such that d(r) = 0.
-2/7, 2, 3
Suppose 2*l - 152 = -l + m, -4*l + 4*m + 208 = 0. Let h be 230/l - (-6)/(-10). Factor 2/3*z**3 + 0 + 2/9*z**h + 2/9*z + 2/3*z**2.
2*z*(z + 1)**3/9
Suppose -3*d + 4 = -2*l - 1, -2*d = 5*l - 16. Let v(p) be the third derivative of 0*p**3 + 0*p + 1/48*p**4 + 1/240*p**5 + p**l + 0. Factor v(r).
r*(r + 2)/4
Let y = 5 - 5. Suppose y*i - 4 = -i. Suppose 13*b**4 - 8 + 3*b**4 - 34*b**2 + 16*b**i - 146*b**3 + 10*b**4 + 48*b + 98*b**5 = 0. Calculate b.
-1, 2/7, 1
Let j(i) be the third derivative of i**5/210 + i**4/14 + 3*i**3/7 + i**2. Factor j(h).
2*(h + 3)**2/7
Factor 4/7*a - 2/7*a**2 + 0.
-2*a*(a - 2)/7
Suppose 15*r = 10*r + 15. Let s(y) be the third derivative of -1/100*y**6 + 0*y**r - 1/75*y**5 + y**2 + 0*y + 0*y**7 + 0*y**4 + 0 + 1/840*y**8. Factor s(w).
2*w**2*(w - 2)*(w + 1)**2/5
Let z(s) be the second derivative of -s + 1/90*s**6 - 1/36*s**4 + 0*s**3 + 0 + 0*s**2 + 0*s**5. Solve z(v) = 0.
-1, 0, 1
Let d be 55/(-11) + (-42)/(-8). Let z be (-6)/(-4) + (1 - 2). What is p in z*p - 1/4*p**2 - d = 0?
1
Let y be 1 + 0 + (-54)/72. Let -1/4 - y*x**3 - 3/4*x**2 - 3/4*x = 0. What is x?
-1
Suppose 0*y = -0*y + 3*y. What is m in 0 + y*m**2 + 1/4*m - 1/4*m**3 = 0?
-1, 0, 1
Factor 1/2*k**4 + 0 - 3/4*k**2 + 0*k + 5/4*k**3.
k**2*(k + 3)*(2*k - 1)/4
Let z = 82163/5180 - 52/1295. Let w = -61/4 + z. Solve 2/7*d + 0 - 2/7*d**3 + 4/7*d**4 - w*d**2 = 0 for d.
-1, 0, 1/2, 1
Factor -8/3*o**2 + 8/3*o**3 + 0 + 2/3*o.
2*o*(2*o - 1)**2/3
Suppose 5*s = s - 3*q + 14, -5*s + 3*q + 4 = 0. Factor 1/3 - 1/3*o**3 + 1/3*o - 1/3*o**s.
-(o - 1)*(o + 1)**2/3
Let t(d) be the third derivative of d**5/12 - d**4/3 - d**3/3 - 2*d**2. Let l(i) = -21*i**2 + 33*i + 9. Let p(w) = -2*l(w) - 9*t(w). Factor p(r).
-3*r*(r - 2)
Find f, given that -2/11*f**3 + 0 - 2/11*f**2 + 4/11*f = 0.
-2, 0, 1
Let n(h) be the third derivative of 3*h**7/77 - 31*h**6/330 - 7*h**5/330 + 5*h**4/33 + 4*h**3/33 - 18*h**2. Determine y so that n(y) = 0.
-2/5, -2/9, 1
Factor -6/5*u**2 - 2/15*u**3 - 2*u - 14/15.
-2*(u + 1)**2*(u + 7)/15
Suppose -4*f + 3*c = 3, 2*f + 2 = -c + 3*c. Let n be (-12)/14 + (-1 - -3). Suppose -18/7*u**4 + f + 4/7*u**5 + 22/7*u**3 - n*u + 0*u**2 = 0. What is u?
-1/2, 0, 1, 2
Factor -2/15*u**3 - 2/3*u - 8/15*u**2 - 4/15.
-2*(u + 1)**2*(u + 2)/15
Let n(r) = -11*r**2 + 10*r + 12. Let t(g) = -g**2 - g. Let y(d) = n(d) - 2*t(d). Solve y(q) = 0 for q.
-2/3, 2
Let q(t) be the third derivative of 3*t**2 + 1/1344*t**8 + 0*t**5 + 0*t + 0*t**3 - 1/840*t**7 + 0 + 0*t**6 + 0*t**4. Factor q(k).
k**4*(k - 1)/4
Let n be -4 - (-2)/(-4)*27/(-3). Solve 1/4*w - 1/4*w**3 + 1/2*w**2 - n = 0.
