t(f) = -6*g(f) - 22*z(f). Factor t(k).
2*(k - 2)*(5*k - 2)
Let t be (3/24)/((-1)/(-4)). Factor -1/4*x - 1/4*x**5 + 1/4 + t*x**3 + 1/4*x**4 - 1/2*x**2.
-(x - 1)**3*(x + 1)**2/4
Let l be 12/(-42) - 145/7. Let y = -21 - l. Solve 0 + y*h**3 + 0*h**2 + 0*h - 2/3*h**4 = 0 for h.
0
Determine f, given that 2/3*f**2 - 8/3 - 2*f = 0.
-1, 4
Let g = -5 - -6. Let w = g + 1. Let 0 - 4 - m**5 - m + 2*m**3 + 5 + m**4 - w*m**2 = 0. Calculate m.
-1, 1
Let b(u) = 9*u**4 + 3*u**3 + 21*u**2 + 6*u. Let l(g) = 4*g**4 + 2*g**3 + 10*g**2 + 3*g. Let s(c) = 3*b(c) - 7*l(c). Find v such that s(v) = 0.
-3, -1, 0
Let p(a) be the third derivative of 0 + 1/84*a**4 + 1/210*a**5 - 1/21*a**3 - 1/420*a**6 + 0*a + a**2. Find w, given that p(w) = 0.
-1, 1
Let u(n) be the third derivative of -n**7/70 - n**6/10 + 11*n**5/20 - 3*n**4/4 + 25*n**2. Suppose u(q) = 0. What is q?
-6, 0, 1
Suppose -2*u = 2*u - 2*v - 2, -v = -3. Factor -2*h**2 + 20*h**3 - 22*h**3 + 2*h**u + 2*h.
-2*h*(h - 1)*(h + 1)
Factor 1/2*y**3 + 1 + 2*y**2 + 5/2*y.
(y + 1)**2*(y + 2)/2
Suppose 0 = -2*b - 0*b + 6. Let s be (2 - 1) + (b - 4). Factor s - g**3 + g**2 - 1/3*g + 1/3*g**4.
g*(g - 1)**3/3
Let g(d) = -3*d**2 + 9*d. Let i(o) = -3*o**2 + 10*o + 1. Let y(j) = -4*g(j) + 3*i(j). Factor y(z).
3*(z - 1)**2
Let c(p) = p**2 - 2*p - 3. Let l(g) = g**2 - 1. Let a = 17 + -19. Let x(s) = a*l(s) + c(s). Factor x(j).
-(j + 1)**2
Let g(p) be the first derivative of -2/9*p**3 + 0*p + 1/4*p**4 + 0*p**2 + 2. Let g(v) = 0. What is v?
0, 2/3
Let u = -4 + 6. Suppose -d - u*d + 15 = 0. Factor 2 - 4*k**4 + 5*k - k**d + 3*k**2 - 2*k**3 - 2*k**3 - k**2.
-(k - 1)*(k + 1)**3*(k + 2)
Let r(i) = -3 - 1 - 1 - i**2 - i. Let j(w) = 4*w + 5. Let f be j(0). Let a(u) = 2. Let b(p) = f*a(p) + 2*r(p). Factor b(z).
-2*z*(z + 1)
Let z(p) = p**2 + 2*p. Let y be z(-2). Suppose 4*c + 23 = g, y = 6*c - c + 25. Let 0*r**2 + 0*r**g + 0 + 2/3*r**4 - 2/3*r**5 + 0*r = 0. What is r?
0, 1
Factor -7*h**2 + 5*h**2 - 3*h + 5*h**2.
3*h*(h - 1)
Let s(m) be the first derivative of m**6 + 16*m**5/5 + 2*m**4 - 4*m**3 - 7*m**2 - 4*m + 21. Find q, given that s(q) = 0.
-1, -2/3, 1
Let m = 3 + 5. Suppose 6*i**2 - 2*i**4 + 2*i**3 - 9*i + m*i - i - 4 = 0. What is i?
-1, 1, 2
Suppose 5*q = 21 + 29. Let p = -5 + q. What is f in -4*f**2 + 2*f**p - 2*f**4 - 2*f + 0*f**2 + 6*f**4 = 0?
-1, 0, 1
Let o(h) be the first derivative of h**4/48 - h - 2. Let u(i) be the first derivative of o(i). Determine s so that u(s) = 0.
0
Let r be 6/(-27) + 87/27. Factor 2*x + 8*x**3 - 2*x**2 + r*x**2 + 5*x**2 - 2*x**3 + 2*x**4.
2*x*(x + 1)**3
Suppose -5*c + 2*c - 4*m = 0, -2*m - 18 = -3*c. Let s(z) be the first derivative of -4/5*z**2 + 3/10*z**c - 2/3*z**3 - 1 + 8/5*z. Factor s(g).
