2 - 4*x. Let t(k) be the second derivative of c(k). Factor t(q).
2*(q - 1)**3*(q + 1)
Let a(z) be the first derivative of z**8/1512 - z**7/315 + z**6/270 + 3*z**2 + 2. Let v(k) be the second derivative of a(k). Solve v(r) = 0.
0, 1, 2
Suppose 30 = -49*x + 54*x. Let r(b) be the second derivative of b + 0*b**5 + 0*b**3 - 1/15*b**x - b**2 + 1/3*b**4 + 0. Factor r(z).
-2*(z - 1)**2*(z + 1)**2
What is t in 1/3*t**3 + 0*t + 1/9*t**5 + 1/9*t**2 + 0 + 1/3*t**4 = 0?
-1, 0
Let o(r) = -r**5 - r**4 + r**3 - r**2 - 1. Let q(y) = -y + 4. Let x be q(2). Let h(s) = 2*s**4 + 4*s**3 - 1. Let f(p) = x*o(p) - 2*h(p). Factor f(z).
-2*z**2*(z + 1)**3
Suppose 4*m + m = 0. Suppose -5*p - 2*s + 23 = m, 6*s - 4 = 4*p + 2*s. Find g such that 0 + 0*g**2 + 1/4*g**5 + 0*g**4 - 1/4*g**p + 0*g = 0.
-1, 0, 1
Let h(p) be the second derivative of -p**5/5 - 2*p**4/3 + 2*p**3/3 + 4*p**2 - 3*p. Let h(o) = 0. Calculate o.
-2, -1, 1
Let r(h) = -h - 4. Let g(n) = -1. Let o(q) = 2*g(q) + r(q). Let b be o(-9). Let z**2 - 2 - 4*z + 2*z**2 + b*z**2 = 0. What is z?
-1/3, 1
Let y be (-13)/39 + (-7)/(-12). Factor -1/2*b**2 + y + 1/4*b.
-(b - 1)*(2*b + 1)/4
Let s(a) = 5*a. Let d be s(1). Let u(i) be the third derivative of 0*i + 0 - 1/10*i**d + 0*i**3 - 1/105*i**7 - 1/12*i**4 + 2*i**2 - 1/20*i**6. Factor u(f).
-2*f*(f + 1)**3
Factor 2/3*n**2 + 2 + 8/3*n.
2*(n + 1)*(n + 3)/3
Let i(n) be the third derivative of -1/180*n**5 - 1/72*n**4 + 0*n**3 + 0*n + 0 + 5*n**2. Factor i(v).
-v*(v + 1)/3
Suppose v - 35 = -33. Let k(a) be the third derivative of 1/24*a**4 - 1/9*a**3 + 0 - 4*a**v + 0*a - 1/180*a**5. Factor k(o).
-(o - 2)*(o - 1)/3
Let t(o) be the first derivative of -3*o**4/4 - 4*o**3 - 15*o**2/2 - 6*o + 41. Let t(g) = 0. What is g?
-2, -1
Suppose 4*t - 3 = 13. Factor -5*r**5 - r**4 + r**3 + r**t + 4*r**5.
-r**3*(r - 1)*(r + 1)
Let v(t) = -3*t - t**3 - 2*t + t - 3 + t**2. Let m(n) = -2*n**3 - 2 - 6 + n**2 + 3 - 7*n. Let q(w) = 3*m(w) - 5*v(w). Factor q(c).
-c*(c + 1)**2
Let s(w) be the second derivative of -w**5/150 - w**4/90 + 14*w. Factor s(f).
-2*f**2*(f + 1)/15
Let g(y) be the first derivative of 0*y - 1/5*y**2 - 1/15*y**6 - 1 - 3/5*y**4 + 8/25*y**5 + 8/15*y**3. Solve g(x) = 0.
0, 1
Let y = 49 + -95/2. Factor y + 15/2*l**2 + 6*l + 3*l**3.
3*(l + 1)**2*(2*l + 1)/2
Determine k so that -2/5*k + 1/5 + 1/5*k**2 = 0.
1
Let s = 1829/7 + -261. Let -s*a - 2/7*a**2 + 0 + 2/7*a**4 + 2/7*a**3 = 0. What is a?
-1, 0, 1
Let o be 3 - (3 + (2 - 4)). Suppose y = 2*y - o. Factor -3/4*v**y + 1/4*v**4 + 1/2*v + 0*v**3 + 0.
v*(v - 1)**2*(v + 2)/4
Let n(f) be the first derivative of -17*f**3 + 3*f**2 + 6. What is h in n(h) = 0?
0, 2/17
Let k(z) be the first derivative of 2*z**3/9 + 2*z**2 + 6*z + 3. Let k(n) = 0. What is n?
-3
Let p(b) be the second derivative of -b**5/10 + b**4/2 - 2*b**3/3 - 5*b. Let p(z) = 0. What is z?
