l = -32 - -321/10. Let m(t) be the first derivative of 1/4*t**2 + 0*t - 1 - l*t**5 + 3/8*t**4 - 1/2*t**3. Let m(d) = 0. Calculate d.
0, 1
Factor 12/7*i**3 + 5/7*i**4 + 2/7*i + 9/7*i**2 + 0.
i*(i + 1)**2*(5*i + 2)/7
Let g be 2*((-80)/(-15) + -5). Find k, given that 8/3*k - 2 - g*k**2 = 0.
1, 3
Suppose r + 3*t - 9 = 0, -3 = -0*r - r - t. Solve r + 0*j + 0*j**2 - 2/9*j**4 + 2/9*j**3 = 0 for j.
0, 1
Suppose 0*r + 2*r + 3*i + 12 = 0, -4*i = 3*r + 16. Factor -1/4*u**5 + 0*u**2 - 1/4*u**3 + r + 1/2*u**4 + 0*u.
-u**3*(u - 1)**2/4
Let f = 2 + -4. Let s(h) = -3*h**2 + 3. Let n(o) = -7*o**2 + 7. Let w(y) = f*n(y) + 5*s(y). Let w(m) = 0. What is m?
-1, 1
Suppose 2*r**2 + 14/9 - 2/9*r**3 - 10/3*r = 0. What is r?
1, 7
Let o be -2 + 1/2*8. Factor 2 + 3 + 2*u**3 - 3*u**4 + 5*u**4 - 1 - 6*u**o - 2*u.
2*(u - 1)**2*(u + 1)*(u + 2)
Let f be 3/15 + (-58)/(-10). Factor -2*x**2 + 4*x - 2*x**2 + f*x**2.
2*x*(x + 2)
Suppose 5*s - 11 = 2*o - 1, -o = -s + 2. Factor 1/3*j**3 + o + 0*j + 1/3*j**2.
j**2*(j + 1)/3
Let j(l) be the third derivative of l**7/525 + l**6/300 - 2*l**5/75 - l**4/15 - 30*l**2. Factor j(o).
2*o*(o - 2)*(o + 1)*(o + 2)/5
Let m(y) be the third derivative of -1/24*y**6 - 1/10*y**5 - 4/15*y**3 + 0*y + 0 + y**2 + 3/10*y**4. Factor m(k).
-(k + 2)*(5*k - 2)**2/5
Let z(q) be the second derivative of q**4/18 + q**3/9 + 7*q. Factor z(a).
2*a*(a + 1)/3
Let a(b) be the second derivative of 1/3*b**2 + 0 - 5*b + 1/18*b**3 - 1/36*b**4. Suppose a(v) = 0. Calculate v.
-1, 2
Find p, given that 0*p**2 + 2*p**2 + 5*p**2 - 6*p**2 + p**3 = 0.
-1, 0
Let s(z) = 3*z**2 - 26*z + 18. Let n be s(8). Let 0*j + 1/2 - 1/2*j**n = 0. What is j?
-1, 1
Suppose 3*y + 3 = -3*v, y - 3 = 2*v + 5. Solve -3*b**y + 2*b + 2*b**3 - 4*b + 5*b**2 + 0*b - 2 = 0.
-1, 1
Let y(l) = l**2 + 10*l + 18. Let k be y(-8). Let d be (-16)/(-28)*7/k. Suppose 1/4*g**3 - 1/4*g**d - 1/4*g + 1/4 = 0. What is g?
-1, 1
Let a = 5 - 12. Let g = 25/3 + a. Factor -g + 1/3*l**2 + 0*l.
(l - 2)*(l + 2)/3
Let o be 2/((-294)/(-9))*-1. Let b = o - -205/147. Factor b*s**2 + s - 1/3.
(s + 1)*(4*s - 1)/3
Let y(t) = t**2 + 5*t + 6. Let p be y(-6). Let l = 12 - p. Suppose 0 + 1/2*s**4 + 0*s**2 - 1/2*s**3 + l*s = 0. Calculate s.
