*d**2. Factor b(i).
-2*i*(3*i - 2)/3
Let h(u) be the third derivative of -u**8/8400 - u**7/2100 - u**3/3 - 5*u**2. Let q(p) be the first derivative of h(p). Factor q(i).
-i**3*(i + 2)/5
Factor 2/3 + 2/9*o**2 + 10/9*o - 2/9*o**3.
-2*(o - 3)*(o + 1)**2/9
Let f(u) = 11*u**3 - 126*u**2 + 954*u - 2554. Let v(s) = 155*s**3 - 1765*s**2 + 13355*s - 35755. Let q(o) = 85*f(o) - 6*v(o). Factor q(k).
5*(k - 8)**3
Let c(d) be the second derivative of d**6/240 + d**5/120 + d**2/2 - 3*d. Let g(x) be the first derivative of c(x). Factor g(t).
t**2*(t + 1)/2
Let j = -23 + 34. Suppose -x + j = 3*i, i + 5 = x + 2*i. Determine g so that -g**x - 1/2*g + 0 - 1/2*g**3 = 0.
-1, 0
Factor -3 + i**3 - 14*i**2 + 4*i + 5*i + 2*i**3 + 5*i**2.
3*(i - 1)**3
Let -24*a**2 + 0*a**3 + 4*a**4 - 12*a + 2*a**3 - 17*a**3 - 7*a**4 = 0. Calculate a.
-2, -1, 0
Let b(h) = 2*h**2 - 3*h + 3. Let w be b(2). Factor -4*k**5 + k**w + 8*k**3 - k**5 - 4*k.
-4*k*(k - 1)**2*(k + 1)**2
Let f(t) be the second derivative of 0 - 2/15*t**3 + 4*t - 1/30*t**4 - 1/5*t**2. Determine j, given that f(j) = 0.
-1
Let f(p) be the second derivative of p**8/8064 + 11*p**7/15120 + 7*p**6/4320 + p**5/720 + p**4/3 + 4*p. Let d(q) be the third derivative of f(q). Factor d(h).
(h + 1)**2*(5*h + 1)/6
Factor 1 + 4*d**3 - 5*d**3 + 0*d**3 - 3*d + 3*d**2.
-(d - 1)**3
Let f be 4/6 + (4 - (-427)/(-105)). Suppose 0 + 1/5*t**5 - 1/5*t**4 + 1/5*t**2 - f*t**3 + 2/5*t = 0. Calculate t.
-1, 0, 1, 2
Factor -z - 3*z**3 + z**2 + 0*z**2 + 5*z**3.
z*(z + 1)*(2*z - 1)
Let a(y) be the first derivative of 7*y**3/9 - y**2/3 - 6. Solve a(i) = 0.
0, 2/7
Let j(y) be the second derivative of y**7/60 - y**6/90 - 5*y**3/6 - 2*y. Let p(g) be the second derivative of j(g). Determine r so that p(r) = 0.
0, 2/7
Let p(u) = 7*u**2 - 2*u. Let c(k) = 10*k**2 - 3*k + 3. Let m(i) = 40*i**2 - 12*i + 13. Let w(b) = -26*c(b) + 6*m(b). Let j(f) = -14*p(f) - 5*w(f). Factor j(x).
2*x*(x - 1)
Suppose -m - 3*m = i + 5, 4*m = 4*i + 20. Determine q, given that m + 0*q**3 + 2/11*q**2 - 2/11*q**4 + 0*q = 0.
-1, 0, 1
Let m(u) be the first derivative of 1/4*u**2 + 0*u + 0*u**3 - 3 + 1/12*u**6 + 0*u**5 - 1/4*u**4. Determine k so that m(k) = 0.
-1, 0, 1
Let r be 10/45*54/3. Factor -1/2*a**2 - 1/6*a**r + 0 - 1/6*a - 1/2*a**3.
-a*(a + 1)**3/6
Let t(z) be the first derivative of z**4/8 - z**3/6 - z**2/4 + z/2 + 5. Solve t(h) = 0.
-1, 1
Let k(l) be the third derivative of 0 + 1/96*l**4 - 1/240*l**5 + 0*l**3 + 0*l + 2*l**2. Find b such that k(b) = 0.
0, 1
Let v(s) = -s + 3. Let w be v(-3). Let l(q) be the second derivative of 1/12*q**3 - q - 1/40*q**5 + 0*q**2 + 0 - 1/30*q**w + 1/12*q**4. Factor l(g).
-g*(g - 1)*(g + 1)*(2*g + 1)/2
Find s, given that 1 + 3/5*s**2 + 1/5*s**3 - 9/5*s = 0.
