 + -6. Let j(m) = -2*m**2 - 4*m - 12. Let l(x) = -2*x**2 - 5*x - 11. Let n(w) = v*j(w) - 4*l(w). Suppose n(k) = 0. Calculate k.
-2
Let a be (27/10)/1 + 0. Let i = -11/5 + a. Factor -i*m**2 + 1/2*m + 1.
-(m - 2)*(m + 1)/2
Let b(w) be the second derivative of 2*w + 0 + 0*w**3 - 1/40*w**6 + 1/28*w**7 + 0*w**2 - 3/40*w**5 + 1/16*w**4. Solve b(c) = 0.
-1, 0, 1/2, 1
Let u(y) be the third derivative of 0 + 0*y - y**2 - 1/2*y**3 + 1/30*y**5 + 0*y**4 - 1/180*y**6. Let o(b) be the first derivative of u(b). Factor o(m).
-2*m*(m - 2)
Factor -37/2*m + 3 + 33*m**2 - 35/2*m**3.
-(m - 1)*(5*m - 3)*(7*m - 2)/2
Let y be (-14)/(-42) + (-59)/(-3). Let l be y/72 + 2/9. Determine a, given that -1/2*a**2 + 1/4*a**4 + 1/4*a + 1/4 + 1/4*a**5 - l*a**3 = 0.
-1, 1
Let c = 18 - 15. Suppose 0 = c*f + f. Factor f*m + 0 + 0*m**2 + 3/4*m**5 + 0*m**4 - 3/4*m**3.
3*m**3*(m - 1)*(m + 1)/4
Let c(d) = 11*d**2 + 32*d + 11. Suppose 2*o - 6 = -2*a, 3*a - 26 = 3*o - 5. Let p(t) = -12*t**2 - 32*t - 10. Let q(l) = o*c(l) - 3*p(l). Factor q(i).
2*(i + 2)*(7*i + 2)
Let n(c) = -c + 10. Let p be n(10). Find x such that p - 2 + x**2 - 1 + 2*x + 4 = 0.
-1
Let w(k) be the third derivative of -k**7/420 - k**6/60 - 14*k**2. What is l in w(l) = 0?
-4, 0
Suppose 0 = -2*r - 4*b - 0*b + 10, 59 = 4*r - 5*b. Let k be (-5)/(((-2)/32)/1). Find l such that -3*l + 90*l**4 + 234*l**3 + 72*l**4 + r*l + k*l**2 = 0.
-1, -2/9, 0
Let o(c) = 2*c**2 - 4*c + 11. Let q = -13 + 4. Let v(s) = -s**2 + 2*s - 5. Let z(r) = q*v(r) - 4*o(r). Let z(h) = 0. What is h?
1
Let u be (-6)/(-51) - 2502/(-408). Let w(b) be the first derivative of 8/3*b**6 - 1 + b + 8*b**5 - 5/2*b**2 - 5/3*b**3 + u*b**4. Suppose w(q) = 0. Calculate q.
-1, 1/4
Suppose -7*n + 4*n + 6 = 0. Factor -4*o + 12 - 8 - 3*o**2 + 4*o**n.
(o - 2)**2
Suppose 0 = -5*r - 0 + 15. Let m(p) = p**3 - 6*p**2 + 7*p - 6. Let y be m(5). Suppose -2*f**4 - 2*f**5 - 1 + 4*f**2 + 4*f + y*f**r - 6*f - 1 = 0. Calculate f.
-1, 1
Suppose -17*m**4 + 27*m**2 + 3*m - 5*m - 32*m**4 - 84*m**3 = 0. Calculate m.
-2, 0, 1/7
Factor 1/7*s**3 + 1/7*s**5 - 2/7*s**4 + 0*s + 0*s**2 + 0.
s**3*(s - 1)**2/7
Let d(a) be the first derivative of 0*a**2 + 3 + 0*a + 1/3*a**3. Factor d(g).
g**2
Suppose 5*q - 35 = -5*b, 4*b = -5*q + 5*b + 41. Suppose -9*t**2 + 2*t**5 - 4*t**2 + 6*t**5 - q*t**3 + 9*t**2 + 4*t**4 = 0. What is t?
-1, -1/2, 0, 1
Let x(s) be the second derivative of -s**3/6 + 41*s**2/2 - s. Let z be x(0). Let -z*g + 98*g**2 + 1 - 15*g + 7 = 0. What is g?
2/7
Suppose 9 = 3*v - 21. Let 5*z**2 + 4*z - 17*z**2 + v*z**2 - 2 = 0. What is z?
1
Let c(m) = m**2 - 6*m + 9. Let y be c(6). Let q = -7 + y. What is x in 6/7*x**q + 2/7 + 6/7*x + 2/7*x**3 = 0?
