -b*k**2 + p*k + 0*k + 3*k**3 + 3*k**2.
3*k**2*(k - 1)
Let o be (-3)/2*20/(-6). Let -20*j**2 + 24*j**5 + 30*j**3 + o*j - 47*j**5 + 28*j**5 - 20*j**4 = 0. What is j?
0, 1
Suppose 0 = 6*t - 19 + 7. Suppose 0*u**4 - 4*u + 4*u**3 + 3*u**4 + u**4 - 4*u**t + 0*u**2 = 0. Calculate u.
-1, 0, 1
Let z(w) = -496*w + 2482. Let o be z(5). Factor 135/8*s - 75/4 + 3/8*s**3 - 9/2*s**o.
3*(s - 5)**2*(s - 2)/8
Let u = -467/780 - -8/13. Let v(s) be the third derivative of 0 + u*s**5 + 0*s - 1/120*s**6 + 1/630*s**7 - 1/72*s**4 + 2*s**2 + 0*s**3. Factor v(l).
l*(l - 1)**3/3
Let d(g) be the second derivative of 0 - 1/112*g**7 + 1/16*g**4 + 1/16*g**3 + 0*g**2 - 25*g + 0*g**5 - 1/40*g**6. Find j such that d(j) = 0.
-1, 0, 1
Let b be (-5)/(-55) + (-416)/(-143). Let 1 + 2*a**2 + 1/2*a**b + 5/2*a = 0. Calculate a.
-2, -1
Factor -16/3 + 22/3*h**3 + 2/3*h**5 + 4*h**4 - 8*h + 4/3*h**2.
2*(h - 1)*(h + 1)*(h + 2)**3/3
Suppose 12 = 3*q + 3. Suppose q*m + m = 8. Factor 33*d + 30*d**3 - 92*d**2 - 4 - m + 35*d**2.
3*(d - 1)*(2*d - 1)*(5*d - 2)
Let v = -2149 - -2151. Determine i, given that 4/7*i**v + 8*i + 28 = 0.
-7
Let d(i) = -i**2 - 55*i + 4. Let q be d(-55). Suppose 3/2 - 3/4*x**q - 3/4*x**2 - 9/4*x + 9/4*x**3 = 0. Calculate x.
-1, 1, 2
Let s(h) = 6*h**3 + 15*h**2 - 11*h + 11. Suppose 87*j - 86*j = -6. Let u(a) = a**3 + 3*a**2 - 2*a + 2. Let g(c) = j*s(c) + 33*u(c). Factor g(q).
-3*q**2*(q - 3)
Let n be 1 + (3 - 0)*-1. Let m(l) = 5*l**2 - l + 2. Let g be m(n). Let 1 + 4*h**2 + g*h - 4*h**3 - 1 - 20*h - 4*h**4 = 0. What is h?
-1, 0, 1
Let i(t) be the second derivative of -t**7/504 + t**6/144 + t**5/12 + t**4/4 - 8*t. Let s(w) be the third derivative of i(w). Factor s(b).
-5*(b - 2)*(b + 1)
Let g(r) be the third derivative of 3/7*r**3 + 0 + 0*r + 2/21*r**4 - 1/210*r**5 - 7*r**2. Suppose g(k) = 0. What is k?
-1, 9
What is o in 64/5*o**3 + 4/5*o**4 + 384/5*o**2 + 1024/5 + 1024/5*o = 0?
-4
Let x be (-5 + 8)*1/3. Let z(i) = 3*i + 1. Let f be z(x). Find m such that 0*m**2 + 4*m**2 - 6*m + f*m**2 - 5*m**2 = 0.
0, 2
Let f(a) = 2*a**2 - 10*a + 8. Let m be f(1). Let -9/5*z**2 + 3/5*z**3 + 6/5*z + m = 0. Calculate z.
0, 1, 2
Suppose -5*u - 5 = 0, 0 = -2*j - 5*u - 0 + 1. Let o(d) be the first derivative of -4 - 3/5*d**5 + 0*d + j*d**2 + d**3 - 3/2*d**4. Factor o(z).
-3*z*(z - 1)*(z + 1)*(z + 2)
Let t be -1 - -17 - (-1)/(-1). Let y(g) = -g**3 + 16*g**2 - 14*g - 13. Let o be y(t). Factor -6*v + 2 - v**o - 11 + 4*v**2.
3*(v - 3)*(v + 1)
Let y(l) = l**3 - 6*l**2 - 6*l + 1. Let n be y(7). Let g = 10 - n. Find i such that -i - i**g + 3 + 2*i**2 - 1 - 4 = 0.
-1, 2
Determine o so that 0*o - 12*o**3 - 3/2*o**5 + 0 + 15/2*o**4 + 6*o**2 = 0.
0, 1, 2
Factor 8 + 125*y**2 + 18*y**3 - 5*y**4 + y**5 - 66*y**2 + 28*y - 21*y**2 + 13*y**4 + 7*y**3.
(y + 1)**2*(y + 2)**3
Let w = -64 + 39. Let r = -20 - w. Solve -4/3*j**4 - 2/9*j**r - 4/9 - 28/9*j**3 - 2*j - 32/9*j**2 = 0.
-2, -1
Let d(r) = 6*r**3 + 4*r**2 - r - 8. Let m be d(4). Solve 2 + m*y - 27 - 466*y - 5*y**2 = 0 for y.
-5, -1
Let l be (-6*8/(-432))/(8/6). Let y(s) be the first derivative of 1/4*s**2 + 1/4*s + 8 + l*s**3. Factor y(g).
(g + 1)**2/4
Let v(o) be the first derivative of 2*o**5/65 + 71*o**4/26 - 2*o**3/39 - 71*o**2/13 + 815. Determine u, given that v(u) = 0.
-71, -1, 0, 1
Let p(m) = -m**3 + 12*m**2 + 27*m + 23. Let d be p(14). Let i be d - 7 - 0*(-2)/6. Find n such that -2/5*n + 7/5*n**3 + 0 + n**i = 0.
-1, 0, 2/7
Let c = -93 - -96. Factor -7*w**4 - c*w**5 + 7*w**5 + 3*w**4.
4*w**4*(w - 1)
Let q(z) be the third derivative of -z**5/12 + 85*z**4/12 + 175*z**3/6 + 15*z**2 + 2. Factor q(i).
-5*(i - 35)*(i + 1)
Let q = 213 - 208. Let i(m) be the third derivative of -1/10*m**q + 1/45*m**7 - 5/36*m**4 + 0 + 0*m + 1/36*m**6 + 2/9*m**3 - m**2. Suppose i(r) = 0. What is r?
-1, 2/7, 1
Let i = -6764 - -6767. Factor -2/7*l**2 - 8/7*l + 2/7*l**i + 8/7.
2*(l - 2)*(l - 1)*(l + 2)/7
Let t(g) = -g**4 - g**3 - g**2 - 1. Let w(n) = 80*n**3 + 460*n**2 + 875*n + 485. Let l(j) = 5*t(j) - w(j). Factor l(a).
-5*(a + 1)*(a + 2)*(a + 7)**2
Let z(n) be the first derivative of -n**6/8 + 3*n**4/4 + 144. Factor z(h).
-3*h**3*(h - 2)*(h + 2)/4
Let n be ((-45)/(-130) - (-19)/(-38))/(2/(-12)). Determine r so that 0 - n*r + 2/13*r**2 = 0.
0, 6
Let m(a) be the first derivative of a**4/22 - 14*a**3/33 - 5*a**2/11 + 1