0, 1, 2
Factor 3*f**2 - f + 31*f**3 + f**4 + 2 - 2 - 34*f**3.
f*(f - 1)**3
Let o(f) be the second derivative of -1/12*f**3 + 0*f**2 + 0 + 2*f + 1/24*f**4. Determine b, given that o(b) = 0.
0, 1
Suppose g - 10 = -4*g. Suppose -r = -p, 0 = 4*r + p - g*p. Find i such that -2/3*i**5 + 2/3*i + 4/3*i**4 - 4/3*i**2 + 0 + r*i**3 = 0.
-1, 0, 1
What is l in 2/5*l**3 - 1/5*l**5 + 6/5 - 1/5*l - 12/5*l**2 + 6/5*l**4 = 0?
-1, 1, 6
Suppose 2*t + 3*v - 3 = -t, 2*t = v + 8. Factor -11*p**3 - p**4 + 0*p**t - 39*p**4 - 18*p**5 + 3*p**3.
-2*p**3*(p + 2)*(9*p + 2)
Let d = 3 - 0. Let f = d - 3. Factor -2/7*x**3 + 2/7*x**2 + f + 0*x.
-2*x**2*(x - 1)/7
Let b(v) = v**3 + 11*v**2. Let n be b(-11). Factor -r**2 - r + n*r - r.
-r*(r + 2)
Let s be (3 - 11)/((-10)/2 - 0). Suppose 2/5*d**2 - s*d + 8/5 = 0. What is d?
2
Suppose 8/5*h**3 + 0*h - 2/5*h**5 - 32/5 - 6/5*h**4 + 32/5*h**2 = 0. What is h?
-2, 1, 2
Let f(a) = -10*a**2 + 9*a - 9. Let y(d) be the third derivative of -d**5/60 + d**4/24 - d**3/6 + 3*d**2. Let i(w) = 2*f(w) - 18*y(w). Factor i(j).
-2*j**2
Let f be 0 - (2 + 2) - (-440)/99. Factor -2/9*z + f*z**2 - 4/9 + 2/9*z**3.
2*(z - 1)*(z + 1)*(z + 2)/9
Let t be 3/2 + (-24)/16. Let v be 18/6 - (1 - 0). Solve -2*c**3 + 0 - 4/5*c**v + t*c = 0.
-2/5, 0
Suppose -x = -7 + 1. Let f(o) = -o**2 + 6*o + 4. Let m be f(x). Factor -i**m - 5*i**3 + 3*i**4 + 6*i**2 - 2*i - i**3.
2*i*(i - 1)**3
Let c(d) be the third derivative of 4/3*d**3 + 2*d**2 + 0 + 0*d - 7/30*d**5 + 0*d**4 + 1/20*d**6. Determine x, given that c(x) = 0.
-2/3, 1, 2
Let u = -56 + 117/2. Let -5/4*z - 1/4*z**5 + 1/4 - 5/2*z**3 + 5/4*z**4 + u*z**2 = 0. Calculate z.
1
Let 21 - 3/2*k**4 + 33/2*k**3 + 117/2*k**2 + 123/2*k = 0. What is k?
-1, 14
Factor -104*i + 104*i + 3*i**2 - 3.
3*(i - 1)*(i + 1)
Determine l so that 5/4 - 4*l + 9/2*l**2 + 1/4*l**4 - 2*l**3 = 0.
1, 5
Let j be ((-27)/6 + 3)*6. Let o(q) = -q**2 - 10*q - 6. Let t be o(j). Factor -2*n - n + 2*n - 1 + n**t - 3*n**2 + 4*n.
(n - 1)**3
Let m(v) = 3*v**2 + 2*v + 1. Let g be m(-1). Let q be 4/(-1) - (-29)/g. Let 6 - q*p**3 + 18*p - 27/2*p**2 = 0. What is p?
-2, -2/7, 1
Let h(q) = -8*q**4 + 4*q**2 - 2. Let j(a) = -9*a**4 + a**3 + 3*a**2 - a - 2. Let f(d) = 4*h(d) - 3*j(d). Suppose f(i) = 0. Calculate i.
-1, 2/5, 1
Let d(m) be the third derivative of 1/600*m**6 + 1/300*m**5 + 0 + 0*m**4 - 4*m**2 + 0*m**3 + 0*m. Factor d(w).
w**2*(w + 1)/5
Let o = -50 - -28. Let t be (-4)/6*o/33. Factor 4/9*w**2 - 10/9*w - t + 10/9*w**3.
2*(w - 1)*(w + 1)*(5*w + 2)/9
Let y be 14/6 + (-1 - 0). Suppose 2*f = r - 20, -18 + 13 = -r - f. Determine i so that -r*i**3 + y*i - 14/3*i**5 + 2/3*i**2 + 0 + 38/3*i**4 = 0.
