t y(m) = -9*m**4 - 17*m**3 + 2*m**2 + 24*m + 4. Let n(t) = t**3 + t - 1. Let i(z) = 4*n(z) - y(z). Factor i(p).
(p - 1)*(p + 2)*(3*p + 2)**2
Let q(l) be the third derivative of -l**5/50 + l**4/12 + 4*l**3/5 - 109*l**2 + 1. Factor q(o).
-2*(o - 3)*(3*o + 4)/5
Let o be (0 - 15/(-50))/((-4)/((-100)/15)). Factor -1/2*y**2 + 1/2 + o*y - 1/2*y**3.
-(y - 1)*(y + 1)**2/2
Factor 2/3*g + 2/3 + 1/6*g**2.
(g + 2)**2/6
Solve 1/2*i**3 - 1/4*i**4 - 2*i + 3/4*i**2 + 1 = 0.
-2, 1, 2
Let k = -435/28 - -443/28. Factor -2/7*l**3 - 6/7*l + 6/7*l**2 + k.
-2*(l - 1)**3/7
Suppose 116 + 12 = 4*a. Let g = a + -32. Find x such that -1/2*x**2 + x + g = 0.
0, 2
Let d(t) be the third derivative of -t**5/60 - 25*t**4/6 - 1250*t**3/3 - 18*t**2. What is n in d(n) = 0?
-50
Suppose -3*q = -p - 10, q + 4*p = 2*p + 8. Suppose w = s - 2*s, 0 = q*w + 16. Factor -7*b**5 - 2*b**4 + 2*b**5 + 5*b**3 + 2*b**s.
-5*b**3*(b - 1)*(b + 1)
Let r(y) be the third derivative of -y**6/240 + y**5/30 - y**4/12 - 2*y**2. Factor r(t).
-t*(t - 2)**2/2
Let x be (42/70)/(42/105). Factor -3/4*m**2 + x*m + 9/4.
-3*(m - 3)*(m + 1)/4
Solve 7/2*b**4 + 0 - 5/2*b**3 - 8*b**2 - 2*b = 0.
-1, -2/7, 0, 2
Let b be 80/30*(14/4 - 2). Let s(o) be the third derivative of 0*o**3 + 0 + 2/45*o**5 + 1/36*o**b + 0*o + 7*o**2. Factor s(p).
2*p*(4*p + 1)/3
Suppose -2*k + 3*p = 11, 5 = 69*p - 68*p. Let 4/7*x**k - 4/7 + 4/7*x**3 - 4/7*x = 0. What is x?
-1, 1
Let c(p) be the first derivative of -1/15*p**5 + p + 40 - 2/9*p**3 - 1/3*p**4 + 2/3*p**2. Determine n, given that c(n) = 0.
-3, -1, 1
Let s be ((-36)/(-6) + -4)/24. Let t(b) be the third derivative of 1/15*b**5 - 3*b**2 + 1/60*b**6 + 0*b**3 + 0 + s*b**4 + 0*b. Factor t(i).
2*i*(i + 1)**2
Let b(j) = 4*j + 5. Let v be b(-3). Let m(y) = y**2 + 4*y - 5. Let g be m(v). Suppose -g*x**2 - 2 - 6*x**2 - 8*x**2 - 2*x**2 - 16*x = 0. What is x?
-1/4
Let c = 47 - -73. Determine z so that -132*z**3 - 183*z**2 + 116*z**3 - c*z + 331*z**3 - 18 + 6 = 0.
-2/7, -2/15, 1
Let w be (19/10)/((-30)/60). Let k = 43/10 + w. Suppose -2*j + 3/2 + k*j**2 = 0. Calculate j.
1, 3
Factor 2/5*j**2 + 34*j + 168/5.
2*(j + 1)*(j + 84)/5
Let q be (-3)/15 + (-72)/40. Let b be q - ((-21)/(-9))/(-1). Determine h so that -1/3*h - 1/3 + b*h**3 + 1/3*h**2 = 0.
-1, 1
Factor 5*j**5 + 3110*j**3 + 6*j**4 + 7020*j**2 - 266*j**4 + 2566*j + 1079*j.
5*j*(j - 27)**2*(j + 1)**2
Let v be (-8 - -4)*4/(-8). Factor -2/5*f**v - 7/5*f + 1/5*f**3 - 4/5.
(f - 4)*(f + 1)**2/5
Let f(c) be the second derivative of c**6/360 - c**5/40 + c**4/12 - c**3/3 - 4*c. Let q(d) be the second derivative of f(d). Determine w so that q(w) = 0.
1, 2
Factor -24*w**4 - 2018*w**2 + 3*w**3 + 2042*w**2 - 8*w**5 - 7*w - w - 5*w**3.
-2*w*(w + 2)**2*(2*w - 1)**2
Suppose 2*x = -27*x + 7*x. Factor -c**2 - 5/4*c**3 + 0 - 1/4*c**4 + x*c.