0, 1
Suppose 5*r - 3*y + 9 = 0, -12 = -2*y - 2*y. Solve -a**3 + r*a**3 + 1 - a**2 + 0*a**3 + a = 0.
-1, 1
Let b(c) = -15*c**4 + 3*c**3 + 18*c**2. Let x(r) = -r**3 - 7*r**2 + 9*r + 7. Let p be x(-8). Let l(w) = -w**4 + w**2. Let o(y) = p*b(y) + 18*l(y). Factor o(n).
-3*n**3*(n + 1)
Let u(m) = m**3 + m + 1. Let x(o) = 2*o**3 - 15*o**2 - 3*o + 17. Let s(h) = -3*u(h) - x(h). What is b in s(b) = 0?
-1, 2
Let f(j) = -2*j**3 - 1. Let s(c) be the first derivative of c**4/4 - c**3/3 + c - 2. Let o = 4 - 5. Let y(q) = o*s(q) - f(q). Factor y(i).
i**2*(i + 1)
Let j(i) be the first derivative of -2*i**5/5 + i**4 - 2*i**3 + 5*i**2/2 - i - 1. Let p(r) = -r**4 + r. Let b(o) = j(o) - p(o). Let b(d) = 0. What is d?
1
Let d(y) = -y**3 + 7*y**2 + 9*y - 7. Let m be d(8). Let k(s) = 2*s. Let t be k(m). Let 0*f**2 - 2*f**2 - f + f**t = 0. What is f?
-1, 0
Factor 6/7*u + 3/7*u**4 - 3/7*u**2 + 0 - 6/7*u**3.
3*u*(u - 2)*(u - 1)*(u + 1)/7
Let r be (-2 + 1)*(-7 + 2). Suppose 5*l - 7*l**2 - 20 - 2*l**3 + 19 + r*l**3 = 0. Calculate l.
1/3, 1
What is r in 724 - 10*r**3 - 725 - 17*r**2 - 12*r - 4*r**2 = 0?
-1, -1/10
Let t(k) be the second derivative of 0 - 4*k**3 - 16*k**2 - 1/40*k**5 + 4*k - 1/2*k**4. Suppose t(d) = 0. Calculate d.
-4
Suppose -27 = 2*g - 3. Let y be 0/(-1) - g/21. What is d in -2/7 + 0*d**2 + y*d + 2/7*d**4 - 4/7*d**3 = 0?
-1, 1
Let l(m) be the first derivative of -25*m**6/6 + 18*m**5 - 15*m**4 - 40*m**3/3 - 44. Factor l(s).
-5*s**2*(s - 2)**2*(5*s + 2)
Suppose -9 = 274*l - 277*l. Factor 0 + 1/5*n**2 + 0*n**l - 1/5*n**4 + 0*n.
-n**2*(n - 1)*(n + 1)/5
Let r(h) be the second derivative of 0 + 0*h**3 + 1/45*h**5 - 2*h - 1/135*h**6 + 0*h**2 - 1/54*h**4. Factor r(a).
-2*a**2*(a - 1)**2/9
Let z be ((-14)/(-35))/((-2)/(-10)). Let -2*w**z - 2*w + 5 - 3 + 3 - 1 = 0. Calculate w.
-2, 1
Let r be 4/(16/(-12)) - -5. Solve -2/5 + 4/5*b - 2/5*b**r = 0 for b.
1
Let a(o) be the third derivative of -7/60*o**4 + 0 + 1/5*o**3 + 1/30*o**5 - 3*o**2 - 1/300*o**6 + 0*o. Solve a(i) = 0 for i.
1, 3
Suppose -2*u - 9 = -4*u - 5*l, 9 = 4*u + l. Factor 2*f + f**3 - f + f + 3*f**u.
f*(f + 1)*(f + 2)
Let k(y) be the third derivative of y**8/336 - y**6/30 + y**5/30 + y**4/8 - y**3/3 + 3*y**2. Factor k(q).
(q - 1)**3*(q + 1)*(q + 2)
Let c = -46/9 - -284/45. Factor 0 - 3/5*n**5 - c*n**2 + 0*n - 3*n**3 - 12/5*n**4.
