).
-(r - 3)*(r + 1)/2
Suppose -3*j + 2*j = 3*z - 9, 3*z - 5*j = 27. Factor -15*c**z + 14*c**4 - 2*c**3 - 4*c**3 + 4*c**3.
-c**3*(c + 2)
Let z(q) = -10*q**3 + 560*q**2. Let a(c) = c**3 - 51*c**2. Let j(y) = 45*a(y) + 4*z(y). Factor j(p).
5*p**2*(p - 11)
Let i = 15545 - 15542. Let f = 9/2 - 37/10. Determine c, given that -1/5*c**4 + 2/5*c**2 + 8/5*c**i - f*c - 1/5 - 4/5*c**5 = 0.
-1, -1/4, 1
Let d(a) be the third derivative of -a**8/26880 + a**7/2880 - a**6/1440 - a**5/60 - 35*a**2. Let t(m) be the third derivative of d(m). Factor t(y).
-(y - 2)*(3*y - 1)/4
Let c = 135 + -100. Let p be 1/(-3)*(49/c - 5). Find t, given that -2/5*t**2 - 4/5 - p*t = 0.
-2, -1
Let m(u) be the third derivative of -u**5/60 - 3*u**4/2 - 35*u**3/6 - 247*u**2. Factor m(t).
-(t + 1)*(t + 35)
Let u(x) = -x**2 + x - 2. Let v(z) = -2*z**2 + 3*z - 7. Let n(b) = -3*u(b) + v(b). Find c such that n(c) = 0.
-1, 1
Let c = 20 - 14. Let q(t) = 4*t**4 - 12*t**3 + 14*t**2 - 6*t - 6. Let m(j) = -j**2 + j + 1. Let h(k) = c*m(k) + q(k). Factor h(v).
4*v**2*(v - 2)*(v - 1)
Let l(q) be the first derivative of q**4/24 - 7*q**3/24 + 3*q**2/8 - 4*q + 22. Let u(x) be the first derivative of l(x). Factor u(p).
(p - 3)*(2*p - 1)/4
Factor -9/2*z + 3/2*z**2 + 0.
3*z*(z - 3)/2
Let f(h) = h + 3 + 0*h**2 + 4*h**2 - 5*h**2. Let s be f(0). Factor -g**3 - 23 - 1 + s*g**3 + 60*g - 42*g**2 + 7*g**3.
3*(g - 2)**2*(3*g - 2)
Let d = -10 + 52/5. Suppose -3*j = 12, 5*r - j = 13 + 6. Determine b so that -4/5 - 6/5*b**2 + d*b**4 + 2*b - 2/5*b**r = 0.
-2, 1
Let j(i) be the first derivative of 1/23*i**2 + 27 - 1/69*i**6 + 0*i**4 + 0*i - 4/69*i**3 + 4/115*i**5. Factor j(g).
-2*g*(g - 1)**3*(g + 1)/23
Let x(c) be the third derivative of 14 + 0*c + 5/3*c**4 - 6*c**3 - 1/15*c**5 + c**2. Factor x(z).
-4*(z - 9)*(z - 1)
Suppose 0 + 11/2*i**3 + 1/2*i**5 - 5/2*i**2 - 7/2*i**4 + 0*i = 0. Calculate i.
0, 1, 5
Let m = -1334 + 7975/6. Let y = -10/3 - m. Factor -y*u**2 + 9/4*u**5 + 1/4 + 5/2*u**3 + 21/4*u**4 - 3/4*u.
(u + 1)**3*(3*u - 1)**2/4
Let m = 10883/19932 + -1/1812. Factor 12/11*t - m*t**2 - 6/11.
-6*(t - 1)**2/11
Let r be -9*(-215)/225 - 8. Factor 0 + 3/5*q**5 - r*q**3 + 3/5*q**2 + 0*q - 3/5*q**4.
3*q**2*(q - 1)**2*(q + 1)/5
Let n(k) be the second derivative of 1/90*k**6 + 0 - 1/12*k**4 - 5/18*k**3 + 25*k - 1/3*k**2 + 1/60*k**5. Factor n(i).
(i - 2)*(i + 1)**3/3
Let n be (-8)/(-6) + 8/12. Suppose -6 = 5*w + 4, 4*m - 18 = -3*w. Factor m*c - n*c + 2*c**2 - 8*c**3 + 6*c**3.
-2*c*(c - 2)*(c + 1)
Factor 50/3*v - 1250/3 - 1/6*v**2.
-(v - 50)**2/6
Suppose 0 = -8*g + 11*g - 15. Suppose g*d - 4*m - 21 = -7*m, 7 = -d + 5*m. Solve -1/2*s**4 + s - s**d + 0*s**2 + 1/2 = 0.