-c**2*(c + 1)*(c + 4)/4
Let x(k) be the second derivative of -k**8/5880 - k**7/2940 + k**6/1260 + k**5/420 - 13*k**3/6 - 5*k. Let q(l) be the second derivative of x(l). Factor q(n).
-2*n*(n - 1)*(n + 1)**2/7
Let z(w) = 2*w**3 + 6*w**2 - 8*w - 4. Let i(x) = -4*x**3 - 5*x**2 + 9*x + 6. Let v(p) = -2*i(p) - 3*z(p). Determine s, given that v(s) = 0.
0, 1, 3
Let s be -6 - (6 - (-8)/120*-186). Factor 4*m - 10 - s*m**2.
-2*(m - 5)**2/5
Let i(h) = -h**3 - 5*h**2 + 4*h - 11. Let t be i(-6). Let l be (6/(-15))/(t/(-10) + 0). Factor 0*z - 2/7*z**l - 2/7 + 0*z**3 + 4/7*z**2.
-2*(z - 1)**2*(z + 1)**2/7
Factor 8/15 - 2/15*a**3 - 2/5*a**2 + 0*a.
-2*(a - 1)*(a + 2)**2/15
Let c = -670/3 + 230. Let -5/2*g - 25/3*g**3 + 5*g**4 - 7/6*g**5 + 1/3 + c*g**2 = 0. What is g?
2/7, 1
Let s(l) be the first derivative of -l**4/2 - 16*l**3 + 51*l**2 - 52*l + 31. Let s(m) = 0. What is m?
-26, 1
Let s(g) be the first derivative of -95*g**3/18 - 15*g**2/2 + 5*g/6 - 255. Solve s(u) = 0.
-1, 1/19
Let k = -22 + 13. Let v = k - -11. What is r in -2 - 35*r**2 - v + 10*r + 27*r**2 + 2*r**3 = 0?
1, 2
Let m(w) be the first derivative of -w**3 + 15*w**2 + 33*w - 159. Factor m(h).
-3*(h - 11)*(h + 1)
Suppose -44 = 3*y - 25*y. Factor 16*s**y + s**5 + 2242*s + 54*s**3 - 2161*s - 12*s**4 - 124*s**2.
s*(s - 3)**4
Let c(m) be the third derivative of 0 + 0*m**3 + 0*m + 5/12*m**5 + 5*m**2 + 5/12*m**4 + 1/8*m**6. Factor c(o).
5*o*(o + 1)*(3*o + 2)
Let k = -49 + 54. Factor 296 + 15*s + k*s**2 - 296.
5*s*(s + 3)
Let p(k) = -k**3 - 6*k**2 + 14*k - 11. Let d be p(-8). Determine q so that -20*q**2 - 4 - 22*q + q + d*q - 8*q**3 = 0.
-1, -1/2
Let h be -17 - -9 - (-3 - 5). Let o(n) be the second derivative of -1/2*n**5 + h + 2*n**2 - 1/3*n**4 - 3*n + 5/3*n**3. Factor o(x).
-2*(x - 1)*(x + 1)*(5*x + 2)
Let b(l) be the third derivative of -7*l**5/12 + 25*l**4/24 + 5*l**3/3 + 46*l**2. Factor b(i).
-5*(i - 1)*(7*i + 2)
Suppose -5*k + 9 + 21 = -2*g, 3*k = 2*g + 26. Let m = -5 - g. Factor w**5 - 5*w**5 + 0*w**4 + 7*w**m + 3*w**4.
3*w**4*(w + 1)
Let c(z) be the first derivative of 3/2*z + 5/8*z**2 - 4 + 1/12*z**3. Factor c(i).
(i + 2)*(i + 3)/4
Let d(g) be the first derivative of -136/9*g**3 - 8/3*g + 10 + 10*g**2 + 7*g**4. Let d(m) = 0. What is m?
2/7, 1/3, 1
What is t in -47/7*t**4 - 1/7*t**5 - 82*t**3 + 529/7 + 575/7*t - 482/7*t**2 = 0?
-23, -1, 1
Let f be ((-6)/5055)/((-2)/(-30)). Let b = 1956/3707 - f. Find w, given that 2/11*w**2 + b*w + 4/11 = 0.
-2, -1
Suppose 1525*k - 1484*k = 0. Let -8/9*f**2 + k - 4/3*f**3 + 0*f - 4/9*f**4 = 0. What is f?
-2, -1, 0
Let y = -633 - -26587/42. Let w(f) be the second derivative of 0*f**2 + 1/21*f**3 + 4*f + 0 + y*f**4. Factor w(c).
