 1. Suppose 2*h - 2 = -i. Let x(o) = -o + 1. Let n(y) = h*x(y) + l(y). Find v, given that n(v) = 0.
1, 4
Let s = 301 - 295. Let j(k) be the first derivative of 2 + k + 8/3*k**3 - 1/12*k**s - 9/4*k**2 - 7/4*k**4 + 3/5*k**5. Let j(o) = 0. What is o?
1, 2
Let y(s) be the third derivative of s**7/1890 - s**6/108 + s**5/45 + s**4/3 + 40*s**2. Suppose y(m) = 0. What is m?
-2, 0, 6
Solve 1/2*h**3 + 5/2*h**2 + 2 + 4*h = 0.
-2, -1
Suppose 7*f = 12*f - 15. Suppose -5*h = -f*h. Factor 0 + 0*g + 49/6*g**4 + h*g**3 - 2/3*g**2.
g**2*(7*g - 2)*(7*g + 2)/6
Let y(v) be the second derivative of v**4/18 + 10*v**3/3 + 75*v**2 + 6*v + 8. Find q such that y(q) = 0.
-15
Find x, given that 365*x**3 - 605*x**5 + 825*x**4 + 149*x - 6 - 14 + 91*x - 805*x**2 = 0.
-1, 2/11, 1
Suppose 0 = 4*m - 44 + 24. Factor 8 - 105*p + 93*p + m*p**2 - 4*p**2 + 3*p**2.
4*(p - 2)*(p - 1)
Let m(r) be the first derivative of -r**7/840 + r**6/120 - r**4/6 - 7*r**3/3 - 14. Let v(w) be the third derivative of m(w). Factor v(n).
-(n - 2)**2*(n + 1)
Let u(c) be the first derivative of 2*c**7/105 - c**6/10 - 4*c**5/15 + 3*c**2 + 7. Let v(p) be the second derivative of u(p). Factor v(j).
4*j**2*(j - 4)*(j + 1)
Suppose 17*v + 0*v + 7*v = 0. Factor 4/7*q**2 + v + 4/7*q - 4/7*q**3 - 4/7*q**4.
-4*q*(q - 1)*(q + 1)**2/7
Let d(t) be the second derivative of t**10/15120 - t**8/1680 + t**6/360 - t**4/2 - 3*t. Let b(k) be the third derivative of d(k). Let b(r) = 0. What is r?
-1, 0, 1
Let x(b) = -b**3 - 9*b**2 + b + 23. Let j be x(-9). Suppose -j*w + 32 = -24. Determine g so that 5/2*g**2 + 2 - w*g - 1/2*g**3 = 0.
1, 2
Let f(y) = 11*y**2 + 7*y - 16. Let m(o) = 2*o**2 - 1. Let j(h) = 5*f(h) - 30*m(h). Factor j(b).
-5*(b - 5)*(b - 2)
Suppose 34*h = 16*h. Let w(k) be the third derivative of -5*k**2 + 25/12*k**3 + 0*k + 5/24*k**4 + h + 1/120*k**5. Factor w(c).
(c + 5)**2/2
Let s be 9/(-6)*-3 - (-3)/(-2). Factor 24 - 12*p**4 + 2*p**5 - 28*p**s - 32*p**2 - 18*p + 2*p**5 - 28 - 6*p**5.
-2*(p + 1)**4*(p + 2)
Let v(q) be the second derivative of q**4/8 - 4*q**3 + q - 12. Suppose v(z) = 0. What is z?
0, 16
Let j(s) be the first derivative of s**6/66 - s**5/55 - s**4/44 + s**3/33 - 13. Factor j(z).
z**2*(z - 1)**2*(z + 1)/11
Solve 73*g**2 + 40*g**3 - 57*g**4 - 76*g**3 - 17*g**3 + 9*g**5 + 32*g - 28 = 0.
-1, 2/3, 7
Let i(d) = d**3 + 13*d**2 + 8*d - 26. Let b be i(-12). Let s be (-20)/25*(b/(-12) + 1). Factor -s*q**2 + 2/3*q + 0.
-2*q*(q - 1)/3
Let f = -81 - -121. Suppose 5*u - f = -5*c, 3 = 5*u - 4*c - 1. Factor -s**3 + 2*s**u - s**4 + s - 52*s**2 + 51*s**2.
s*(s - 1)**2*(s + 1)
Factor 3/2 + 13/2*v**2 + 8*v.
(v + 1)*(13*v + 3)/2
Let d(w) be the second derivative of w**5/10 - 10*w**4/3 - 67*w**3/3 - 46*w**2 - 174*w. Factor d(m).
2*(m - 23)*(m + 1)*(m + 2)
Let l be -6 - (2/1 - 11). Let u be l/21 - 88/(-168). Factor u*j**2 - 4/3*j - 2.
