- 2*t**2 - 6*t.
-2*t*(t + 3)
Let o(g) = -7*g**2 + 49*g + 41. Let h(z) = z**3 - 4*z**2 - 3*z + 6. Let u be h(4). Let t(y) = -y**2 + 8*y + 7. Let i(d) = u*o(d) + 39*t(d). Factor i(b).
3*(b + 3)**2
Suppose 0 = 5*m + 10, 14*t - 18*t + 4 = -2*m. Factor 0*s**2 - 3/2*s**4 + 0*s - 3/2*s**3 + t.
-3*s**3*(s + 1)/2
Find x, given that 6*x**3 - x**3 + 30*x**2 + 0*x**3 - 35*x**2 - 10*x = 0.
-1, 0, 2
Let b(w) be the second derivative of -1/30*w**6 + 2/3*w**3 + 0 + w - 1/2*w**4 - 1/2*w**2 + 1/5*w**5. Solve b(f) = 0.
1
Let t = -6 - -8. Suppose t*o = -2*o. Factor 0*q + 1/4*q**2 + o.
q**2/4
Let r(n) = n**3 - 7*n**2 - 6*n + 5. Let o be r(6). Let w = o + 336/5. Factor 2/5*d - w - 1/5*d**2.
-(d - 1)**2/5
Let g = 31 + -30. Let d be g - (-2)/(-12)*3. Suppose -d*i**2 - 5/4*i + 1/2 + 5/4*i**3 = 0. What is i?
-1, 2/5, 1
Suppose 0*f**3 + 0*f**2 + 0*f + 2/9*f**5 - 2/9*f**4 + 0 = 0. Calculate f.
0, 1
Factor 0*g + 2/9*g**4 + 2/9*g**2 - 4/9*g**3 + 0.
2*g**2*(g - 1)**2/9
Let j(w) = -9*w - 68. Let k be j(-8). Let y(b) be the third derivative of -1/12*b**k - 2/9*b**3 + 0 + 0*b + b**2 + 1/18*b**5. Solve y(m) = 0 for m.
-2/5, 1
Let g(i) = -i**2 + 19*i - 22. Let o be g(18). Let p be (3 - 3)/o + 2. Factor -6/5*r + 4/5 + 2/5*r**p.
2*(r - 2)*(r - 1)/5
Let a = -11 - -16. Suppose 0*b + a*b - 10 = 0. Factor 6*h**3 - 7*h**3 + h**5 + 0*h - h**b + h**4 + 0*h.
h**2*(h - 1)*(h + 1)**2
Factor 3*j**2 - 2*j**3 + 5*j**2 - 10*j**2.
-2*j**2*(j + 1)
Let t(v) be the second derivative of v**6/120 - v**5/80 - v**4/48 + v**3/24 - 7*v. Suppose t(c) = 0. Calculate c.
-1, 0, 1
Let u(f) be the second derivative of 0*f**2 + 0 + 0*f**3 - 1/6*f**4 - f - 1/5*f**5 - 1/15*f**6. Let u(m) = 0. What is m?
-1, 0
Let r(l) be the first derivative of l**3/6 + l**2/4 + 6. Factor r(n).
n*(n + 1)/2
Suppose a = -12 + 4. Let n be 4/50*(-40)/a. Factor 0 + 0*y - 6/5*y**3 - 6/5*y**4 - n*y**5 - 2/5*y**2.
-2*y**2*(y + 1)**3/5
Let m(n) be the second derivative of -n**5/20 - 7*n**4/12 + n**2 + 3*n. Let i be m(-7). Solve 4*c**i - 2 - 4*c**3 - 2*c + 1 - 3 + 6*c**3 = 0 for c.
-2, -1, 1
Let v(c) = c**3 - 3*c**2 - 3*c - 2. Suppose 5*b - 17 = j + 2*j, -2*j - 2 = -b. Let f be v(b). Find o, given that 2*o - 3*o**2 - f*o**3 + 2*o**3 + o**4 = 0.
-2, 0, 1
Let b(l) be the second derivative of -l**7/357 + l**5/170 + 19*l. Determine n, given that b(n) = 0.
-1, 0, 1
Let v(y) be the third derivative of -23/180*y**5 + 19/360*y**6 - 1/9*y**4 + 25/1008*y**8 - 2*y**2 + 0 + 0*y + 2/9*y**3 + 11/126*y**7. Factor v(m).
(m + 1)**3*(5*m - 2)**2/3
Let d(g) = 46*g**3 - 36*g**2 + 12*g + 4. Let p(n) = 91*n**3 - 71*n**2 + 25*n + 9. Let t(r) = -9*d(r) + 4*p(r). Factor t(x).
-2*x*(5*x - 2)**2
Let h(k) be the first derivative of -7*k**4/2 + 4*k**3 + 8*k - 1. Let v(j) = -9*j**3 + 8*j**2 + 5. Let y(a) = -5*h(a) + 8*v(a). Factor y(w).
