c + 85. Let r be j(8). Solve -8/11*f**4 + 8/11*f**3 - 10/11*f + 4/11 + 4/11*f**2 + 2/11*f**r = 0.
-1, 1, 2
Let r(t) be the second derivative of 9/10*t**2 + 0 + 1/20*t**4 - 3/100*t**5 - 3*t + 1/2*t**3. Let r(c) = 0. What is c?
-1, 3
Let l be -2 + 18/20*25/10. Factor 1/4*m - l*m**2 + 0.
-m*(m - 1)/4
Let a(s) be the third derivative of -1/96*s**4 + 0*s - 1/240*s**5 + 0*s**3 + 0 + s**2. Determine d so that a(d) = 0.
-1, 0
Suppose v = -o, -6*v = 4*o - 5*v - 6. Let -12/5*a + 3/5*a**o + 12/5 = 0. What is a?
2
Let -4*l**3 + l**2 + 2*l**4 + l + 0*l**3 + 3*l**3 - 3*l**4 = 0. Calculate l.
-1, 0, 1
Let x = 4501/5 - 896. Factor -33/5*s - x*s**3 + 48/5*s**2 + 6/5.
-3*(s - 1)**2*(7*s - 2)/5
Let p(m) be the first derivative of -4/9*m**3 + 2/5*m**5 + 1/9*m**6 - 2/3*m - m**2 + 1/3*m**4 - 4. Factor p(i).
2*(i - 1)*(i + 1)**4/3
Let y(j) be the second derivative of -1/2*j**3 - 1/4*j**4 - 6*j + 0 + 0*j**2. What is q in y(q) = 0?
-1, 0
Let p be 1/3 - (-5 - -5). Let r(s) be the second derivative of 1/3*s**3 - p*s**2 + 0 + 2*s + 1/30*s**5 - 1/6*s**4. Factor r(g).
2*(g - 1)**3/3
Let q be (-6)/(-4) + 8 + -9. Let r = -14 - -14. Determine n so that n**3 + 1/2*n**2 + 0 + r*n + q*n**4 = 0.
-1, 0
Let h be 1/1 + (2/(-4))/1. Let c(i) be the second derivative of 1/3*i**4 + 0*i**2 + i + 0*i**3 + h*i**5 + 0. Solve c(a) = 0 for a.
-2/5, 0
Let h = 15 + -15. Let o be (10/6)/((-1)/(-3)). Factor 2*z**5 + h*z**o - 2*z**4 - 2*z**4.
2*z**4*(z - 2)
Find f such that 2/3 + 7*f**2 + 5/3*f**4 - 17/3*f**3 - 11/3*f = 0.
2/5, 1
Factor 3/5 - 4/5*k + 1/5*k**2.
(k - 3)*(k - 1)/5
Let t(f) be the third derivative of -f**7/280 - f**6/60 + f**5/40 + f**4/4 - f**3 - 3*f**2. Let y(x) be the first derivative of t(x). Factor y(p).
-3*(p - 1)*(p + 1)*(p + 2)
Let l(z) be the third derivative of -z**5/270 - z**4/54 + z**3/9 + 12*z**2. What is m in l(m) = 0?
-3, 1
Let c(f) = -f**2 + 11*f - 13. Let i be 1/(-2) + (-19)/(-2). Let m be c(i). Suppose -5 + m - 2*o**2 = 0. What is o?
0
Suppose z = -2*z + 78. Let f be z/10 + (-2 - -1). Factor -2/5*t**4 - 2/5 + f*t**3 - 12/5*t**2 + 8/5*t.
-2*(t - 1)**4/5
Let f(p) be the second derivative of p**6/60 + p**5/60 - 2*p. Solve f(l) = 0 for l.
-2/3, 0
Let q be (0/(-6))/(5/25*5). Let 0*o + q*o**2 + 0*o**3 - 1/5*o**4 + 0 = 0. Calculate o.
0
Factor 0*v - 6/11*v**4 - 4/11*v**3 + 2/11*v**2 + 0.
-2*v**2*(v + 1)*(3*v - 1)/11
Let q(s) be the second derivative of s**6/57 - 7*s**5/190 - s**4/38 + 7*s**3/57 - 2*s**2/19 + 8*s. Suppose q(z) = 0. Calculate z.
-1, 2/5, 1
Let c(y) be the second derivative of -y**7/5040 + y**6/1440 - y**4/12 + 2*y. Let u(i) be the third derivative of c(i). What is k in u(k) = 0?
0, 1
Suppose 5*f = -15, -2*s - 5*f + 2 = -1. Let q be 5/12 - s/(-36). Factor -7/3*n**2 + q*n**3 + 7/3*n**4 + 0 - 2/3*n.
n*(n - 1)*(n + 1)*(7*n + 2)/3
Let p(x) be the third derivative of x**7/210 - x**6/120 - x**2. Determine f so that p(f) = 0.
