f. Let x(c) = -6*d(c) + 34*s(c). What is w in x(w) = 0?
-1/2, 0, 3
Suppose 4*b + 5*v = 16, -5 = b + 2*v - 9. Determine j, given that 0 + 0*j**b + 0*j + 3/4*j**3 + 0*j**2 - 3/4*j**5 = 0.
-1, 0, 1
Suppose 0 = -0*a + 3*a - 9. Find k such that 50*k**5 + 13*k**4 + 12*k**3 + 27*k**4 - 2*k**3 - 2*k**a = 0.
-2/5, 0
Let c(v) be the third derivative of -v**8/560 + 3*v**6/40 - v**5/10 - 3*v**4/2 + 36*v**3/5 - 27*v**2. Suppose c(f) = 0. Calculate f.
-3, 2
Let z(c) be the third derivative of c**8/3360 + c**7/1680 - c**3/2 - 2*c**2. Let y(d) be the first derivative of z(d). Factor y(x).
x**3*(x + 1)/2
Let u(g) be the second derivative of -g**7/21 - 17*g**6/60 - 2*g**5/5 + 13*g**4/24 + 5*g**3/3 + g**2 + 25*g. What is o in u(o) = 0?
-2, -1, -1/4, 1
Let g(u) be the second derivative of 3*u**5/10 + 5*u**4/4 + u**3 + 5*u. Factor g(s).
3*s*(s + 2)*(2*s + 1)
Let h(l) be the first derivative of -l**3/9 - 2*l**2/3 - 9. Factor h(o).
-o*(o + 4)/3
Suppose -3*j + 2*j + 2 = 0. Find g such that -10*g**3 + 18*g**2 - 14*g + j*g**4 + 1 + 7 - 4 = 0.
1, 2
Let n be (-3)/4*(12 + 24). Let o = -24 - n. Find f, given that 0*f + 0 + 1/3*f**o + 2/3*f**2 = 0.
-2, 0
Let k be (-4 + 5 + -2)*(-4)/1. Let -1/3*q - 1/3*q**k - q**3 - q**2 + 0 = 0. What is q?
-1, 0
Factor 6*j**3 + 5*j**4 - 10*j**3 - 6*j**3.
5*j**3*(j - 2)
Let p(a) be the second derivative of -a**4/12 - a**3/3 - a**2/2 + 7*a. Suppose p(d) = 0. What is d?
-1
Let s = -11 - -9. Let y be 1/s + (-22)/(-28). Determine d, given that 2/7*d**2 + 0 + 2/7*d**5 + 0*d - y*d**3 - 2/7*d**4 = 0.
-1, 0, 1
Let f(s) be the first derivative of -s**7/420 + s**6/180 + s**5/60 - s**4/12 - s**3/3 + 1. Let z(q) be the third derivative of f(q). What is d in z(d) = 0?
-1, 1
Let v be ((-2)/6)/((-26)/(-24)). Let y = v - -46/65. Factor -y*h + 0 - 2/5*h**2.
-2*h*(h + 1)/5
Let g = -1/12 + 1/3. Let u be (-4)/(-24) - 34/(-12). Let -g*p + 1/4 + 1/4*p**u - 1/4*p**2 = 0. What is p?
-1, 1
Suppose -10/3*g**3 - 4*g**2 + 0 - 2/3*g = 0. Calculate g.
-1, -1/5, 0
Suppose 4*h + 31 + 9 = 5*l, -4*h - 8 = 3*l. Factor -1/2*f**2 + 1/6*f**l - 1/6*f + 1/6*f**3 + 1/3.
(f - 1)**2*(f + 1)*(f + 2)/6
Let x be (-1 + (-14)/(-8))*2*2. Factor -1/2*a - 1/2*a**5 + a**2 - 1/2 + a**x - 1/2*a**4.
-(a - 1)**2*(a + 1)**3/2
Let u be (-4)/(8 + 0) + (-145)/(-130). Solve -2/13*x**2 - 6/13 + u*x = 0 for x.
1, 3
Let z(w) be the second derivative of -w**7/420 - w**6/90 + w**3/6 - 3*w. Let b(o) be the second derivative of z(o). Factor b(q).
-2*q**2*(q + 2)
Let o(z) be the first derivative of -2*z**6/21 - 4*z**5/35 + 2*z**4/7 - 6. Solve o(k) = 0 for k.
-2, 0, 1
Let i = -6/19 + 37/57. Let g(o) be the second derivative of -5/9*o**3 - 5/9*o**4 - o - 1/3*o**2 - 1/9*o**6 - i*o**5 - 1/63*o**7 + 0. Find f such that g(f) = 0.
-1
Let t(c) be the third derivative of 2*c**2 + 0*c + 1/150*c**5 + 1/30*c**4 + 0 + 1/15*c**3. Factor t(p).