-2*w**2*(w - 2)
Suppose 12 = -2*l + 4*v, 0 = -l - 3*v + 4 + 5. Let -32/3*k**5 + l - 2/3*k - 2/3*k**3 + 16*k**4 - 4*k**2 = 0. Calculate k.
-1/4, 0, 1
Let y(d) be the first derivative of d**3/9 + d**2/3 + 1. Find f such that y(f) = 0.
-2, 0
Let d(z) be the first derivative of -z**9/756 + z**7/210 + 7*z**3/3 + 5. Let k(s) be the third derivative of d(s). Factor k(c).
-4*c**3*(c - 1)*(c + 1)
Let u(a) = 6*a + 3. Let n be u(-2). Let i be (1/n)/(4/(-12)). Factor -2/3*q + 0 - i*q**3 + q**2.
-q*(q - 2)*(q - 1)/3
Let f(t) be the second derivative of -t**6/150 - 2*t**5/25 - 2*t**4/5 - 16*t**3/15 - 8*t**2/5 - 38*t. Suppose f(x) = 0. Calculate x.
-2
Let o(b) = b - 3. Let m be o(5). Let r(a) be the first derivative of 2 + 0*a + 1/2*a**4 - 4/3*a**3 + a**m. Let r(x) = 0. Calculate x.
0, 1
Let h(i) = i**2 + 6*i - 1. Let a(f) = -6*f**2 - 17*f - 2. Let v(l) = l**2 + l + 1. Let p(k) = -a(k) - 4*v(k). Let u(j) = 13*h(j) - 6*p(j). Solve u(n) = 0 for n.
-1, 1
Determine i so that 0*i**3 + 18*i - 16*i**3 + 3*i**2 + 13*i**3 = 0.
-2, 0, 3
Let m(u) be the second derivative of u**6/70 - 3*u**5/70 - 3*u**4/7 - u**3 - 15*u**2/14 - 24*u. Factor m(w).
3*(w - 5)*(w + 1)**3/7
Factor -h**2 + 0 + 5/2*h**3 - 3/2*h.
h*(h - 1)*(5*h + 3)/2
Let c(h) be the first derivative of h**4/24 - 5*h**3/18 + 2*h**2/3 - 2*h/3 + 3. Factor c(z).
(z - 2)**2*(z - 1)/6
Let -1/3*j**5 - j**2 + 2/3*j + 0 + j**4 - 1/3*j**3 = 0. What is j?
-1, 0, 1, 2
Factor -2*t**5 + 3*t**2 - 41*t**3 + 43*t**3 + 2*t**4 - 5*t**2.
-2*t**2*(t - 1)**2*(t + 1)
Let t be -3*(2 - 1)*-1. Factor 31*z**4 - 18*z**t - 9*z**4 + 2*z**4 - 10*z**5 + 4*z**2.
-2*z**2*(z - 1)**2*(5*z - 2)
Let d(y) be the first derivative of y**5/5 + y**4/2 - y**3 - 2*y**2 + 4*y - 7. Suppose d(j) = 0. What is j?
-2, 1
Find f, given that 4*f**2 + 5 + f**3 - 5 - 6*f**2 = 0.
0, 2
Let t(o) be the second derivative of 0 + 1/90*o**5 - 3*o - 1/9*o**3 + 0*o**4 - o**2. Let b(a) be the first derivative of t(a). Factor b(p).
2*(p - 1)*(p + 1)/3
Suppose -13*y = -16*y + 12. Let p(z) be the first derivative of -1/24*z**6 - 3/16*z**4 + 0*z + 1/12*z**3 - y + 0*z**2 + 3/20*z**5. What is n in p(n) = 0?
0, 1
Suppose 0*b = 2*b - 24. Factor -7*h**4 - 5*h**2 - h**3 + 9*h**3 - 9*h**4 + b*h**2 + h.
-h*(h - 1)*(4*h + 1)**2
Let 4/7*k**3 + 0*k - 2/7*k**4 + 0 - 2/7*k**2 = 0. Calculate k.
0, 1
Let f(g) be the second derivative of g**4/12 - g**3/3 + g**2/2 - 11*g. Determine t so that f(t) = 0.
1
Let d = 32 + -30. Let o(z) be the third derivative of 0*z + 0*z**3 + 1/630*z**7 + 0 + 1/360*z**6 - 1/72*z**4 - 1/180*z**5 - d*z**2. Factor o(v).
v*(v - 1)*(v + 1)**2/3
Let i(q) = 5*q**2 + q - 8. Let k(d) = -d. Let w(o) = i(o) - 2*k(o). Let t(z) = 4*z**2 + 2*z - 7. Let m(y) = -6*t(y) + 5*w(y). Factor m(r).