-1
Suppose c**3 - 8*c**3 + 9*c + 6 + 15*c**4 - 21*c**2 + 6*c**3 - 8*c**3 = 0. Calculate c.
-1, -2/5, 1
Let s = 1015/3 - 337. Factor -4/3*b + 0 - s*b**3 + 10/3*b**2.
-2*b*(b - 2)*(2*b - 1)/3
Let k(u) be the first derivative of u**4 + 8*u**3/3 + 2*u**2 + 37. Solve k(m) = 0 for m.
-1, 0
Suppose v = 2*v - 7*v. Let f = 1 - -1. Factor v*q - 1/2*q**f + 1/2.
-(q - 1)*(q + 1)/2
Let c be (-4)/(-5) + 117/(-15). Let p = c - -9. Suppose 28/3*q**p - 23*q**3 + 70/3*q**4 + 0 - 4/3*q - 25/3*q**5 = 0. What is q?
0, 2/5, 1
Let k = -3 + 6. Let -3*a + a**3 + 4*a + a**2 - k*a**2 = 0. What is a?
0, 1
Suppose 4*b = -3*y + 6, 2*b = 4*b - 4*y - 14. Factor -b*c - 89*c**2 + 92*c**2 - 3 + 6*c**3 - 3*c**3.
3*(c - 1)*(c + 1)**2
Factor 12/5 + 3/5*g**2 - 12/5*g.
3*(g - 2)**2/5
Solve 13*t - 31*t + 4*t**2 + 36 - 15*t - 7*t = 0.
1, 9
Let v(c) = -11*c**3 - 36*c**2 - 40*c - 6. Let f(r) = -32*r**3 - 107*r**2 - 120*r - 17. Let w(j) = -6*f(j) + 17*v(j). Find h such that w(h) = 0.
-4, -2, 0
Suppose -g + 4*g = 0. Let o(l) be the second derivative of -1/2*l**5 + g*l**4 + 1/3*l**6 - 2*l - 1/14*l**7 + 0 - l**2 + 5/6*l**3. Factor o(f).
-(f - 1)**4*(3*f + 2)
Let c = -12 + 3. Let x be 2/c - 29/(-9). Factor -51*s**4 + 6*s + 8*s**2 + 15*s**5 + s - 41*s**2 + 63*s**x - s.
3*s*(s - 1)**3*(5*s - 2)
Let c(h) be the third derivative of -h**8/252 + 2*h**7/315 + h**6/90 - h**5/45 + 43*h**2. Suppose c(f) = 0. What is f?
-1, 0, 1
Let l(s) be the second derivative of -2/35*s**7 + 0 + 1/10*s**3 + 1/10*s**6 + 0*s**2 + 4*s - 1/4*s**4 + 9/100*s**5. Solve l(u) = 0 for u.
-1, 0, 1/4, 1
Factor 5/3*w + 5/2*w**4 + 35/6*w**2 + 20/3*w**3 + 0.
5*w*(w + 1)**2*(3*w + 2)/6
Let l = 1022/3 + -340. Solve 2/3 + 2/3*m**3 - l*m - 2/3*m**2 = 0 for m.
-1, 1
Let h(i) be the first derivative of i**5/30 + i**2/2 + 2. Let v(y) be the second derivative of h(y). Solve v(s) = 0 for s.
0
Let u(t) = 8*t**5 + 6*t**4 - 5*t**3 - t**2 + 2*t + 5. Let p(r) = 7*r**5 + 6*r**4 - 4*r**3 - 2*r**2 + r + 4. Let j(m) = -5*p(m) + 4*u(m). Factor j(d).
-3*d*(d - 1)*(d + 1)**3
Let t(m) be the second derivative of -2*m - 1/30*m**6 - 1/9*m**3 + 7/60*m**5 + 0 + 0*m**2 - 5/126*m**7 + 1/12*m**4. Find v such that t(v) = 0.
-1, 0, 2/5, 1
Suppose 0 = n + 2*v - 11, -5*n + 5*v + 3 = 2*v. Find q, given that 2*q**3 + 4*q**2 + 4*q - n*q**3 - 3*q**3 + 5*q**3 = 0.
-2, 0
Let j(n) be the second derivative of n**4/66 + n**3/11 + 6*n. Factor j(f).
2*f*(f + 3)/11
Let w = 176 - 101. Let r be ((-6)/w)/(2/(-20)). Factor 0*j**2 - r*j**3 + 2/5*j**4 - 2/5 + 4/5*j.
2*(j - 1)**3*(j + 1)/5
Let g(j) = 2 - 12 + j**2 + 4*j**2 + 4*j. Suppose -3*l = -5*a + 43 + 2, 3*a + 2*l - 8 = 0. Let h(s) = -s**2 + 1. Let m(o) = a*h(o) + g(o). Factor m(q).
-(q - 2)**2
Let a(v) be the second derivative of v**3/6 - v**2/2 + 6*v. Let k be a(3). Factor 0*f + 0 + 2/7*f**3 - 4/7*f**k.