2*(p + 1)**2/5
Let p = -6/163 - -368/1141. Factor 0*f + p*f**3 - 1/7*f**2 + 0.
f**2*(2*f - 1)/7
Let d = -20 - -20. Suppose 2/11*q + d - 2/11*q**2 = 0. What is q?
0, 1
Let q(k) be the first derivative of 1/210*k**5 - 1/84*k**4 + 2 - 1/2*k**2 + 0*k**3 + 0*k. Let b(m) be the second derivative of q(m). Factor b(r).
2*r*(r - 1)/7
Let a(b) be the second derivative of 2/9*b**2 - 7/90*b**5 - 2*b - 1/9*b**3 - 2/9*b**4 + 0. Find p such that a(p) = 0.
-1, 2/7
Let g(f) be the third derivative of -1/48*f**4 + 0*f + 0*f**3 + 1/240*f**5 + 1/480*f**6 + 0 - 2*f**2. Factor g(c).
c*(c - 1)*(c + 2)/4
Factor 6*m**2 - 15*m**2 + 12*m**4 + 2*m**4 - 8*m - 15*m**2 + 18*m**3.
2*m*(m - 1)*(m + 2)*(7*m + 2)
Suppose -25 = 5*i + 5*a, -2*a - 9 + 1 = 0. Let j be 0 - i - (-2)/(-6). Factor 1/3 - 2/3*l + 0*l**2 + j*l**3 - 1/3*l**4.
-(l - 1)**3*(l + 1)/3
Find j such that -4/3*j**5 + 1/3*j**4 - 4/3*j + 1/3 - 2/3*j**2 + 8/3*j**3 = 0.
-1, 1/4, 1
Let n(b) be the second derivative of -b**7/105 - b**6/25 + b**5/50 + 7*b**4/30 - 4*b**2/5 + 7*b. Let n(i) = 0. What is i?
-2, -1, 1
Let s(j) be the second derivative of -1/21*j**3 + 1/70*j**5 + 0*j**2 + 1/21*j**4 - 2/105*j**6 + 0 + 5*j. Find y, given that s(y) = 0.
-1, 0, 1/2, 1
Let k(o) = o**3 + o**2 - o. Let q(d) = -21*d**4 + 3*d**3 - 3*d**2 + 3*d. Let c(s) = -3*k(s) - q(s). Let c(x) = 0. What is x?
0, 2/7
Let f(p) be the third derivative of 0 + 2*p**2 + 0*p**3 + 1/15*p**5 - 1/120*p**6 + 0*p - 1/6*p**4. Solve f(l) = 0.
0, 2
Suppose 12*y + 87 - 81 + 4*y**2 - y**3 - y = 0. Calculate y.
-1, 6
Suppose -12 = -3*x + p, 4*x - 2*p = -6*p. Determine c so that -3/5*c**2 - 1/5*c**x - 1/5 - 3/5*c = 0.
-1
Let z(t) be the first derivative of -1/6*t**3 - 9 - 1/2*t + 1/2*t**2. Factor z(w).
-(w - 1)**2/2
Let j(i) be the second derivative of i**7/630 + i**6/360 - i**5/180 - i**4/72 + 3*i**2/2 + 3*i. Let s(n) be the first derivative of j(n). Factor s(l).
l*(l - 1)*(l + 1)**2/3
Let c(v) = -2*v**4 - 18*v**3 - 34*v**2 - 30*v - 6. Let z(j) = 3*j**4 + 35*j**3 + 67*j**2 + 61*j + 11. Let u(q) = -5*c(q) - 2*z(q). Factor u(i).
4*(i + 1)**3*(i + 2)
Let x(l) = -l**4 - 2*l. Let g(c) = 2*c**4 - c**3 + 7*c. Let d(i) = -2*g(i) - 7*x(i). Let d(o) = 0. What is o?
-2/3, 0
Let f(n) be the first derivative of n**4/24 + 7*n**3/18 + 5*n**2/4 + 3*n/2 - 55. Factor f(p).
(p + 1)*(p + 3)**2/6
Determine p so that -4/3*p**2 + 7/6*p - 1/3 + 1/3*p**4 - 1/6*p**5 + 1/3*p**3 = 0.
-2, 1
Let n(d) be the third derivative of -d**9/30240 + d**8/6720 + d**7/5040 - d**6/720 - d**4/24 - 5*d**2. Let s(v) be the second derivative of n(v). Factor s(o).
-o*(o - 2)*(o - 1)*(o + 1)/2
Let q(c) = -c**2 - c - 2. Let x(g) = 16*g**2 + 14*g + 10. Let v(m) = -6*q(m) - x(m). Factor v(s).