0, 1
Let v(w) be the first derivative of -w**3/15 - w**2/10 - 19. Factor v(k).
-k*(k + 1)/5
Let w be (-136)/(-24)*1*-3. Let u = w - -19. Find k, given that 4/7 - 2/7*k - 2/7*k**u = 0.
-2, 1
Let m(b) be the first derivative of -b**7/21 - b**6/5 - 3*b**5/10 - b**4/6 - 5*b - 2. Let v(u) be the first derivative of m(u). Let v(r) = 0. What is r?
-1, 0
Let a(h) = -h**2 + 12*h + 13. Let z be a(13). Let x be -1 - (0 + 10/(-6)). Solve 0 + x*r**2 + z*r = 0 for r.
0
Suppose -2*y = -5*y + 27. Factor 9*j**2 + y*j**4 + 8*j**4 + 3*j**3 - 3*j - 6 - 20*j**4.
-3*(j - 2)*(j - 1)*(j + 1)**2
Let v(r) be the second derivative of r**5/10 - r**4/2 + 2*r**3/3 - 12*r. Find s such that v(s) = 0.
0, 1, 2
Let j = -695 - -697. Let -1/2*z + 3/4*z**j - 1/4*z**3 + 0 = 0. Calculate z.
0, 1, 2
Let j(s) be the second derivative of -2*s - 1/4*s**4 + 0*s**3 + 0 + 3/20*s**5 + 0*s**2. Factor j(w).
3*w**2*(w - 1)
Let k(y) be the first derivative of y**7/2940 + y**6/1260 - 4*y**3/3 + 8. Let w(t) be the third derivative of k(t). Factor w(c).
2*c**2*(c + 1)/7
Let n(z) be the first derivative of -1/5*z - 2/15*z**3 + 3/25*z**5 - 8 - 1/10*z**4 - 1/30*z**6 + 3/10*z**2. Factor n(b).
-(b - 1)**4*(b + 1)/5
Let z(q) be the second derivative of 2/15*q**3 + 0 - 1/75*q**6 + 1/5*q**2 - 4*q + 0*q**4 - 1/25*q**5. Factor z(p).
-2*(p - 1)*(p + 1)**3/5
Factor 3 - 22*h + 9 + 8*h**2 - 2*h**2.
2*(h - 3)*(3*h - 2)
Let f = 20 - 17. Let o(s) be the second derivative of 1/2*s**4 - 4*s + 0 + 1/10*s**5 + 0*s**2 + 2/3*s**f. What is p in o(p) = 0?
-2, -1, 0
Let l(o) = -5*o**3 - 6*o**2 + 5*o + 14. Let t(c) be the first derivative of -3*c**4/4 - 4*c**3/3 + 3*c**2/2 + 9*c - 1. Let z(i) = -5*l(i) + 8*t(i). Factor z(v).
(v - 2)*(v - 1)*(v + 1)
Let y(h) = h - h**2 + 0 + 1 - 1. Let l(p) = -3*p**2 + 6*p - 3. Let b(z) = -l(z) - 6*y(z). Factor b(t).
3*(t - 1)*(3*t - 1)
Suppose 0 = b + 4*b - 110. Let a = b - 152/7. Factor 0*p + 0 + 0*p**2 + a*p**3 - 2/7*p**4.
-2*p**3*(p - 1)/7
Factor -16*x + 194*x**3 - 4*x**2 + 4*x**4 - 22*x**2 - 202*x**3 - 2*x**2.
4*x*(x - 4)*(x + 1)**2
Let l(u) = -5*u - 1. Let q be l(-1). Suppose -3*s - 9 = -3*y, -4*y + s = 5*s - q. Let 2/3*x**y + 4/9*x + 0*x**3 - 2/9*x**4 + 0 = 0. What is x?
-1, 0, 2
Let h be 3 - (-1 + 2)*3. Let f(x) be the third derivative of 1/105*x**7 + 1/60*x**6 + 0*x + 2*x**2 + 0 + 0*x**3 + h*x**4 + 0*x**5. Factor f(u).
2*u**3*(u + 1)
Let f = 1284 + -1284. Factor -1/4*j**3 - 1/4*j**2 + 0 + f*j.
-j**2*(j + 1)/4
Let c(a) be the second derivative of -a**7/273 - a**6/195 + a**5/65 + 7*a. Factor c(s).
-2*s**3*(s - 1)*(s + 2)/13
Let x be (-1)/(-3)*9/540. Let g(h) be the third derivative of 0*h + 0 + 1/18*h**3 - 1/36*h**4 - 3*h**2 + x*h**5. Let g(a) = 0. What is a?