-1, 1
Let k(v) = 4*v - 52. Let x be k(12). Let l be (-4)/(-11)*3/x*-4. Factor l*j**4 - 2/11*j**5 - 26/11*j**3 - 8/11*j + 0 + 24/11*j**2.
-2*j*(j - 2)**2*(j - 1)**2/11
Let f(c) be the first derivative of c**5/20 + 5*c**4/12 + c**3/2 - 9*c**2/2 - 30*c - 1. Let k(i) be the first derivative of f(i). Suppose k(v) = 0. Calculate v.
-3, 1
Let z be 12/84 - 1*3/(-28). Factor z*l - 1/4*l**3 - 1/4 + 1/4*l**2.
-(l - 1)**2*(l + 1)/4
Let i = 832/201 + -54/67. Suppose i*d - 1/3*d**2 - 25/3 = 0. What is d?
5
Let i be (891/(-45) + 19)*(-15)/2. Factor 33*o + 375/4*o**5 - 345/4*o**3 - i - 57/2*o**2 + 75*o**4.
3*(o + 1)**2*(5*o - 2)**3/4
Let b = 102/13 - 165/26. Determine s so that b*s**4 - 9/2*s**2 + 6 + 3*s**3 - 6*s = 0.
-2, 1
Let z(d) be the third derivative of 0*d**4 - 1/30*d**5 - 1/84*d**7 + 0*d - 4*d**2 + 0*d**3 - 1/30*d**6 + 0 - 1/672*d**8. Factor z(p).
-p**2*(p + 1)*(p + 2)**2/2
Let k(r) = -r**2 - 96*r + 259. Let l(y) = 34*y - 86. Let w(f) = 2*k(f) + 7*l(f). Find x such that w(x) = 0.
2, 21
Suppose 16*z = -32 - 0. Let f = z + 20/9. Suppose -f - 2/9*w**2 - 4/9*w = 0. Calculate w.
-1
Let d(b) be the second derivative of -b**5/90 - b**4/6 - 20*b**3/27 - 308*b. Solve d(n) = 0 for n.
-5, -4, 0
Factor 66*t - 9*t**2 - 8*t**3 - 56 + 4*t**3 + 4*t**3 - t**3.
-(t - 4)*(t - 1)*(t + 14)
Suppose 2*y = -4*b + 76, -196 = -5*y - 3*b - b. Let z be (y/(-50))/(2/(-10)). Factor 3*a**z + 2*a**3 - 7*a**5 - 2*a**3 - a**4.
-a**4*(7*a - 2)
Let r(x) be the first derivative of 2/15*x**6 + 0*x + 0*x**2 - 4 + 0*x**3 - 8/25*x**5 + 0*x**4. Suppose r(n) = 0. Calculate n.
0, 2
Let y(b) be the first derivative of -2*b**3/27 - b**2/3 - 4*b/9 + 692. Let y(k) = 0. Calculate k.
-2, -1
Suppose -6*m = 150 + 36. Let y = 35 + m. Factor 2/7*q**y - 3/7*q**3 + 0*q**2 + 0 + 1/7*q.
q*(q - 1)**2*(2*q + 1)/7
Let f(s) = 21*s**2 - 81*s + 96. Let o(v) = -6*v**2 + 23*v - 27. Let h(k) = -5*f(k) - 18*o(k). Factor h(x).
3*(x - 2)*(x - 1)
Determine q, given that -14/3 - 24*q - 10/3*q**2 = 0.
-7, -1/5
Let n be (35/(-20))/((-1)/28). Let q be (14/n)/((-2)/(-14)). Factor -4/5*j + 6/5*j**q - 2/5.
2*(j - 1)*(3*j + 1)/5
Factor -169*r + 143*r - 6*r**2 - 4 - 6*r**2.
-2*(r + 2)*(6*r + 1)
Suppose -3*p - 4*m = -31, 45 = -0*p + 5*p + 5*m. Find z such that 23*z + 162 + 13*z - p*z**2 + 7*z**2 = 0.
-9
Let n(m) be the second derivative of -m**6/180 + m**5/15 - m**4/4 + 9*m**2/4 + 5*m - 2. Factor n(z).
-(z - 3)**3*(z + 1)/6
Let t(o) be the second derivative of -o**5/240 + o**4/4 - 6*o**3 - 33*o**2/2 + 24*o. Let i(f) be the first derivative of t(f). Suppose i(d) = 0. What is d?
12
Let p be ((-46)/(-483))/(120/(-6286)) + 5. Let n(z) be the third derivative of p*z**5 - 3*z**2 + 0 + 0*z + 0*z**3 - 1/108*z**4. Solve n(b) = 0 for b.
0, 1/3
Let w(l) be the second derivative of l**6/45 + 14*l**5/45 - 10*l**4/27 + 5*l - 49. Factor w(b).
