10*u + 2. Let k(t) = -5*t**4 + 7*t**3 - 9*t**2 - 11*t - 2. Suppose -8 = 2*v + 2. Let h(c) = v*k(c) - 6*d(c). Factor h(p).
(p - 2)*(p + 1)**3
Let o(y) be the third derivative of y**5/270 - 5*y**4/54 + 25*y**3/27 + 11*y**2. Find q such that o(q) = 0.
5
Let f(x) = x**3 - 10*x**2 - x + 13. Let a = 6 - -4. Let n be f(a). Factor 0*o + 0 + 7/3*o**n + 2/3*o**2.
o**2*(7*o + 2)/3
Let i(a) = -a**3 + 8*a**2 - 8*a + 7. Let r be i(7). Factor h**5 - 2*h**2 - h**3 - h**4 + r*h**5 + 3*h**2.
h**2*(h - 1)**2*(h + 1)
Suppose 0 = 2*r + 8, -d = 4*r + 2 + 11. Find g, given that -3*g**d - 4*g**2 + 8*g + 1 + 5*g**2 + 3 = 0.
-1, -2/3, 2
Let s = -5 - -11. Suppose -2*n + 3*n = -4, -5*y - s = 4*n. Suppose 4/3*u**y - 14/3*u + 14/3*u**3 - 4/3 = 0. What is u?
-1, -2/7, 1
Let i be 0/(((-2)/1)/1). Let l = 65/2 - 32. Find w such that i + l*w**3 - 1/2*w + 0*w**2 = 0.
-1, 0, 1
Let o(y) = -3*y**2 - 53*y - 192. Let a(h) = 12*h**2 + 213*h + 768. Let u(i) = -5*a(i) - 21*o(i). Factor u(g).
3*(g + 8)**2
Let f(p) be the first derivative of 1/6*p**6 + 23/12*p**4 - 1 + 2/3*p**2 - 14/15*p**5 + 0*p - 16/9*p**3. Let f(i) = 0. Calculate i.
0, 2/3, 1, 2
Suppose 22/9*w - 28/9*w**2 + 4/3*w**3 + 2/9*w**4 - 2/9*w**5 - 2/3 = 0. What is w?
-3, 1
Let i(y) be the first derivative of -2 - 1/4*y**4 - 1/3*y**3 + 1/5*y**5 + 0*y**2 + 0*y + 1/6*y**6. Solve i(f) = 0 for f.
-1, 0, 1
Suppose -8*k = 3*k - 55. Factor -k*t**4 + 0*t - 13/4*t**3 + 0 - 1/2*t**2 - 9/4*t**5.
-t**2*(t + 1)**2*(9*t + 2)/4
Factor 3/2*k + 8*k**4 + 20*k**3 + 0 - 23/2*k**2.
k*(k + 3)*(4*k - 1)**2/2
Let m(v) be the second derivative of -v**6/240 - v**5/60 - v**4/48 + v**2 + v. Let j(q) be the first derivative of m(q). Factor j(o).
-o*(o + 1)**2/2
Let n be -10*4/(-8) + -4. Factor 5*z**3 + 4*z**2 - 1 + n - z - 8*z**3.
-z*(z - 1)*(3*z - 1)
Let l(i) = 2*i**3 - 3*i**2 + i + 3. Let y(q) = -3*q**3 + 4*q**2 - q - 4. Let j(o) = -4*l(o) - 3*y(o). Solve j(c) = 0 for c.
-1, 0, 1
Factor 16*r**3 - 16*r**3 - 2*r**2 + 2*r**4.
2*r**2*(r - 1)*(r + 1)
Let v(n) be the first derivative of -n**5/5 + 4*n**3/3 - 3. Factor v(x).
-x**2*(x - 2)*(x + 2)
Let r(o) be the second derivative of 2*o**6/105 + o**5/28 + o**4/84 - 24*o. Factor r(v).
v**2*(v + 1)*(4*v + 1)/7
Let b(a) = -7*a**3 + 6*a**2 + 7*a. Let h(m) = -m**3 + m**2 + m. Let g(s) = -b(s) + 6*h(s). Factor g(j).
j*(j - 1)*(j + 1)
Let h(a) be the first derivative of a**5/80 + a**4/48 - 2*a - 3. Let v(j) be the first derivative of h(j). Find l, given that v(l) = 0.
-1, 0
Let y = -361/4 - -363/4. Factor -5/2*k + 3/2 + 1/2*k**2 + y*k**3.
(k - 1)**2*(k + 3)/2
Let -6*x - 2*x + 2*x**2 - 17 + 23 = 0. Calculate x.
1, 3
Suppose -3*k + 51*k**2 + 0*k - 52*k**2 = 0. Calculate k.
-3, 0
Factor 20/9 + 2/9*o**2 + 14/9*o.
