actor -b*f**2 + 0*f**2 + 3*f**4 + f**2 - f**2.
3*f**2*(f - 1)*(f + 1)
Let v(t) be the third derivative of -t**6/80 + t**5/5 - t**4 - 65*t**2. Find y, given that v(y) = 0.
0, 4
Let j be (-6)/8*(-8)/9. Suppose 3*x + 3 = 0, -3*i + x = -8*i + 14. Factor -2/3*p**5 + 0*p + 0*p**2 + 0*p**4 + j*p**i + 0.
-2*p**3*(p - 1)*(p + 1)/3
Find t such that 7/3*t**3 - 4/3 + 4/3*t**2 - 7/3*t = 0.
-1, -4/7, 1
Let i(r) be the second derivative of r**6/36 - r**5/8 - 5*r**4/18 - r + 21. Factor i(o).
5*o**2*(o - 4)*(o + 1)/6
Let h be (-12)/(-70) + (-4)/(-10). Let l(b) = b**3 + 18*b**2 + 31*b - 16. Let d be l(-16). Factor 0*p**2 + h*p**3 + d*p**4 - 2/7*p + 0 - 2/7*p**5.
-2*p*(p - 1)**2*(p + 1)**2/7
Let t(n) be the first derivative of 7*n**6/18 - 3*n**5/5 + n**4/6 + 5. Factor t(q).
q**3*(q - 1)*(7*q - 2)/3
Let y(n) = -2*n**3 + n + 1. Suppose 0 = 2*x + 2*x + v + 7, x - 11 = 4*v. Let o(g) = g**3 - g - 1. Let c(j) = x*o(j) - y(j). What is s in c(s) = 0?
0
Let y be -3*6*(-2)/9. Let w(r) = r**3 + 3*r**2 - 4*r + 3. Let n be w(-4). Suppose 2*c**y + 3*c**n - 3*c - 8 - 5*c + 5*c**3 + 6*c**2 = 0. Calculate c.
-2, -1, 1
Let c(p) be the third derivative of 0*p**4 - 1/360*p**6 + 0*p - 3*p**2 - 1/180*p**5 + 0 + 0*p**3. Suppose c(l) = 0. Calculate l.
-1, 0
Suppose -4*h + 10 = 2. Solve -h*i**3 + i + 3*i**3 - 2*i = 0.
-1, 0, 1
Let y(a) be the third derivative of a**8/168 - 4*a**7/105 + a**6/20 - 7*a**2. Suppose y(j) = 0. Calculate j.
0, 1, 3
Suppose 10 = -6*t + 11*t. Factor -5*q**t - 2*q**3 + 0*q**3 + 7*q**2.
-2*q**2*(q - 1)
Let k be 1/(-3) - (-35)/21. Let -k + 2/3*f + 2/3*f**2 = 0. What is f?
-2, 1
Let v(j) be the third derivative of 2*j**7/105 + 4*j**6/15 + 2*j**5/5 - 4*j**4/3 - 14*j**3/3 + 4*j**2. Factor v(f).
4*(f - 1)*(f + 1)**2*(f + 7)
Let u(w) = w + 19. Let y be u(-11). Solve -8*q - 6*q**4 + 12*q**2 + 2*q**4 + y*q**4 - 8*q**4 = 0.
-2, 0, 1
Let f(a) be the third derivative of a**6/90 - 7*a**5/45 + 5*a**4/6 - 2*a**3 + 33*a**2. Solve f(s) = 0 for s.
1, 3
Let g = 9 - 1. Factor 3*c**2 - 5*c**4 - 11*c**2 - g*c + 14*c**3 + c**4 + 0*c**4.
-2*c*(c - 2)**2*(2*c + 1)
Let a = 1 + 2. Let m = -1 + a. Let 2/7*h**3 + 0 + 0*h**m + 0*h - 12/7*h**4 + 18/7*h**5 = 0. What is h?
0, 1/3
Let -21/5*l**2 + 9/5*l + 0 + 12/5*l**3 = 0. What is l?
0, 3/4, 1
Let o = -1 - 3. Let q(p) = 2*p**3 - 8*p**2 - 14*p. Let f(w) = w**3 - w + 1. Let v(c) = o*f(c) + q(c). Factor v(i).
-2*(i + 1)**2*(i + 2)
Let w(z) be the second derivative of z**5/10 + z**4/6 - 2*z**3/3 - 38*z. Determine f, given that w(f) = 0.
-2, 0, 1
Suppose -3*f = 3 - 9. Factor -3*b - b**2 - 2*b**f - 3*b + 3*b.
-3*b*(b + 1)
Let u(a) be the second derivative of -a**5/210 - a**4/84 + 3*a**2/2 + a. Let c(p) be the first derivative of u(p). Factor c(k).