2*(j - 3)*(j + 1)/3
Let i(b) be the third derivative of 0 - 1/18*b**4 - 14*b**2 + 1/90*b**6 - 1/45*b**5 + 0*b**3 + 0*b + 2/315*b**7. Factor i(j).
4*j*(j - 1)*(j + 1)**2/3
Let m = -2470 + 2472. Solve 2/5*b**4 + 18/5*b**m + 14/5*b + 2*b**3 + 4/5 = 0.
-2, -1
Let l = -107 + 110. Solve 0 + 0*j - 1/3*j**4 + 1/3*j**2 + 0*j**l = 0.
-1, 0, 1
Suppose 0 = -5*g - t + 17, -8*g - 5*t = -4*g - 1. Let w be (-51)/21 - (-3 - 0/g). Factor -8/7 + 4/7*x**2 - w*x.
4*(x - 2)*(x + 1)/7
Factor -25*v**2 - 65*v - 3*v**3 + 7*v**3 - 5*v**3 + 6*v**3 - 35.
5*(v - 7)*(v + 1)**2
Let r(y) be the second derivative of y**8/1400 + y**7/2100 - y**6/450 + 3*y**3 - 23*y. Let i(s) be the second derivative of r(s). Solve i(m) = 0 for m.
-1, 0, 2/3
Let d(u) = 60*u**3 + 72*u**2 + 3*u + 9. Let v(k) = k**4 + 30*k**3 + 35*k**2 + 2*k + 4. Let n(b) = -4*d(b) + 9*v(b). Solve n(o) = 0.
-2, -1, -1/3, 0
Let r(v) = 3*v + 1. Let y be r(1). Suppose -y*o = -0*o - 12. Factor o*c**2 - 8*c**2 + 3*c**2.
-2*c**2
Suppose -15 = 3*i + 24. Let c(d) = -19*d**3 - 5*d**2 - 5*d - 19. Let w(a) = -9*a**3 - 3*a**2 - 3*a - 9. Let g(u) = i*w(u) + 6*c(u). What is s in g(s) = 0?
-1
Let n(k) be the third derivative of -k**5/210 - k**4/84 + 2*k**3/21 + k**2 - 10. Find t such that n(t) = 0.
-2, 1
Let m(o) be the second derivative of -10/11*o**3 + 0 + 1/66*o**4 + 225/11*o**2 + 7*o. Find c such that m(c) = 0.
15
Suppose -22*y + 11 + 33 = 0. Factor -39/2*s**3 + 0 - 3/2*s**5 - 6*s + 18*s**y + 9*s**4.
-3*s*(s - 2)**2*(s - 1)**2/2
Suppose -14 = 86*u - 93*u. Let n be 4/(-6) + u*4/8. Factor -4/3*b**3 - b**2 + n*b + 0.
-b*(b + 1)*(4*b - 1)/3
Let t(h) be the second derivative of 0 - 3/2*h**2 - 2*h**3 + 5/4*h**4 - 5*h. Find x, given that t(x) = 0.
-1/5, 1
Suppose -3*j = -4*y - 7, 5*y + 3*j = y + 23. Let v be ((y + 0)*1)/1. Factor -r**3 - 2 - 3*r**v + 5 - 3*r - 4.
-(r + 1)**3
Suppose -19*o + 17*o + 15 = -3*b, 0 = 3*b + 9. Let s(t) be the first derivative of -1/14*t**2 + 1/7*t**o + 9 + 1/28*t**4 - 3/7*t. Solve s(n) = 0.
-3, -1, 1
Determine v, given that v**3 + 1/2 - 2/3*v - 4/3*v**2 - 1/3*v**5 + 5/6*v**4 = 0.
-1, 1/2, 1, 3
Let r = 245 + -245. Let s(x) be the third derivative of -2*x**2 + x**3 + 0*x - 7/12*x**4 + 1/6*x**5 - 1/60*x**6 + r. Let s(o) = 0. What is o?
1, 3
Let j = 7633/24 - 318. Let b(g) be the third derivative of j*g**4 + 0 + 0*g + 1/120*g**5 + 6*g**2 + 0*g**3. Let b(s) = 0. Calculate s.
-2, 0
Find y, given that 50*y**2 + 625/3 + 1/3*y**4 - 500/3*y - 20/3*y**3 = 0.
5
Let g(f) be the second derivative of 1/18*f**4 + 0 + 0*f**2 - 5*f + 0*f**3. Let g(b) = 0. Calculate b.
0
Suppose -133*o + 128*o = 3*y - 11, -3*y = 4*o - 10. Factor -1/4*z + 0 + 1/4*z**3 + 0*z**y.
z*(z - 1)*(z + 1)/4
Let n be -1*(2 - -1) - (-5 + -1). Let h be (n - (-34)/(-12))/((-3)/(-60)). Factor -16/3*j - 2 - h*j**2.