-5, 1
Let j be 70/42 - (-1)/(-6). Factor -1/2*r + 1/2*r**4 + 0 + j*r**2 - 3/2*r**3.
r*(r - 1)**3/2
Let r(h) = 18*h**4 + 22*h**3 - 12*h**2 - 24*h - 8. Let l(i) = i**3 + i**2. Let x(y) = 2*l(y) + r(y). Let x(g) = 0. What is g?
-1, -2/3, 1
Factor -l - 1/6*l**2 + 7/6.
-(l - 1)*(l + 7)/6
Let h(p) be the first derivative of -1 + 4*p - 2*p**2 + 1/3*p**3. Determine n so that h(n) = 0.
2
Let g(r) = 7*r**2 - 8*r - 5. Let a(v) = 8*v**2 - 9*v - 6. Let f(l) = l**2 - 7*l + 6. Let i = -6 - -13. Let u be f(i). Let z(w) = u*a(w) - 7*g(w). Factor z(b).
-(b - 1)**2
Let w(i) = i**3 + 9*i**2 - 9*i + 7. Let f be 5*1*(-8)/10. Let l(k) = k**3 + 1. Let o(x) = f*l(x) + w(x). Find p such that o(p) = 0.
1
Suppose -12*p = -15*p. Let v(q) = 2*q**2 - 2*q + 1. Let m be v(2). Determine h so that 2*h**4 + p + 0*h + 1/2*h**3 - h**2 - 3/2*h**m = 0.
-2/3, 0, 1
Let i(p) be the first derivative of p**8/4200 + p**7/2100 - p**6/900 - p**5/300 - p**3/3 - 3. Let f(k) be the third derivative of i(k). Factor f(z).
2*z*(z - 1)*(z + 1)**2/5
Let n = 25 + -23. Determine h so that -n*h**4 + 1/2*h - 9/2*h**2 + 1/2 + 11/2*h**3 = 0.
-1/4, 1
Let k be 14 + -14 + (-3)/(-9). What is w in 0 + 2/3*w + k*w**5 + 1/3*w**4 - w**3 - 1/3*w**2 = 0?
-2, -1, 0, 1
Let k(z) be the first derivative of -z**5/120 + z**4/48 + z**3/6 + z**2/2 - 1. Let f(q) be the second derivative of k(q). Determine g so that f(g) = 0.
-1, 2
Let g(q) = q**3 - 7*q**2 + 8*q - 10. Let z be g(6). Let a(b) be the first derivative of 3 + 2/9*b**3 + 0*b + 5/18*b**4 - 2/9*b**z. Factor a(m).
2*m*(m + 1)*(5*m - 2)/9
Let k(q) = 10*q + 50. Let d be k(-5). Let p(n) be the second derivative of d + n + 1/33*n**3 + 1/110*n**5 - 1/33*n**4 + 0*n**2. Determine b so that p(b) = 0.
0, 1
Suppose 17 = 3*b + 11. Solve 0 + 0*t - 2/7*t**4 + 2/7*t**3 + 2/7*t**b - 2/7*t**5 = 0.
-1, 0, 1
Suppose 48*x - 42 = 41*x. Let b(n) be the second derivative of 0*n**2 + 1/3*n**3 + 1/2*n**4 + 3/10*n**5 + 0 - 4*n + 1/15*n**x. Factor b(v).
2*v*(v + 1)**3
Let p be (-4 + 12/3)/(1 - -1). Factor 1/3*v**2 + 0 - 1/3*v**3 + p*v.
-v**2*(v - 1)/3
Suppose -1/5*u**2 - 4/5 - 4/5*u = 0. What is u?
-2
Let -2/9 + 2/9*g**3 + 2/3*g - 2/3*g**2 = 0. Calculate g.
1
Let j(l) = 2*l**2 + 34*l + 206. Let x(r) = 2*r**2 + 35*r + 205. Let z(f) = -5*j(f) + 6*x(f). Find d such that z(d) = 0.
-10
Let g(h) be the second derivative of -1/12*h**4 + 0 - 3*h - 1/3*h**3 + 0*h**2. Factor g(n).
-n*(n + 2)
Let a = 2 - 7. Let m be (a/(-10))/((-5)/(-2)). Let 1/5*z**3 + 1/5*z**4 + 0 - m*z**2 - 1/5*z = 0. What is z?
-1, 0, 1
Factor 1/3 - 1/6*f**2 + 1/6*f.
-(f - 2)*(f + 1)/6
Let y(x) be the first derivative of -x**6/15 + 8*x**5/25 - 3*x**4/5 + 8*x**3/15 - x**2/5 + 4. Solve y(l) = 0.
0, 1
Let c(h) be the second derivative of 0 - 5*h + 0*h**3 + 1/3*h**2 - 1/18*h**4. Factor c(w).