2*(o + 2)*(o + 5)/9
Let a(i) = -i**2 - 7*i - 5. Let g be a(-7). Let m = g + 7. Suppose 2/3 - 1/3*d - 1/3*d**m = 0. Calculate d.
-2, 1
Let d(g) = -3*g**2 + 21*g + 6. Let x(p) = -p**3 + 4*p**2 - 22*p - 6. Let h(j) = 7*d(j) + 6*x(j). Factor h(s).
-3*(s - 2)*(s + 1)*(2*s + 1)
Let r(b) be the third derivative of -b**9/83160 - b**8/9240 - b**7/2772 - b**6/1980 - b**4/8 + 2*b**2. Let l(n) be the second derivative of r(n). Factor l(v).
-2*v*(v + 1)**2*(v + 2)/11
Let x(a) be the first derivative of 0*a - a**2 + 0*a**3 + 0*a**4 + 1 - 1/240*a**5. Let r(w) be the second derivative of x(w). Factor r(q).
-q**2/4
Let g = -108 - -108. Factor -1/2*h**2 + 0 - 1/2*h**3 + g*h.
-h**2*(h + 1)/2
Let u(h) be the third derivative of -h**7/630 - h**6/90 + h**5/10 + 3*h**4/8 + 3*h**2. Let a(j) be the second derivative of u(j). Factor a(y).
-4*(y - 1)*(y + 3)
Let d(w) = w**2 + 5*w + 7. Let h be d(-4). Let g(t) be the second derivative of -1/6*t**4 - t + 1/2*t**2 + 0 - 1/6*t**h. What is s in g(s) = 0?
-1, 1/2
Let f(c) = c**3 + 3*c**2 - 2. Let a be f(-2). Let t be 7 - ((-30)/(-9))/((-10)/(-12)). Factor 4/3*n + 2/3*n**4 - 4/3*n**t - 2/3 + 0*n**a.
2*(n - 1)**3*(n + 1)/3
Let k(n) be the third derivative of n**8/504 - 4*n**7/315 + n**6/45 + n**5/45 - 5*n**4/36 + 2*n**3/9 + 13*n**2. Factor k(o).
2*(o - 2)*(o - 1)**3*(o + 1)/3
Let q be 0/2*1/(-2). Suppose 2 - 17*f - 5*f**3 + 5*f**3 - 16*f**4 + 39*f**2 + q*f**3 - 8*f**3 = 0. What is f?
-2, 1/4, 1
Let z(x) be the third derivative of 0 + 0*x + 0*x**3 + 4*x**2 - 1/12*x**4 - 1/60*x**5. Find h such that z(h) = 0.
-2, 0
Let m = -59/4 + 15. Let u(g) be the second derivative of 0 - g - m*g**2 - 1/8*g**4 - 1/40*g**5 - 1/4*g**3. Find y such that u(y) = 0.
-1
Let y(q) be the third derivative of 0*q + 0*q**3 + 1/540*q**6 + 1/270*q**5 + 0*q**4 + 0 + 6*q**2. Factor y(f).
2*f**2*(f + 1)/9
Let l = 1/38 + 295/342. Factor -l - 8/9*s - 2/9*s**2.
-2*(s + 2)**2/9
Let y be 26/45 + 6/27. Let f(x) = x**3 - 8*x**2 + 3. Let q be f(8). What is i in 2/5*i**q + 2/5*i**2 - y*i + 0 = 0?
-2, 0, 1
Let z be (8/(-12))/((-10)/6 - 0). Let -2/5*t**4 + 2/5*t + z*t**5 - 4/5*t**3 + 4/5*t**2 - 2/5 = 0. Calculate t.
-1, 1
Let r = 9 + -4. Suppose l - r*l = -8. Solve -2/7*v + 2/7*v**l + 0 = 0.
0, 1
Let j be (4/70)/(15*(-8)/(-600)). Factor -4/7*h**3 + 2/7*h + 0*h**4 + j*h**5 + 0 + 0*h**2.
2*h*(h - 1)**2*(h + 1)**2/7
Suppose -5*t + 17 + 14 = -4*i, -3*i - 18 = -2*t. Suppose -t = -3*d + 3. Factor -2*y**4 + 4*y**2 - d*y**3 + 2*y - 2*y**2 + 0*y**3.
-2*y*(y - 1)*(y + 1)**2
Let z(v) = 8*v**2 + 2*v + 1. Let o be z(-1). Factor -68*j**5 - 608*j**5 - 224*j**3 - o*j**2 - 9*j**2 - 884*j**4.
-4*j**2*(j + 1)*(13*j + 2)**2
Factor g + 1/2*g**3 + 3/2*g**2 + 0.
g*(g + 1)*(g + 2)/2
Suppose 0*q = 4*b - 2*q - 14, -2 = b + 5*q. Factor -2/9*n**b + 0 + 4/9*n**2 + 0*n - 2/3*n**4.