-2/7, 0, 1
Let k(t) be the third derivative of t**5/12 - 5*t**3/6 + 10*t**2 - 1. Factor k(z).
5*(z - 1)*(z + 1)
Determine g, given that -2 + 6*g**3 + 12*g + 6 + 0 + 13*g**2 + g**4 = 0.
-2, -1
Determine f, given that 1/5*f**2 + 4/5 - 4/5*f = 0.
2
Let r(z) be the second derivative of 56*z**7 + 28*z**6/5 - 333*z**5/20 - z**4 + 2*z**3 - 16*z. Solve r(i) = 0.
-2/7, 0, 1/4
Let a(v) be the second derivative of 9/70*v**5 + 1/21*v**4 + 0*v**2 + 0 + 0*v**3 - 2*v. Factor a(m).
2*m**2*(9*m + 2)/7
Suppose 2*m + 3*c = -3, 2*m - c + 5 = -10. Let n be 1 + (1 - m/(-5)). Find f such that 2/5 - n*f + 2/5*f**2 = 0.
1
Let u(y) be the first derivative of y**5/30 + y**4/12 - 5*y**2/2 + 4. Let h(d) be the second derivative of u(d). Solve h(n) = 0 for n.
-1, 0
Let c(m) = -4*m**2 - 6*m - 5. Let z(w) = 3*w**2 + 5*w + 4. Let n(y) = 4*c(y) + 5*z(y). Factor n(h).
-h*(h - 1)
Let d(q) be the first derivative of q**4/28 - 4*q**3/21 + 5*q**2/14 - 2*q/7 - 23. Determine o so that d(o) = 0.
1, 2
Let k(g) = g - 5. Let r be k(7). Suppose -5*j + 7 = -3. Factor -d + r - d**j + 3*d**2 + 5*d.
2*(d + 1)**2
Factor 2/7 - 10/7*z**2 - 8/7*z.
-2*(z + 1)*(5*z - 1)/7
Suppose 20 = -3*a - 22. Let m = a - -14. Factor m*g**2 + 3/2*g**4 - 9/2*g**5 + 0 + 3*g**3 + 0*g.
-3*g**3*(g - 1)*(3*g + 2)/2
Let c be ((-2)/32 + 0)*4/(-9). Let z(j) be the second derivative of 0 - 1/60*j**5 - 1/90*j**6 + c*j**4 - 3*j + 1/18*j**3 + 0*j**2. Factor z(t).
-t*(t - 1)*(t + 1)**2/3
Let l(k) be the second derivative of k**5/5 - 4*k**4/3 + 10*k**3/3 - 4*k**2 + 14*k. Factor l(d).
4*(d - 2)*(d - 1)**2
Let r(u) be the first derivative of -u**5/40 - u**4/24 - u + 1. Let x(v) be the first derivative of r(v). Let x(h) = 0. Calculate h.
-1, 0
Factor 5/2*h**2 + 5/2*h**3 + 0 - 15*h.
5*h*(h - 2)*(h + 3)/2
Let q(l) be the second derivative of l**7/399 + l**6/57 + l**5/19 + 5*l**4/57 + 5*l**3/57 + l**2/19 - 9*l. Factor q(w).
2*(w + 1)**5/19
Let n = 120 - 116. Let 8/7*o**2 + 0 - 8/7*o**3 + 0*o + 2/7*o**n = 0. Calculate o.
0, 2
Let d(w) be the second derivative of 4*w**7/21 + 2*w**6/3 - 4*w**5/5 - 19*w**4/3 - 32*w**3/3 - 8*w**2 + 9*w. Find j such that d(j) = 0.
-2, -1, -1/2, 2
Let n(j) be the second derivative of 25*j**4/6 + 15*j**3/2 + 5*j**2 + 12*j. Suppose n(o) = 0. Calculate o.
-1/2, -2/5
Find y, given that 1/4 - 1/4*y**2 + 1/4*y - 1/4*y**3 = 0.
-1, 1
Let r(i) be the first derivative of -4/15*i**3 + 0*i**2 - 1/15*i**6 + 0*i**5 + 5 + 3/10*i**4 + 0*i. Factor r(d).
-2*d**2*(d - 1)**2*(d + 2)/5
Let f(c) = -c**2 - 3*c + 2. Let v(m) be the first derivative of -m**3/3 - m**2 + 2*m - 1. Let j(h) = -3*f(h) + 4*v(h). Solve j(q) = 0 for q.
-1, 2
Factor -2/11*p**3 - 4/11*p**2 + 0 + 2/11*p**4 + 0*p.
2*p**2*(p - 2)*(p + 1)/11
Factor 0 + 5/4*u + 1/4*u**2.
u*(u + 5)/4
Let y(w) be the second derivative of -1/90*w**5 + 2/9*w**2 + 