2*b**2*(b + 10)*(3*b - 2)/9
Suppose -3/2*y**3 + 69/2*y**2 - 216 - 180*y = 0. Calculate y.
-1, 12
What is q in 6*q + 4 - q**2 - 3/2*q**3 = 0?
-2, -2/3, 2
Let w(y) be the third derivative of -1/96*y**5 + 0 - 7/48*y**3 - 44*y**2 + 0*y - 13/192*y**4 + 1/960*y**6. Determine d so that w(d) = 0.
-1, 7
Suppose -2*d + 114 = 4*c + 98, 2*d = -2*c + 12. Factor 2/3*u + 8/9 - 2/9*u**c.
-2*(u - 4)*(u + 1)/9
Let g(h) be the third derivative of -h**7/1260 - h**6/120 + h**5/15 + h**4/24 - 11*h**2. Let o(l) be the second derivative of g(l). Factor o(j).
-2*(j - 1)*(j + 4)
Let y = -66 - -60. Let t(j) = -10*j**4 + 4*j**3 + 14*j**2 + 6*j. Let a(w) = -9*w**4 + 4*w**3 + 13*w**2 + 5*w. Let b(c) = y*a(c) + 5*t(c). Factor b(r).
4*r**2*(r - 2)*(r + 1)
Factor 34/3*o + 1/6*o**2 + 22.
(o + 2)*(o + 66)/6
Suppose 104/9*u - 4/9*u**2 - 676/9 = 0. What is u?
13
Let k(q) be the first derivative of -1/6*q**3 + 1/4*q**4 - 1/24*q**6 - 3/8*q**2 + 1/2*q + 0*q**5 - 14. Let k(b) = 0. What is b?
-2, -1, 1
Solve -2/9*g**2 - 8/9*g + 2/9*g**4 + 8/9*g**3 + 0 = 0 for g.
-4, -1, 0, 1
Let n(g) be the first derivative of 3*g**6/2 - 34*g**5/5 - 125*g**4/4 + 10*g**3/3 + 58*g**2 + 24*g + 326. Find j such that n(j) = 0.
-2, -1, -2/9, 1, 6
Let q(h) be the second derivative of 1/5*h**2 - 1/12*h**4 + 1/30*h**3 + 1/50*h**5 + 0 + 11*h. Suppose q(w) = 0. What is w?
-1/2, 1, 2
Let l(y) = y**3 + 6*y**2 - 2*y - 5. Let k be l(-6). Factor -4*t**2 - k*t - 9*t - 1 + 8*t**2 + 17.
4*(t - 2)**2
Let x(v) = 11*v**2 - 24*v + 29. Let g(k) = -5*k**2 + 12*k - 14. Let o be (-6)/(-45) - 219/(-45). Let c(p) = o*g(p) + 2*x(p). Factor c(m).
-3*(m - 2)**2
Let b = 17629/7 - 2517. Factor 6/7 + 2*c + b*c**2 + 2/7*c**3.
2*(c + 1)**2*(c + 3)/7
Let g(i) be the first derivative of 5*i**6/3 + 18*i**5/5 - i**4 + 77. Factor g(r).
2*r**3*(r + 2)*(5*r - 1)
Let i be ((-6)/(-45))/(4/5). Let u be ((-7276)/(-816) - 6/8) + -8. Find d such that 1/6*d**3 + 0*d - 1/6*d**5 + 0 + u*d**2 - i*d**4 = 0.
-1, 0, 1
Let d(i) be the second derivative of -2/21*i**7 + 2/3*i**4 + 2/3*i**3 - 4*i - 4/15*i**6 + 0*i**5 + 0 + 0*i**2. Let d(p) = 0. Calculate p.
-1, 0, 1
Solve 2/9*y**5 + 0*y**2 + 0*y - 8/3*y**3 + 8/9*y**4 + 0 = 0 for y.
-6, 0, 2
Let m(z) be the first derivative of 0*z - 3/2*z**2 + 1 + 3/2*z**3. What is x in m(x) = 0?
0, 2/3
Suppose 99*j = 34*j + 780. Solve 0*z**3 - 16/3*z**4 + j*z + 44/3*z**2 + 8/3 = 0 for z.
-1, -1/2, 2
Let w(q) be the third derivative of -3/350*q**7 - 41*q**2 - 1/150*q**5 + 0 + 0*q + 0*q**3 - 11/600*q**6 + 0*q**4. Solve w(v) = 0.
-1, -2/9, 0
Let l(r) be the first derivative of r**7/56 - 3*r**6/20 + 39*r**5/80 - 3*r**4/4 + r**3/2 - 5*r - 3. Let p(f) be the first derivative of l(f). Factor p(o).
3*o*(o - 2)**2*(o - 1)**2/4
Let r(a) be the third derivative of a**5/30 - 17*a**4/12 + 14*a**3 - 4*a**2 + 4. Factor 