2*f**2*(f - 2)/7
Let y(m) be the third derivative of -m**9/19656 + m**8/10920 + m**3/6 + m**2. Let x(k) be the first derivative of y(k). Find s, given that x(s) = 0.
0, 1
Let c = -574 + 2297/4. Factor 0*p - 1/4*p**4 + 1/4*p**3 + c*p**2 + 0 - 1/4*p**5.
-p**2*(p - 1)*(p + 1)**2/4
Let t(h) be the second derivative of h**6/12 - 5*h**5/4 + 65*h**4/24 + 25*h**3 + 45*h**2 + 41*h. Factor t(n).
5*(n - 6)**2*(n + 1)**2/2
Suppose 2*c = -0*q - 5*q + 20, 35 = 5*q + 5*c. Suppose 0 = 3*v + q*v. Factor -1/2*u**2 + 1/2*u**3 - u + v.
u*(u - 2)*(u + 1)/2
Let z(r) be the third derivative of -r**6/150 + 7*r**4/30 + 4*r**3/5 - 22*r**2. Find p, given that z(p) = 0.
-2, -1, 3
Let f(h) be the first derivative of 2*h**5/25 + h**4/10 - 8*h**3/15 - 4*h**2/5 + 32. Factor f(d).
2*d*(d - 2)*(d + 1)*(d + 2)/5
Let m(c) be the second derivative of 35*c**4/12 - 15*c**3/2 + 5*c**2 + 9*c. What is j in m(j) = 0?
2/7, 1
Let h(n) be the second derivative of 2*n**7/525 - n**6/150 - 2*n**5/75 - 7*n**2/2 + 2*n. Let b(x) be the first derivative of h(x). Factor b(k).
4*k**2*(k - 2)*(k + 1)/5
Let f(p) be the second derivative of -p**6/6 - 3*p**5/4 - 5*p**4/4 - 5*p**3/6 + 2*p. Factor f(w).
-5*w*(w + 1)**3
Let w(z) = 3*z**2 - 5*z + 1. Let v be w(2). Let l(o) be the first derivative of 2/21*o**3 + 8/7*o + 4/7*o**2 + v. What is y in l(y) = 0?
-2
Let a(f) be the second derivative of 3*f**6/50 - 3*f**5/50 - f**4/5 + f**3/5 + 3*f**2/10 + 3*f. Let a(l) = 0. What is l?
-1, -1/3, 1
Let c(i) = -i**5 + i**4 + 2*i**3 - i - 3. Let r(j) = j**4 - 1 - j**2 + 0 + 0. Let k(n) = 3*c(n) - 6*r(n). Factor k(s).
-3*(s - 1)**2*(s + 1)**3
Let z(h) be the third derivative of 3*h**2 + 1/70*h**7 + 0 + 7/8*h**4 + h**3 + 9/20*h**5 + 0*h + 1/8*h**6. Factor z(w).
3*(w + 1)**3*(w + 2)
Factor 24*d**2 - 21*d**3 - 3/2*d**5 - 27/2*d + 3 + 9*d**4.
-3*(d - 2)*(d - 1)**4/2
Suppose -3*n - 54 = -12. Let f be (12/n)/(40/(-70)). Factor -3/2*i - f*i**4 + i**3 + 1/2 + 1/2*i**5 + i**2.
(i - 1)**4*(i + 1)/2
Suppose 0*u + 8 = 4*u. Let w be (0 - -3) + 9/(-18). Factor -7/2*b**u + b + w*b**3 + 0.
b*(b - 1)*(5*b - 2)/2
Let q(p) be the first derivative of p**3/3 + p**2/2 - 2*p - 1. Let q(t) = 0. Calculate t.
-2, 1
Let n(d) = -8*d**2 + 3*d + 2. Let f(z) = -z**2 + z - 1. Let y(g) = -3*f(g) + n(g). Determine r, given that y(r) = 0.
-1, 1
Let p(d) be the first derivative of -5*d**4 - 12*d**3 + 0*d - 4*d**2 + 36/5*d**5 - 6 + 14/3*d**6. Suppose p(o) = 0. What is o?
-1, -2/7, 0, 1
Let r be 7 + -11 + 13/3. Determine x so that -r - 1/3*x**2 + 2/3*x = 0.
1
Let h(y) be the first derivative of 3 + 0*y - 2/3*y**3 - y**2. Factor h(n).
-2*n*(n + 1)
Let n(m) be the second derivative of -2*m**6/75 + 12*m**5/25 - 22*m**4/15 - 56*m**3/5 - 98*m**2/5 - 3*m + 3. Factor n(p).
-4*(p - 7)**2*(p + 1)**2/5
Suppose 4*y - 6*y = -90. Let c be (-3)/2 + y/20.