-2*n**2*(n + 1)*(3*n - 2)/9
Let h = 1/690 + 2/207. Let i(y) be the third derivative of -3*y**2 + h*y**5 + 0*y + 0*y**3 + 1/36*y**4 + 0. Suppose i(w) = 0. What is w?
-1, 0
Suppose 26 = 4*k - 2*q, k - 24 = -0*k + 4*q. Suppose -3 = y - k*y + 3*z, 5*y = -3*z + 21. Factor -2/5*x**y + 4/5*x + 0 + 2/5*x**2.
-2*x*(x - 2)*(x + 1)/5
Let o be 2/11 + 252/66. Suppose -o*i = -i. Solve 0*j - 1/3*j**4 - 1/3 + i*j**3 + 2/3*j**2 = 0 for j.
-1, 1
Let z(s) = -s**2 + 2*s + 2. Let v be z(3). Let c be 2 + 0 + (1 - v). Determine f so that -f**4 + 8*f**3 + 5*f**4 - 6*f**c - 8*f**2 = 0.
0, 2
Let x = 3/55 + 34/385. Let a(w) be the second derivative of 0 + 1/14*w**4 + x*w**2 + 1/70*w**5 + 3*w + 1/7*w**3. Solve a(z) = 0.
-1
Let p(m) be the third derivative of 1/48*m**4 + m**2 + 0 + 1/420*m**7 + 1/672*m**8 - 1/120*m**6 + 0*m + 1/12*m**3 - 1/60*m**5. Factor p(r).
(r - 1)**2*(r + 1)**3/2
Let g be 2/6*3*35. Let v be (2/10)/(14/g). Determine q, given that -1/2 - v*q**2 + q = 0.
1
Let f be 16/9 - 6/(-27). Find l, given that -15*l**f + 2*l**2 - l**4 - 4*l**3 - 4*l - 1 + 7*l**2 = 0.
-1
Find w, given that -13*w**3 - 3*w**4 + 4*w**3 + 0 + 5*w**2 - 2 + 8*w**3 + w = 0.
-1, 2/3, 1
Let j(y) be the first derivative of -y**9/21168 + y**8/5880 - y**7/5880 + y**3 + 7. Let r(d) be the third derivative of j(d). Factor r(o).
-o**3*(o - 1)**2/7
Let r(k) be the second derivative of 3*k**5/10 - k**4/4 - 4*k. Determine v so that r(v) = 0.
0, 1/2
Let -30/7 + 33/7*w - 3/7*w**2 = 0. What is w?
1, 10
Let o(r) be the second derivative of -r**6/15 + 3*r**5/50 + 7*r**4/30 - r**3/5 - 2*r**2/5 - 48*r. What is q in o(q) = 0?
-1, -2/5, 1
Let r(t) be the third derivative of t**8/1680 - t**7/525 - t**6/300 + 2*t**5/75 - 7*t**4/120 + t**3/15 + 16*t**2. Factor r(w).
(w - 1)**4*(w + 2)/5
Factor 431*u + 4*u**3 - 435*u - 2 - 8*u**2 + 10.
4*(u - 2)*(u - 1)*(u + 1)
Let t(k) be the second derivative of -k**5/80 - k**4/16 - k**3/12 + 23*k. Find r, given that t(r) = 0.
-2, -1, 0
Let z(x) be the second derivative of 0*x**2 + 0*x**4 + 2/45*x**6 + 0 + 6*x + 0*x**3 - 1/15*x**5. Suppose z(s) = 0. Calculate s.
0, 1
Let i = 8 - 6. Suppose -4 = -i*w + 2*t - 6*t, -2*w = t - 4. Factor 2 + 2*k**w - 2*k**2 - 2*k**2.
-2*(k - 1)*(k + 1)
Let u(t) = t**3 - 6*t**2 - t + 8. Let f be u(6). Let d(n) be the first derivative of -f - 8/27*n**3 - 2/3*n - 7/9*n**2. Determine c, given that d(c) = 0.
-1, -3/4
Let i be (2 - 300/147)*-7. Let z = 29/4 - 195/28. Factor -2/7*l - z*l**2 + 2/7 + i*l**3.
2*(l - 1)**2*(l + 1)/7
Let n be 3 - 2 - (-4 - -1). Let q(j) be the third derivative of -1/180*j**5 - 2*j**2 + 0*j**3 + 0 + 1/72*j**n + 0*j. Find y such that q(y) = 0.
0, 1
Let g(z) = z**2 - z - 1. Let x be ((-2)/3)/((-1)/9). Let y(d) = -8*d**2 + 2. Let k(s) = x*g(s) + y(s). Factor k(w).
-2*(w + 1)*(w