-1, 1, 2
Let v(r) be the second derivative of r**5/2 - 15*r**4/8 + 5*r**3/6 - 12*r. Let v(d) = 0. Calculate d.
0, 1/4, 2
Let n(c) be the first derivative of -c**6/90 - c**5/30 + c**3/9 + c**2/6 + 2*c - 3. Let d(x) be the first derivative of n(x). Factor d(j).
-(j - 1)*(j + 1)**3/3
Let c = 621/3155 - -2/631. Factor 0 + 1/5*l - c*l**2.
-l*(l - 1)/5
Let a be -4 + (-6)/(-2) + 4. Let v(s) be the third derivative of 0*s**4 + 0*s + 0 + 1/525*s**7 + 0*s**a + s**2 - 1/150*s**6 + 0*s**5. Factor v(l).
2*l**3*(l - 2)/5
Let i(o) = -o**5 + o**3 - o**2 + o - 1. Let m(k) = 10*k**5 - 35*k**4 + 75*k**3 - 35*k**2 - 85*k + 85. Let q(p) = 5*i(p) + m(p). Let q(d) = 0. Calculate d.
-1, 2
Suppose 5*b - 5*c = 5, 2*b + c = -10 + 24. Let t(n) be the first derivative of n + 3*n**2 + 8/3*n**3 - 9/5*n**b + 3 - 3/2*n**4. Suppose t(p) = 0. What is p?
-1, -1/3, 1
Let k be (-2)/4 + (-21)/(-6). Suppose k*f + 2 = 4*f. Factor -f*h**2 - 2 + h**2 + h + 2*h.
-(h - 2)*(h - 1)
Let s = 11 + -9. Factor -w**2 + 2*w**2 - 2*w**s + 3*w - w.
-w*(w - 2)
Let r(d) be the first derivative of -d**5/360 + d**4/144 + d**3/18 + d**2 + 2. Let z(t) be the second derivative of r(t). Factor z(s).
-(s - 2)*(s + 1)/6
Let l(i) be the first derivative of -i**5/5 + i**3/3 - 10. Factor l(v).
-v**2*(v - 1)*(v + 1)
Suppose 3*b - 2*r = -0*r + 3, 0 = b - 5*r + 12. Let s(u) be the first derivative of -1/2*u**2 + 0*u - u**5 + 1/3*u**6 + 3/4*u**4 + 1/3*u**b - 2. Factor s(l).
l*(l - 1)**3*(2*l + 1)
Let i be 7/(-189)*-10*(-6)/(-10). Find y such that -i*y**2 - 2/9*y + 0 = 0.
-1, 0
Let z be (-4 + 3)*2/(-8). Factor 1/4*x**2 + 1/4*x - z*x**3 - 1/4.
-(x - 1)**2*(x + 1)/4
Let p(j) be the third derivative of -j**6/270 + j**4/18 + 5*j**3/6 + 8*j**2. Let l(c) be the first derivative of p(c). Determine k, given that l(k) = 0.
-1, 1
Let p(h) = -2*h**2 + 19 - 7 - h**3 + 11*h**2 - h. Let k be p(9). Solve -5*d**k - 4*d + 5*d + 2*d**3 + 2*d**2 + 4*d**3 = 0.
-1, 0
Let k(z) be the third derivative of -z**8/3360 + z**7/840 - z**6/720 - z**4/8 - 2*z**2. Let h(t) be the second derivative of k(t). What is r in h(r) = 0?
0, 1/2, 1
Let a(t) be the third derivative of 1/12*t**4 - 2*t**2 + 0*t - 2/3*t**3 + 1/30*t**5 + 0. Factor a(r).
2*(r - 1)*(r + 2)
Let o(b) be the third derivative of b**5/20 + b**4/8 - 27*b**2. Suppose o(a) = 0. Calculate a.
-1, 0
Determine h so that 1/9 + 2/9*h**3 - 2/9*h - 1/9*h**2 = 0.
-1, 1/2, 1
Let -10*o**3 + 5*o**2 + 46 - 46 + 11*o**3 = 0. What is o?
-5, 0
Let u(m) = 5*m**2 - 9*m - 12. Let j(c) = -81*c**2 + 144*c + 192. Let s(b) = 2*j(b) + 33*u(b). Let s(l) = 0. What is l?
-1, 4
Let s be (-118 - 1)*(-2)/(-6). Let p = -39 - s. Factor p*v**2 + 1/3*v + 1/3*v**3 + 0.
v*(v + 1)**2/3
Let b(n) be the third derivative of n**8/1680 + n**7/280 + n**6/180 - n**3/3 + 2*n**2. Let z(m) be the first derivative of b(m). Factor z(w).
w**2*(w + 1)*(w + 2)
Let p = 4304/5 + -859. Let 3/5*y**2 - 9/5*y**3 + p*y + 3/5*y**4 - 6/5 = 0. What is y?