-2*(s + 1)*(5*s - 1)
Let z(f) = f**2 + 5*f + 2. Let h be z(-5). Find s such that -2/11*s**h - 2/11*s + 0 = 0.
-1, 0
Let r(u) be the second derivative of -u**6/30 + 7*u**5/20 - 5*u**4/4 + 13*u**3/6 - 2*u**2 + 17*u - 2. Factor r(f).
-(f - 4)*(f - 1)**3
Let t(r) be the third derivative of r**6/1260 - r**5/210 + r**4/84 + 2*r**3/3 - 2*r**2. Let a(k) be the first derivative of t(k). Suppose a(v) = 0. Calculate v.
1
Let i(n) = 4*n**5 + 2*n**4 - 4*n**3 - 12*n**2 - 4*n. Let c(o) = -o**5 - o**3 + o**2. Let j(a) = 2*c(a) + i(a). Factor j(p).
2*p*(p - 2)*(p + 1)**3
Let l(k) be the second derivative of -k**5/20 + k**3/6 + 5*k. Factor l(i).
-i*(i - 1)*(i + 1)
Factor 0*a**4 - 3*a**4 - 9*a**5 + 5*a**3 - a**2 + 0*a**4.
-a**2*(a + 1)*(3*a - 1)**2
Let s(w) be the first derivative of 2 - 1/6*w**4 + 0*w**2 + w - 1/3*w**3. Let y(l) be the first derivative of s(l). Factor y(v).
-2*v*(v + 1)
Let h(k) = -k**3 + 3*k**2 + 8*k - 4. Let u be h(5). Let o(x) = -x - 14. Let l be o(u). Factor -2/9*b**2 + l*b + 0.
-2*b**2/9
Suppose 7*i - 5*i = 24. Suppose 0*l - i = -4*l. Factor 0 - 16*c**l + 32/3*c**4 + 6*c**2 - 2/3*c.
2*c*(c - 1)*(4*c - 1)**2/3
Factor -2/3*b**3 + 4/3 + 2/3*b + 2/3*b**4 - 2*b**2.
2*(b - 2)*(b - 1)*(b + 1)**2/3
Let i(v) be the first derivative of 8*v**6/21 - 48*v**5/35 + 47*v**4/28 - 13*v**3/21 - 3*v**2/14 + v/7 + 2. Suppose i(c) = 0. What is c?
-1/4, 1/4, 1
Let w(a) be the third derivative of 1/480*a**5 + 0*a + 0 - 1/96*a**4 + 3*a**2 + 1/48*a**3. Factor w(n).
(n - 1)**2/8
Let w = -35/9 + 5. Factor -2/9 + w*a - 8/9*a**2.
-2*(a - 1)*(4*a - 1)/9
Let z(b) be the third derivative of b**8/288 - b**7/140 - 19*b**6/720 + 41*b**5/360 - b**4/6 + b**3/9 + 8*b**2. Factor z(i).
(i - 1)**3*(i + 2)*(7*i - 2)/6
Let s be (-12)/(-24) - 3/10. Factor 1/5*m**4 + 3/5*m**2 + 0 - 3/5*m**3 - s*m.
m*(m - 1)**3/5
Let h(k) = 7*k**2 + 3*k. Let o(j) = 3*j**2 + j. Let f(d) = -4*h(d) + 10*o(d). Factor f(x).
2*x*(x - 1)
Suppose 2 = 3*i - o, 4*i - o = 6 - 4. Let s(b) be the first derivative of b**4 - 2/3*b**3 + i*b - 2/5*b**5 + 0*b**2 - 2. Factor s(t).
-2*t**2*(t - 1)**2
Let o = -151/3 + 51. Suppose 0 = -62*b + 58*b + 8. Let 0 + o*v**b + 0*v = 0. What is v?
0
Let d(a) be the second derivative of a**7/2520 - a**6/360 + a**4/18 + 2*a**3/3 + 6*a. Let k(m) be the second derivative of d(m). Factor k(w).
(w - 2)**2*(w + 1)/3
Let w be 2/(1/((-7)/(-35))). Factor -2/5 + 0*b + w*b**2.
2*(b - 1)*(b + 1)/5
Let d = 352 - 3164/9. Factor -2/9*i**2 - 2/9*i + d.
-2*(i - 1)*(i + 2)/9
What is n in -9/2*n - 3 + 3/2*n**3 + 0*n**2 = 0?
-1, 2
Let r(j) be the first derivative of -6*j - j**3 - 9/2*j**2 + 1. Find s such that r(s) = 0.
-2, -1
Let w(g) = -g - 2 + 6 + 2*g. Let j be w(-2). Solve 2*k**2 + 8*k - 2*k - j*k + 4 + 2*k = 0 for k.
-2