2*c*(c + 1)/7
Let a(b) = -12*b**4 + 12*b**3 - 6*b**2 - 12*b + 11. Let t(d) = -3*d**4 + 4*d**3 - 2*d**2 - 4*d + 3. Let v(l) = -6*a(l) + 21*t(l). Solve v(y) = 0.
-1, -1/3, 1
Determine d, given that 481 - 7*d**3 - 615*d - d**3 + 620*d**2 + 3*d**3 - 481 = 0.
0, 1, 123
Let y(h) = -16*h**2 - 14*h**2 - h**3 - 1 - 3*h + 37*h**2 - 10*h**2. Let o be y(-1). Determine c so that -3/2*c - 3/4*c**2 + o = 0.
-2, 0
Let i(r) be the second derivative of -r**5/110 - 61*r**4/66 - 320*r**3/11 - 900*r**2/11 + 134*r. Factor i(h).
-2*(h + 1)*(h + 30)**2/11
Let t be (-2)/(-2) + 5 - 0. Suppose 33 = 4*m - m. Solve 6*u + t*u + 4*u + 59*u**2 - m*u**2 + 20*u**3 = 0.
-2, -2/5, 0
Let w be 1519/294 + 12/(-18)*15/2. Factor -1/6*j**3 - 1/3*j**4 + 0*j**2 + 0 + 0*j - w*j**5.
-j**3*(j + 1)**2/6
Let r(b) be the first derivative of -b**6/15 - 12*b**5/25 - 4*b**4/5 - 120. Factor r(s).
-2*s**3*(s + 2)*(s + 4)/5
Let h(s) be the first derivative of 2/5*s**3 + 0*s + 2/25*s**5 - 1/5*s**2 - 15 - 3/10*s**4. Let h(n) = 0. Calculate n.
0, 1
Factor -22/3*z**3 - 78*z - 45 - 1/3*z**4 - 40*z**2.
-(z + 1)*(z + 3)**2*(z + 15)/3
Suppose 5*v - 3*u = -21, -v + 10*u = 7*u + 21. Determine t, given that v*t + 0 + 2/21*t**3 - 2/21*t**2 = 0.
0, 1
Let i(f) = 2*f**2 + 78*f - 3020. Let m be i(-63). Factor -5/2*y**3 + 1/4*y**m + 25/4*y**2 + 0 + 0*y.
y**2*(y - 5)**2/4
Let c(j) be the first derivative of -4/13*j - 2 - 2/39*j**3 + 3/13*j**2. Factor c(w).
-2*(w - 2)*(w - 1)/13
Let v be -2 + (-15)/(10/(-2)). Let x(c) = c**2 + c. Let w(n) = -9*n**2 - 57*n - 18. Let l(k) = v*w(k) - 12*x(k). Factor l(u).
-3*(u + 3)*(7*u + 2)
Solve 0*d + 5*d**2 - 396*d + 5154 - d**2 + 7914 - d**2 = 0.
66
Let y(s) be the third derivative of 0*s + 28*s**2 - 1/7*s**7 - 1/3*s**5 + 0*s**4 + 0*s**3 - 3/8*s**6 + 0 - 5/336*s**8. Let y(g) = 0. Calculate g.
-4, -1, 0
Let y(i) be the first derivative of 4*i**3 + 62*i**2 + 112*i - 23. Factor y(b).
4*(b + 1)*(3*b + 28)
Let c(h) be the second derivative of -h**8/140 + 9*h**7/280 - h**6/60 - 13*h**3/6 - 7*h. Let s(o) be the second derivative of c(o). Let s(j) = 0. What is j?
0, 1/4, 2
Let w(c) = 8*c**2 - 32*c + 12. Let n(t) = 42*t**2 - 161*t + 59. Let k(a) = -4*n(a) + 22*w(a). Solve k(v) = 0.
1/2, 7
Let d(w) = w**5 - 5*w**4 + 9*w**3 + 8*w**2 - 9*w - 1. Let f(o) = o**4 + o**3 + 2*o**2 - 1. Let a(n) = d(n) - f(n). Solve a(h) = 0 for h.
-1, 0, 1, 3
Factor -3/2*w**3 + 0 - 11094*w - 258*w**2.
-3*w*(w + 86)**2/2
Let y(j) = -2*j**2 - j - 1. Let t(z) = -17*z**2 - 41*z - 6. Let r(v) = -t(v) + 6*y(v). Factor r(l).
5*l*(l + 7)
Let a(n) = 2*n**2 - 4*n. Let m(d) = 8*d**2 - 18*d. Let k = 3 + -12. Let w(c) = k*a(c) + 2*m(c). Factor w(l).
-2*l**2
Factor -16*k**2 - 6*k**3 + 1/2*k**5 + 32*k + 0 + 2*k**4.
k*(k - 2)**2*(k + 4)**2/2
Factor 0 - 1/2*w**3 + 9*w - 1/4*w**4 + 15/4*w**2.
-w*(w - 4)*(w + 3)**