1
Let f(y) = 120*y**2 - 230*y + 110. Let z(p) = 11*p**2 - 21*p + 10. Let m(h) = -6*f(h) + 65*z(h). Let m(o) = 0. Calculate o.
1, 2
Suppose -1/2*o - 1/4*o**2 + 3/4 = 0. Calculate o.
-3, 1
Let z = 263/3 - 87. Suppose -3*g + 9 = -5*d - 0, 0 = -2*d + 5*g - 15. Factor 0*i**2 - 7/3*i**4 + d*i - 5/3*i**5 - z*i**3 + 0.
-i**3*(i + 1)*(5*i + 2)/3
Let d(m) be the third derivative of 2*m**6/15 - 4*m**5/15 - 7*m**4/6 - 4*m**3/3 + 13*m**2. Determine u so that d(u) = 0.
-1/2, 2
Let i(x) be the third derivative of -x**7/70 + x**5/10 - x**3/2 + 5*x**2. Suppose i(y) = 0. Calculate y.
-1, 1
Let w(x) be the third derivative of -x**7/11340 - x**6/3240 + x**5/270 - x**4/6 - 2*x**2. Let p(v) be the second derivative of w(v). Factor p(h).
-2*(h - 1)*(h + 2)/9
Let h(i) be the second derivative of -3*i**5/10 - 4*i**4/3 - 7*i**3/3 - 2*i**2 + 6*i. Factor h(b).
-2*(b + 1)**2*(3*b + 2)
Let s be (-21)/(-42) + 6/4. Factor -10/3*o**s + 10/3*o**3 - 5/3*o**4 + 1/3*o**5 + 5/3*o - 1/3.
(o - 1)**5/3
Let l(m) be the first derivative of 5/14*m**4 + 1 - 2/5*m**5 + 0*m**2 - 2/21*m**3 + 1/7*m**6 + 0*m. Let l(s) = 0. What is s?
0, 1/3, 1
Let g(r) be the first derivative of 2/15*r**3 + 2/25*r**5 + 5 + 0*r + 0*r**2 + 1/5*r**4. Factor g(q).
2*q**2*(q + 1)**2/5
Determine i so that -12*i**2 - 5*i**5 - 3*i**5 + 126*i**4 + 4*i**3 - 114*i**4 + 4*i = 0.
-1, 0, 1/2, 1
Let z(r) be the first derivative of -r**3/24 - 3*r**2/16 + r/2 + 24. Factor z(a).
-(a - 1)*(a + 4)/8
Let c(n) be the second derivative of 3/10*n**5 - 3/2*n**2 + 0 - 1/2*n**3 + 1/2*n**4 - 2*n - 1/14*n**7 - 1/10*n**6. Let c(b) = 0. What is b?
-1, 1
Let f(r) be the third derivative of -r**7/840 + r**5/40 + r**4/24 - 2*r**2. Let d(x) be the second derivative of f(x). Factor d(s).
-3*(s - 1)*(s + 1)
Let d(u) be the first derivative of -u**6/1620 - u**5/540 - u**3 + 2. Let x(c) be the third derivative of d(c). Find h such that x(h) = 0.
-1, 0
Let a(x) be the third derivative of -x**5/10 + x**4/8 + 18*x**2. Solve a(h) = 0 for h.
0, 1/2
Let y(b) = b**3 - 3*b**2 - 11*b + 5. Let f be y(5). Let -1/4*h**4 - 1/2*h**2 + f*h + 0 + 3/4*h**3 = 0. What is h?
0, 1, 2
Determine v so that -1 + 1/2*v**3 + 3/2*v - 3/2*v**4 + 9/2*v**2 = 0.
-1, 1/3, 2
Suppose 3*a - 22 = -4*w - 2*a, 0 = 2*w + 4*a - 14. Find k, given that -k**5 + 3*k**5 - 5*k**3 + 8*k**4 - 4 - 4*k**2 - 4*k**5 - 3*k**w + 10*k = 0.
-1, 1, 2
Let p(q) be the second derivative of 2*q**7/21 - 2*q**6/15 - 3*q**5/5 + q**4/3 + 4*q**3/3 + 36*q. Let p(y) = 0. What is y?
-1, 0, 1, 2
Let i be (44/3)/((-114)/(-15)). Let p = i + -5/19. Factor -3*l**2 + 13/3*l**3 - 1/3*l + 2/3 - p*l**4.
-(l - 1)**3*(5*l + 2)/3
Let j = 43 + -43. Let d(r) be the second derivative of 1/21*r**3 + 0*r**2 + 1/42*r