-2*k*(k + 1)/7
Let t(y) be the second derivative of y**6/60 - y**5/24 - y**4/72 + 5*y**3/36 - y**2/6 - 9*y. Factor t(x).
(x - 1)**2*(x + 1)*(3*x - 2)/6
Let n(u) = -7*u**2 + 8*u + u**2 - 2*u**2 - 3 + u**3. Let p be n(7). Factor 5 - 3 + 2*b**2 - p.
2*(b - 1)*(b + 1)
Suppose 5*p = 6*p + 8*p. Factor p + 2/9*j**4 - 2/9*j - 2/9*j**2 + 2/9*j**3.
2*j*(j - 1)*(j + 1)**2/9
Let y(l) = -l - 1. Let f(g) = -4*g**3 - 5*g - 4*g**2 + 5 - 19*g - 29 + 0*g**3. Let z(i) = f(i) - 24*y(i). What is u in z(u) = 0?
-1, 0
Suppose 8/3 + 4*a + 4/3*a**2 = 0. What is a?
-2, -1
Let k(x) = x**2 + 1. Let u(q) = -3*q**2 + 6*q - 3. Let z(i) = 6*k(i) + u(i). What is s in z(s) = 0?
-1
Let x(y) be the first derivative of 1/6*y**2 + 1/18*y**6 + 0*y**5 + 0*y**3 - 1/6*y**4 + 0*y - 3. Let x(f) = 0. What is f?
-1, 0, 1
Factor -264*k**3 - k**4 - 2*k**2 - 264*k**3 + 531*k**3.
-k**2*(k - 2)*(k - 1)
Let z(s) be the second derivative of -s**8/1344 - s**7/210 - s**6/80 - s**5/60 - s**4/96 - 4*s**2 - 4*s. Let g(q) be the first derivative of z(q). Factor g(n).
-n*(n + 1)**4/4
Let r(k) be the second derivative of -1/70*k**5 + 1/21*k**3 - 2*k + 0 - 1/7*k**2 + 1/42*k**4. Solve r(n) = 0 for n.
-1, 1
Suppose 3*w + 4*h = w + 26, 0 = 5*h - 25. Factor 28*r + 5*r**2 - 31*r - 2*r**2 - 3*r**4 + 3*r**w.
-3*r*(r - 1)**2*(r + 1)
Let d be -1 - (-48)/6 - 4. Let i(b) be the first derivative of 0*b + 3 + 0*b**4 + 4/15*b**5 + 1/3*b**2 - 4/9*b**d - 1/9*b**6. Factor i(z).
-2*z*(z - 1)**3*(z + 1)/3
Let a = 5 - 8. Let u = 7 + a. Find w, given that u + 5*w + 7*w - 3*w**2 - 16 = 0.
2
Let c(o) = 5*o**5 + 5*o**4 + 3*o**3 - o**2 + 4*o + 4. Let h(j) = -11*j**5 - 11*j**4 - 7*j**3 + 2*j**2 - 9*j - 9. Let i(g) = 9*c(g) + 4*h(g). Factor i(x).
x**2*(x - 1)*(x + 1)**2
Let c(b) be the second derivative of -1/10*b**6 + 0*b**4 + 3/2*b**2 + 3*b + 0 + 3/10*b**5 - b**3. Let c(y) = 0. What is y?
-1, 1
Let q(w) be the second derivative of -7*w + 1/4*w**4 + 0 + 6*w**2 - 2*w**3. Find s, given that q(s) = 0.
2
Let y(p) be the second derivative of p**4/78 - 5*p**3/39 + 4*p**2/13 - 8*p. Determine b so that y(b) = 0.
1, 4
Let r(x) be the first derivative of -x**4/18 - 8*x**3/27 - 5*x**2/9 - 4*x/9 - 2. Factor r(t).
-2*(t + 1)**2*(t + 2)/9
Let r(z) be the third derivative of -z**7/42 + z**6/4 - z**5/12 - 5*z**4 - 40*z**3/3 + 27*z**2. Let r(d) = 0. Calculate d.
-1, 4
Let c(o) = -o**2 - 6*o - 6. Suppose -j + 16 = -5*j. Let v be c(j). Find b such that 0*b + 1/2*b**4 + 1/2*b**v + b**3 + 0 = 0.
-1, 0
Let m(i) be the second derivative of -i**7/630 - i**6/180 - 5*i**4/12 + 4*i. Let u(k) be the third derivative of m(k). Factor u(o).
-4*o*(o + 1)
Let d(m) = -m**3 - 6*m**2 - 3*m - 15. Let w be d(-6). Factor 2/7*s**w + 0 - 2/7*s**4 + 2/7*s**2 - 2/7*s.
-2*s*(s - 1)**2*(s + 1)/7
Suppose -4*k - x + 2*x = -15, 3*k - 4*x - 21 = 0. Suppose k*r + 21 = 4*u, u + r - 5*r - 15 = 0. Factor -9/4*h + 3*h**2 + 1/2 - 5/4*h**u.