-2*(j + 1)*(5*j + 3)/3
Let b(s) = -9*s - 28. Let w be b(-10). Let t = w - 59. Factor p**2 + 0 + 19/6*p**t + 0*p - 7/6*p**4.
-p**2*(p - 3)*(7*p + 2)/6
Let a(c) be the first derivative of 0*c**2 - 2/35*c**5 - 15 + 0*c + 2/21*c**4 - 2/63*c**3. What is q in a(q) = 0?
0, 1/3, 1
Let p(y) be the third derivative of 0*y + 0 - 16*y**2 + 1/9*y**3 + 1/72*y**4 - 1/180*y**5. Find i such that p(i) = 0.
-1, 2
Let d(m) = 2*m**5 - 20*m**4 + 78*m**3 - 100*m**2. Let a(f) = -4*f**5 + 39*f**4 - 155*f**3 + 202*f**2. Let l(i) = -2*a(i) - 5*d(i). Suppose l(g) = 0. What is g?
0, 3, 4
Let v(g) = -g**2 - 2*g. Let c be v(0). Let f be (9/6 - 2 - c) + 2. Factor 1 + f*y + 1/2*y**2.
(y + 1)*(y + 2)/2
Let q(j) be the first derivative of j**3/7 - 2*j**2/7 + j/7 + 2. Let q(d) = 0. Calculate d.
1/3, 1
Let i = -447 - -2683/6. Let c(l) be the first derivative of 3/16*l**2 + i*l**3 - 7 - 1/8*l. Factor c(d).
(d + 1)*(4*d - 1)/8
Let j(r) = 2*r**3 - 2*r**2 + 4*r - 10. Let u(h) = 12*h - 5*h**2 - 49 + 5*h**3 - 37 + 65 - 4*h. Let k(m) = 13*j(m) - 6*u(m). Solve k(t) = 0.
-1, 1
Let y(i) = -8*i**2 - 30*i - 16. Let c(r) = -r**3 - 7*r**2 - 32*r - 17. Let z(o) = 2*c(o) - 3*y(o). Solve z(f) = 0 for f.
-1, 7
Let s(y) = -7*y + 147. Let u be s(21). Factor 0 + u*x**3 + 0*x + 0*x**2 + 1/6*x**4.
x**4/6
Let v(j) = 29*j + 19. Let w be v(6). Solve -3*l**4 + 8*l**4 - 10*l - 5 - w*l**3 + 203*l**3 = 0 for l.
-1, 1
Let o(m) be the third derivative of -m**7/105 + 31*m**5/30 - 5*m**4/2 - 2*m**2 - 370*m. Let o(b) = 0. Calculate b.
-6, 0, 1, 5
Let o(y) = 6*y**3 - 38*y**2 + 58*y - 30. Let t(c) = 5*c**3 - 37*c**2 + 59*c - 30. Let q(r) = -3*o(r) + 4*t(r). Solve q(i) = 0 for i.
1, 15
Let l(c) = c**3 - c - 1. Let t(n) = -n**3 - 3*n**2 + 2*n + 7. Let m(a) = -2*l(a) - t(a). Let r(d) be the first derivative of m(d). Factor r(j).
-3*j*(j - 2)
Let f be 2/6 - (-4 - (-190)/45). Let p(s) be the second derivative of -1/150*s**5 + 3*s + 0 + 2/45*s**4 - f*s**3 + 2/15*s**2. Find t such that p(t) = 0.
1, 2
Let y(l) = -l**3 - 11*l**2 + 13*l + 17. Suppose -24 = -3*c + 5*c. Let r be y(c). Find k, given that -6*k**3 + 4*k**4 + 3*k**3 + 2*k**2 - k**r - 2*k**3 = 0.
0, 1, 2
Let d(o) = o + 4. Let f be d(6). Suppose -z - 18 = -3*z. Determine r so that 6*r - r**3 + z*r**4 - f*r**3 - r**3 - 6*r**2 + 3*r**2 = 0.
-2/3, 0, 1
Suppose -59*n - 1195 = -64*n. Let 14*c + n*c**2 - 10*c - 48*c - 241*c**2 - 242 = 0. Calculate c.
-11
Let j(w) be the third derivative of -w**5/15 - 19*w**4/24 - 3*w**3/2 + 8*w**2. Let i be j(-4). Factor -3/2*g**3 + 3/2*g - i + 3*g**2.
-3*(g - 2)*(g - 1)*(g + 1)/2
Let f(k) be the third derivative of k**5/12 + 65*k**4/24 - 25*k**3 + 48*k**2 + 4*k. Factor f(m).
5*(m - 