-2*(w - 1)*(w + 1)/3
Let b(i) be the first derivative of i**6/40 + i**5/10 - 3*i**2/2 - 2. Let v(q) be the second derivative of b(q). Factor v(g).
3*g**2*(g + 2)
Factor -2 + 11/3*z - 2*z**2 + 1/3*z**3.
(z - 3)*(z - 2)*(z - 1)/3
Let x be (-14)/4*3/(-90). Let r = x - -2/15. Factor 1/4*u**4 - 1/4*u**2 - 1/4*u**3 + 0 + r*u.
u*(u - 1)**2*(u + 1)/4
Let p(f) be the first derivative of 5*f**3/21 - 4*f**2/7 - 4*f/7 + 10. Factor p(v).
(v - 2)*(5*v + 2)/7
Let m = 4287841/260 + -66001/4. Let u = 132/13 + m. Factor 2/5*g**5 + 2/5*g + 0 + 12/5*g**3 + u*g**4 + 8/5*g**2.
2*g*(g + 1)**4/5
Let n(t) be the second derivative of t**6/150 - 3*t**5/100 + t**4/30 + 7*t. Determine r so that n(r) = 0.
0, 1, 2
Let b(w) be the first derivative of 1 - 1/54*w**4 - 1/9*w**3 - w - 2/9*w**2. Let i(m) be the first derivative of b(m). Factor i(r).
-2*(r + 1)*(r + 2)/9
Factor -2*i**2 + 0 - 4/3*i.
-2*i*(3*i + 2)/3
Let i(o) be the first derivative of o**4/4 + o**3 - 9*o**2/2 + 2*o - 2. Let b(d) be the first derivative of i(d). Factor b(q).
3*(q - 1)*(q + 3)
Let w = 100/309 - -1/103. What is p in w*p**2 + 1/3*p**3 + 0 - 2/3*p = 0?
-2, 0, 1
Determine d, given that -6*d**2 - d**3 + 2*d**2 - 3*d**3 = 0.
-1, 0
Let s(v) = v**2 + 10*v + 11. Let t be s(-9). Determine i so that 2*i + 0*i - i + i**t = 0.
-1, 0
Let r(b) be the second derivative of b**7/84 + b**6/30 + b**5/40 + 6*b. Suppose r(c) = 0. Calculate c.
-1, 0
Factor -4/9*j - 2/9 - 2/9*j**2.
-2*(j + 1)**2/9
Suppose 4*t + 54 = -0*q + 3*q, 3*t + 65 = 4*q. Solve q + 2*v + 2 + 6*v + v**2 = 0.
-4
Let a(g) be the third derivative of g**8/40320 - g**7/2520 + g**6/360 - g**5/20 - 3*g**2. Let b(t) be the third derivative of a(t). Factor b(i).
(i - 2)**2/2
Let t(v) be the third derivative of -1/90*v**5 + 4*v**2 + 1/126*v**8 - 1/35*v**7 + 0 + 0*v**4 + 1/30*v**6 + 0*v + 0*v**3. Factor t(f).
2*f**2*(f - 1)**2*(4*f - 1)/3
Suppose 0*w - 8 = 2*w. Let u = w - -6. Determine r so that 2 - u*r - r**2 - 2*r + 3*r = 0.
-2, 1
Factor 4/9*d**2 + 0 + 2/3*d**3 + 0*d + 0*d**4 - 2/9*d**5.
-2*d**2*(d - 2)*(d + 1)**2/9
Suppose 4*i = 2*a - 2 - 6, i - 3 = 3*a. Let y be ((-4)/16)/(i - -2). Find b such that y*b**2 - b + 1 = 0.
2
Let s(k) be the third derivative of -k**9/60480 + k**8/20160 + k**5/30 - 2*k**2. Let p(y) be the third derivative of s(y). What is r in p(r) = 0?
0, 1
Let n = -5/7 - -32/35. Let z(w) be the first derivative of 1 + 0*w**3 - n*w**4 + 2/5*w**2 - 2/25*w**5 + 2/5*w. Find t such that z(t) = 0.
-1, 1
Let 0*g - 1/3*g**5 - 2/3*g**4 - 1/3*g**3 + 0*g**2 + 0 = 0. What is g?
-1, 0
Let l(r) = 5*r**2 + 6*r - 3. Let x(f) = -11*f**2 - 12*f + 5. Let b(c) = -13*l(c) - 6*x(c). What is t in b(t) = 0?
3
Let p = -10 - -12. Suppose 3*b - 6 = -0*b. Let -3*v**b + 0 + v**4 + 1 + v**p = 0. What is v?
-1, 1
Let j = 13/1