2*(g - 2)*(g + 1)*(3*g - 2)/5
Let g(a) be the first derivative of 4/15*a**3 + 3/5*a**2 - 1/5*a**4 - 1/15*a**6 - 3 - 6/25*a**5 + 2/5*a. Find s, given that g(s) = 0.
-1, 1
Factor 2*d**5 + 4*d**4 - 3*d**5 + 9*d**3 + 4*d**2 - 3*d**3 + 2*d**5 + d.
d*(d + 1)**4
Let x(y) = y**3 + y + 1. Let g(l) = 196*l**5 + 896*l**4 + 1250*l**3 + 512*l**2 + 66*l + 2. Let k(p) = g(p) - 2*x(p). Find i such that k(i) = 0.
-2, -2/7, 0
Suppose 3*f + 14 = 6*f - t, 2*t + 16 = 2*f. Suppose 0 = -o + f*o. Find g, given that o*g**4 - 3*g**4 + 4*g**4 + g**4 = 0.
0
Factor 3*u**5 - 3*u - 6*u**2 - 3*u + 6*u**4 + 0*u + 3*u.
3*u*(u - 1)*(u + 1)**3
Let f be ((-2)/(-3))/(2/3). Let r(a) be the first derivative of -f + 0*a + 2/3*a**5 + 2/3*a**2 - 4/3*a**4 + 2/9*a**3. Factor r(j).
2*j*(j - 1)**2*(5*j + 2)/3
Let s = 375 + -375. Let -7/2*z**4 + s + 0*z + 2*z**5 + z**3 + 1/2*z**2 = 0. What is z?
-1/4, 0, 1
Suppose 3*i + i + 20 = v, -5*v + i = -5. Factor 0 + v*m**2 + 0*m - 3/2*m**4 - 3/4*m**5 - 3/4*m**3.
-3*m**3*(m + 1)**2/4
Let r(q) be the first derivative of -6*q**6 + 12*q**5 + 11*q**4 - 44*q**3/3 + 4*q**2 - 8. Solve r(k) = 0.
-1, 0, 1/3, 2
Let d(n) be the third derivative of 1/60*n**5 + 2*n**2 + 0*n + 1/24*n**4 + 0 + 0*n**3. Find j such that d(j) = 0.
-1, 0
Let o(m) be the first derivative of 2/15*m**5 + 0*m**3 + 0*m**2 + 0*m - 1/12*m**4 - 1/18*m**6 + 6. Factor o(p).
-p**3*(p - 1)**2/3
Let v(m) = m + 10. Let h be v(-10). Let l(j) be the second derivative of j + 0*j**2 + h*j**5 + 1/15*j**6 + 0*j**3 - 1/6*j**4 + 0. What is x in l(x) = 0?
-1, 0, 1
Let f(p) be the second derivative of p**7/840 - p**6/360 - p**5/120 + p**4/24 - p**3/3 + 2*p. Let b(w) be the second derivative of f(w). What is h in b(h) = 0?
-1, 1
Let r(o) be the first derivative of 0*o + o**2 + 1 + 2/3*o**3. Determine a, given that r(a) = 0.
-1, 0
Let t(g) be the third derivative of -g**8/23520 + g**6/2520 - g**4/12 - 3*g**2. Let b(s) be the second derivative of t(s). Find h such that b(h) = 0.
-1, 0, 1
Suppose 3*a - 9 = a + 5*x, -2*x - 2 = 0. Determine j so that a*j + j**2 - 5 - 1 - 4*j + 3 = 0.
-1, 3
Let h(a) be the third derivative of a**7/14 - a**6/6 - a**5/6 + 5*a**4/6 - 5*a**3/6 + 5*a**2. Factor h(r).
5*(r - 1)**2*(r + 1)*(3*r - 1)
Let o = -8 + 10. Factor -4 + 3*b**2 - 6*b**2 - 13*b**2 - 12*b + o.
-2*(2*b + 1)*(4*b + 1)
Find f such that -19*f**2 + 40*f**2 - 16*f**2 + 50*f + 125 = 0.
-5
Let g(r) be the second derivative of r**4/18 + 14*r**3/9 - 11*r. Determine u so that g(u) = 0.
-14, 0
Factor -2/9*h**2 + 4/9*h + 0.
-2*h*(h - 2)/9
Let s(r) be the third derivative of r**8/2352 - r**7/490 + r**6/280 - r**5/420 + r**2. Suppose s(a) = 0. What is a?
0, 1
Let x(i) be the second derivative of -i**7/168 - i**6/15 - 5*i**5/16 - 19*i**4/24 - 7*i**3/6 - i**2 + 46*i. Factor x(w).
-(w + 1)**2*(w + 2)**3/4
Let p be (333/(-27) - -13)/((-1)/(-3)). Determine m so that 6/5*m + 1/5*m**p + 9/5 = 0.