(r + 1)*(r + 2)
Let o(u) = -5*u**3 + 2*u + 2. Let a be (-1 - (-50)/14)*7. Let z(t) = 19*t**3 + t**2 - 9*t - 9. Let b(n) = a*o(n) + 4*z(n). Find j such that b(j) = 0.
0, 2/7
Solve -16*o + 10*o**2 - 29*o**2 + 23*o**2 - 4 + 16*o**3 = 0 for o.
-1, -1/4, 1
Let r(u) = -u**3 - 3*u**2 - 3*u + 1. Let y = -26 + 4. Let m(z) = -6*z**3 - 16*z**2 - 16*z + 5. Let l(o) = y*r(o) + 4*m(o). Solve l(q) = 0.
-1, 1
Let r(b) = -3*b**2. Let h(d) = -d**3 - 3*d**2. Let u(o) = 3*h(o) - 2*r(o). Solve u(v) = 0 for v.
-1, 0
Let q(i) be the third derivative of -1/90*i**5 - 4/9*i**3 + 0*i - 1/9*i**4 - 8*i**2 + 0. Solve q(n) = 0 for n.
-2
Suppose 0 = c - 0 - 2, -3*c = -m - 8. Let f be m - (-5)/((-10)/(-12)). Factor -12/5*l**3 - 8/5*l**2 - 8/5*l**f - 2/5*l + 0 - 2/5*l**5.
-2*l*(l + 1)**4/5
Let o(k) be the second derivative of -k**6/35 - 2*k**5/5 - 15*k**4/7 - 36*k**3/7 - 27*k**2/7 + 17*k. Factor o(a).
-2*(a + 3)**3*(3*a + 1)/7
Let o(s) = 125*s**4 + 398*s**3 + 362*s**2 + 128*s + 14. Suppose 4 = -5*i - 6. Let l(n) = n**3 - n**2 + 1. Let d(b) = i*o(b) - 4*l(b). Factor d(z).
-2*(z + 2)*(5*z + 2)**3
Let n be (8 - 8)*(-1 - (-6)/4). Factor -2/3*o**2 - 4/3*o + n.
-2*o*(o + 2)/3
Let r = -1 - -4. What is n in 3*n - n**2 - n**2 + n**2 + r*n**3 + 7*n**2 = 0?
-1, 0
Let b = 4 + 11. Let r = b - 11. Factor 0 - 2/3*c**2 + 2/3*c**r + 0*c**3 + 1/3*c - 1/3*c**5.
-c*(c - 1)**3*(c + 1)/3
Determine s so that -26*s**2 - 23*s**2 + s**4 + 48*s**2 = 0.
-1, 0, 1
Factor -60*q - 10 + 7*q**3 + 28*q**2 - 11*q**3 + 46.
-4*(q - 3)**2*(q - 1)
Suppose -5*d - 20 = -5*a, -4 = -0*d + 4*d - a. Factor 92/3*r**2 + 8/3*r + 343/3*r**5 + 637/3*r**4 + d + 126*r**3.
r*(r + 1)*(7*r + 2)**3/3
Suppose 37 = 3*x - 5*w, -6*x + 5*x - 3*w = 11. Let i(z) be the second derivative of -1/6*z**2 - 1/36*z**x - 1/9*z**3 + 0 - z. Factor i(a).
-(a + 1)**2/3
Let t(k) = k**5 - k**3 - k**2. Let j(g) be the third derivative of -g**8/28 + 3*g**6/40 + 3*g**5/20 - g**2. Let o(y) = -j(y) - 9*t(y). Factor o(u).
3*u**5
Let y be (8/10)/((-65)/25 - -3). Determine s so that -4/7*s**y + 0 + 2/7*s**3 + 2/7*s = 0.
0, 1
Suppose -5*s - 248 = -3*k + 449, 3*k + 563 = -4*s. Let b be (-3)/(1 - s/(-32)). Factor 2/9*v**4 + 0 + b*v**3 + 10/9*v**2 + 4/9*v.
2*v*(v + 1)**2*(v + 2)/9
Let m(v) be the first derivative of 0*v**4 + 1/120*v**6 + 0*v + 1/180*v**5 - 2 + 0*v**3 - 3/2*v**2. Let a(k) be the second derivative of m(k). Factor a(c).
c**2*(3*c + 1)/3
Let d(k) = 2*k**2 + 26*k. Let i(p) = -2*p**2 - 24*p. Let r(j) = 4*d(j) + 6*i(j). Factor r(w).
-4*w*(w + 10)
What is z in -6*z**2 - 11/2*z**3 + 0 - 2*z - 3/2*z**4 = 0?
-2, -1, -2/3, 0
Let u(j) be the third derivative of 1/4*j**4 + 1/10*j**5 + 0 + 1/60*j**6 + 1/3*j**3 - 4*j**2 + 0*j. What is w in u(w) = 0?
-1
Factor -3/2*b**3 - 3*b**2 + 3/2*b + 3.
-3*(b - 1)*(b 