-1, 1, 2
Let f(z) be the second derivative of z**4/54 + 4*z**3/27 - 5*z**2/9 + 21*z. Factor f(t).
2*(t - 1)*(t + 5)/9
Let l(j) = -j**3 + 29*j**2 - 19*j - 41. Let r(n) = 30*n**2 - 20*n - 40. Let x(t) = -5*l(t) + 4*r(t). Factor x(p).
5*(p - 3)**2*(p + 1)
Let d = -360892 - -92027624/255. Let k = d + 8/51. Factor 0 + 0*z + 14/5*z**5 + 6/5*z**3 + k*z**2 - 24/5*z**4.
2*z**2*(z - 1)**2*(7*z + 2)/5
Let v(g) = 8*g - 8*g + 10 - 2 - g. Let u be v(8). Factor -2/5*w**5 + u + 0*w**2 + 0*w + 0*w**4 + 2/5*w**3.
-2*w**3*(w - 1)*(w + 1)/5
Let n(j) be the first derivative of j**6/120 + j**5/80 - j**4/48 - j**3/24 + 3*j + 6. Let p(f) be the first derivative of n(f). Solve p(a) = 0 for a.
-1, 0, 1
Let y(q) = -20*q**2 + q + 3. Let k(z) = 7*z**2 - 1. Suppose -2*o - 7 = -3*m, 2*m = -o - 2*m - 20. Let n(f) = o*k(f) - 3*y(f). Factor n(s).
(s - 1)*(4*s + 1)
Let y be 62/20 + (-3 - 0). Let u(b) be the second derivative of -3*b + 0 + 1/25*b**6 - y*b**5 + 1/15*b**4 + 0*b**2 + 0*b**3. Suppose u(x) = 0. Calculate x.
0, 2/3, 1
Suppose s + 2 = l - 5, -5*s = 3*l + 19. Let b(z) be the first derivative of 0*z**2 + 7/4*z**4 - 2/3*z**3 + 0*z - l. Let b(g) = 0. What is g?
0, 2/7
Let r(q) be the first derivative of -3 + 0*q**4 + 0*q + 1/27*q**6 + 4/45*q**5 - 4/27*q**3 - 1/9*q**2. What is z in r(z) = 0?
-1, 0, 1
Factor -9/2*k + 0 - 3/2*k**2.
-3*k*(k + 3)/2
Let s(i) = -7*i - 5 - 7*i**2 - 2 + 3*i**2 + 0. Let c(z) = z + 1. Let u be c(-4). Let t(d) = d**2 + d + 1. Let g(y) = u*t(y) - s(y). Find x such that g(x) = 0.
-2
Let c(u) = u - 21. Let r be c(21). Let z(b) be the second derivative of r*b**3 + 0 - 1/54*b**4 - 1/135*b**6 + 0*b**2 - 1/45*b**5 + b. Find x such that z(x) = 0.
-1, 0
Let k = -11 + 7. Let i = 7 + k. Let 0 - 1/3*w**i - 1/3*w**4 + 1/3*w**2 + 1/3*w = 0. What is w?
-1, 0, 1
Let s be (2/(-3))/(2/9). Let l(t) = t**3 + 2*t**2 - 3*t + 4. Let q be l(s). What is h in -15*h**2 - 3*h**q + 6*h + 0*h**3 + 12*h**3 + 0*h**3 = 0?
0, 1, 2
Factor -2*u + 9*u + 2 - 5*u + 2 - 4*u**2 - 2*u**3.
-2*(u - 1)*(u + 1)*(u + 2)
Let c(t) be the first derivative of 4*t**3/3 + 4*t**2 + 4*t - 11. Factor c(d).
4*(d + 1)**2
Let q(j) = -j**3 - 3*j**2 + 3*j. Let f be q(-4). Factor -8*n**2 - f*n - 4*n**3 + 28 - 28.
-4*n*(n + 1)**2
Let c = 3 + -3. Let n(x) be the third derivative of 0 + c*x - 1/15*x**3 - 1/150*x**5 - x**2 + 1/30*x**4. Factor n(v).
-2*(v - 1)**2/5
Suppose 0 = -0*z + z. Suppose 0*n - 4*n = z. Find i, given that n*i - i**2 - 2*i + 0*i = 0.
-2, 0
Let k be (0 - -2 - -1) + (-5 - -4). Factor 2/3*u**k + 0*u - 2/3.
2*(u - 1)*(u + 1)/3
Suppose 0 = 5*h + 4 - 34. Suppose -3*p + h*p - 6 = 0. Find s such that -3*s**2 - 3*s + p + 2 + 3*s**3 - 1 = 0.
-1, 1
Let o(w) be the second derivative of w**4/12 + 2*w**3 + 18*w**2 + 26