-(h - 1)**2*(5*h - 2)/4
Let t(i) be the third derivative of 1/120*i**6 + 0 - 1/24*i**4 + 0*i - 1/60*i**5 + 1/6*i**3 - i**2. Determine y so that t(y) = 0.
-1, 1
Suppose 17 + 19 = 9*k. Let s(a) be the first derivative of 0*a + 3/4*a**k - 5 + a**3 - 3/2*a**2 - 3/5*a**5. What is n in s(n) = 0?
-1, 0, 1
Let j(y) be the first derivative of -2/3*y**3 + 1/2*y**4 - 2 - 1/3*y**6 + 0*y + 0*y**2 + 2/5*y**5. Factor j(n).
-2*n**2*(n - 1)**2*(n + 1)
Let l(j) be the first derivative of 7*j**3/9 + 8*j**2/3 + 4*j/3 - 8. Factor l(p).
(p + 2)*(7*p + 2)/3
Let u = 0 + -4. Let z(k) = k**2 + 1. Let w(p) = 5*p**2 + p + 5. Let h(j) = u*w(j) + 22*z(j). Factor h(q).
2*(q - 1)**2
Suppose -t = 5*i - 22, -2*t + t - i = -6. Suppose 5 = m + t. Solve -3*h**4 + h**4 + 3*h**2 + 0*h + m*h**4 + 3*h**3 + h = 0 for h.
-1, 0
Suppose -4*k + 9 = -k. Factor -16 + 3*y**4 + 9*y**3 + y**4 - 16*y + 7*y**3 + k*y**2 + 9*y**2.
4*(y - 1)*(y + 1)*(y + 2)**2
Let i be (-104)/(-24) + (-4)/(-6). Factor 0*l**3 + 0 + 4/3*l**4 - 4/3*l**2 - 2/3*l**i + 2/3*l.
-2*l*(l - 1)**3*(l + 1)/3
Determine f, given that 3*f**5 - 3*f + 5*f + 9*f**3 - f**5 - 13*f**3 = 0.
-1, 0, 1
Suppose 5*i - 21 = 2*f, 18*f - 20*f + 3*i = 11. Let 0*g**f - 1/5*g**3 + 1/5*g + 0 = 0. What is g?
-1, 0, 1
Let a(t) = 2*t**2 + t - 3. Let l be ((-15)/10)/((-1)/4). Let s(u) = -3*u**2 + 3. Let w(r) = l*a(r) + 5*s(r). Factor w(b).
-3*(b - 1)**2
Let l = -103/30 - -7/2. Let a(h) be the third derivative of l*h**5 + 0*h**3 - 8/105*h**7 + 1/36*h**4 + 2*h**2 + 0*h + 1/180*h**6 + 2/63*h**8 + 0. Factor a(j).
2*j*(j - 1)**2*(4*j + 1)**2/3
Suppose 4/7 + 4/7*u - 4/7*u**2 - 4/7*u**3 = 0. What is u?
-1, 1
Let t(c) be the first derivative of -c**2/2 + 4*c + 8. Let r be t(2). Find g such that 1/4*g + 1/4*g**r + 0 = 0.
-1, 0
Let d(n) = n**2 - n. Let w(c) = -3*c**2 + 3*c. Suppose -4*x - 72 = -20. Let l = -8 - x. Let s(h) = l*d(h) + 2*w(h). Let s(k) = 0. What is k?
0, 1
Let j(r) be the third derivative of 1/455*r**7 + 7/780*r**6 + 0*r + 0*r**4 + 1/195*r**5 + 0*r**3 - 5*r**2 + 0. Factor j(x).
2*x**2*(x + 2)*(3*x + 1)/13
Let q(d) = -9*d**2 + 6*d + 11. Let i(s) = 35*s**2 - 25*s - 45. Let r(x) = 4*i(x) + 15*q(x). Suppose r(t) = 0. What is t?
-1, 3
Let d be (-627)/315 + 3 + -1. Let h = 176/105 - d. What is t in h*t - 2/3 + t**2 = 0?
-2, 1/3
Let m(o) be the third derivative of 0 + 1/3*o**3 - 1/120*o**6 + 0*o + 1/8*o**4 + 0*o**5 - 2*o**2. Factor m(v).
-(v - 2)*(v + 1)**2
Let t(a) be the third derivative of -a**9/90720 - a**8/30240 + a**5/60 - a**2. Let i(b) be the third derivative of t(b). Let i(h) = 0. Calculate h.
-1, 0
Let m(b) = -25*b**3 + 135*b**2 - 1195*b + 3625. Let z(q) = q**3 - q + 1. Let w(y) = -m(y) - 20*z(y). Factor w(c).