-3
Factor 1/5*u**4 - 3/5*u**2 + 0*u + 0 - 2/5*u**3.
u**2*(u - 3)*(u + 1)/5
Factor 12/5*f**4 + 4/5*f + 0 - 4*f**3 + 4/5*f**2.
4*f*(f - 1)**2*(3*f + 1)/5
Suppose 4*y + 5*k + 51 = 0, -4*k = -20 - 0. Let r = y + 21. Factor -2/5*v + 0 + 0*v**r + 2/5*v**3.
2*v*(v - 1)*(v + 1)/5
Determine z, given that 8 + 4*z**2 - 20 + 8*z - 19 - 1 = 0.
-4, 2
What is q in 9/7*q**2 + 8/7 - 22/7*q - 2/7*q**4 + q**3 = 0?
-2, 1/2, 1, 4
Let d(f) = -3*f**4 + 15*f**3 + 3*f**2 - 15*f + 6. Let o(b) = -3*b**4 + 14*b**3 + 2*b**2 - 14*b + 6. Let x(h) = -5*d(h) + 6*o(h). Factor x(g).
-3*(g - 2)*(g - 1)**2*(g + 1)
Factor 0*n**3 - 2*n**3 - 3*n**3 + 16 - 15*n**2 + 4.
-5*(n - 1)*(n + 2)**2
Let u = -281 + 3093/11. Find n such that -4/11 - 2/11*n + 4/11*n**2 + u*n**3 = 0.
-2, -1, 1
Let r(z) = z**2 + 2*z + 2. Let b be r(-2). Let t be (0 - b)/((-2)/3). Solve -4 + 4*g - g**2 + 0*g + t - 6*g = 0 for g.
-1
Let v(k) be the third derivative of k**6/480 - k**4/32 + k**3/12 + 2*k**2. Factor v(r).
(r - 1)**2*(r + 2)/4
Let t(k) = k**3 + k**2 + 3. Let c = 0 - 0. Let u be t(c). Factor -10*n**3 + 10*n**3 + 10*n + 2 + 20*n**u + 10*n**4 + 2*n**5 + 20*n**2.
2*(n + 1)**5
Find k, given that -4/3*k**2 - 8/9*k - 2/9 - 8/9*k**3 - 2/9*k**4 = 0.
-1
Factor 0 + 5/2*t**2 - 3/2*t - 1/2*t**3 - 1/2*t**4.
-t*(t - 1)**2*(t + 3)/2
Let n = 5 + -5. Let b(d) be the second derivative of 0*d**3 + 0*d**4 + n*d**2 - 1/80*d**5 + 0 + 3*d. Factor b(s).
-s**3/4
Let p be (1122/(-24))/(-11) - 4. Let t(k) be the first derivative of 1/6*k**3 + p*k**2 - 1/2*k - 1/8*k**4 + 5. Factor t(g).
-(g - 1)**2*(g + 1)/2
Let n(i) be the third derivative of i**7/225 + 19*i**6/900 + i**5/30 + i**4/180 - 2*i**3/45 + 2*i**2. Determine y so that n(y) = 0.
-1, 2/7
Let f(m) = -m + 1. Let s(v) = 6*v**3 - 21*v + 21. Let p(z) = 18*f(z) - s(z). Let x(d) = -11*d**3 - d**2 + 5*d - 5. Let i(n) = -5*p(n) + 3*x(n). Solve i(o) = 0.
-1, 0
Let h(w) = -w - 5. Let c be h(-8). Factor 2*q - 2*q**2 + 0*q**2 + 7*q**4 - 5*q**2 - 2*q**c.
q*(q - 1)*(q + 1)*(7*q - 2)
Let h(b) be the third derivative of -b**8/336 - b**7/210 + b**6/40 + b**5/60 - b**4/12 - 7*b**2. Factor h(w).
-w*(w - 1)**2*(w + 1)*(w + 2)
Let q = 8 - 5. Let g(n) be the first derivative of 0*n**2 - 2/3*n**q + 0*n - 9/4*n**4 + 1. Factor g(v).
-v**2*(9*v + 2)
Let g = 5056 + -15305/3. Let s = -45 - g. Factor 2/3 - 2/3*c**3 - 2/3*c**2 + s*c.
-2*(c - 1)*(c + 1)**2/3
Let k(s) = -s**3 - 2*s**2 + 5*s - 2. Let i(a) = 5*a**3 + 11*a**2 - 26*a + 10. Let c(y) = -2*i(y) - 11*k(y). Suppose c(q) = 0. Calculate q.
-2, 1
Let q(w) be the first derivative of 0*w**2 - 2/3*w**3 + 7 - 1/4*w**4 + 0*w. Factor q(k).
-k**2*(k + 2)
Let y(x) be the third derivative of 0*x + 3*x**2 - 1/60*x**5 - 1/240*x**6 + 0*x**3