-3*n**2*(n + 1)**2*(n + 2)/5
Let p = -76 - -81. Let o(f) be the first derivative of 0*f**3 - 1/27*f**6 + 0*f**p + 0*f + 0*f**2 + 3 + 1/18*f**4. Suppose o(w) = 0. What is w?
-1, 0, 1
Let f(u) be the third derivative of u**6/300 - u**5/30 + u**4/15 + 10*u**2. Factor f(q).
2*q*(q - 4)*(q - 1)/5
Let a = 140 + -557/4. Let c(m) be the first derivative of -a*m**4 + 3/5*m**5 - 1/6*m**6 + 1/3*m**3 - 3 + 0*m**2 + 0*m. Factor c(w).
-w**2*(w - 1)**3
Let z be 116/140 + 6/(-14). Factor -4/5*x**2 - z + 6/5*x.
-2*(x - 1)*(2*x - 1)/5
Suppose -18 = 3*f - 6*f. Let h be (-2)/(-3) + f/(-9). Solve h*p**2 - 4/3*p**4 + 0*p + 0*p**3 + 2/3*p**5 + 0 = 0.
0, 2
Let f(r) = 10*r**3 - 3 + 10*r**2 + 8*r**4 - 4*r - 5*r - 4 + 3*r. Let d(p) = p**4 + p**3 + p**2 - p - 1. Let t(g) = 14*d(g) - 2*f(g). Factor t(x).
-2*x*(x + 1)**3
Let v = 4 - 2. Suppose 3*d = v*d + 2. What is g in 18/5*g**3 - 14/5*g**5 + 0 - 2*g**d - 4/5*g + 2*g**4 = 0?
-1, -2/7, 0, 1
Let c be 9/(9/2) + 1/(-2). Factor c*s - 5/2*s**2 + 1.
-(s - 1)*(5*s + 2)/2
Let f(i) = -i**2 + 4*i + 12. Let o be f(6). Let z(j) be the first derivative of 0*j**3 + 2/45*j**5 + 0*j - 1/9*j**4 + o*j**2 + 1. Factor z(x).
2*x**3*(x - 2)/9
Let l be 6*1 + 2/2. Let t be l/(-6)*(-16)/28. Factor -2/3*y**5 + 0*y + 0 - 2/3*y**2 + t*y**3 + 2/3*y**4.
-2*y**2*(y - 1)**2*(y + 1)/3
Determine q so that 1/4*q**2 - 5/4*q + 0 = 0.
0, 5
Let k(p) be the first derivative of -p**9/10584 + p**8/2940 - p**6/630 + p**5/420 - p**3 + 4. Let f(r) be the third derivative of k(r). Factor f(u).
-2*u*(u - 1)**3*(u + 1)/7
Let g be (-3 - -5)/((-2)/3). Let d(k) = -3*k**3 - 4*k**2 - 14*k - 10. Let a(b) = -b**3 + b**2 - b - 1. Let t(q) = g*d(q) + 6*a(q). Suppose t(x) = 0. What is x?
-2
Let n(g) = -g**4 - g**2. Let d(f) = 6*f**4. Let q(m) = d(m) + 3*n(m). Factor q(v).
3*v**2*(v - 1)*(v + 1)
Let r = 0 + 14. Determine v so that 9*v**4 + v**3 - 3*v**5 - 1 + 13 - r*v**2 - 7*v**2 + 2*v**3 = 0.
-1, 1, 2
Let y(t) be the second derivative of -25*t**7/147 - 4*t**6/21 - 2*t**5/35 + 27*t. Factor y(b).
-2*b**3*(5*b + 2)**2/7
Factor -2/5*h**2 - 6/5*h**4 + 0*h + 0 - 2/5*h**5 - 6/5*h**3.
-2*h**2*(h + 1)**3/5
Let p = 33/140 - -1/70. Factor 1/2*a - 1/4*a**2 - p.
-(a - 1)**2/4
Let q(a) be the third derivative of a**5/60 + a**4/8 + a**3/3 + 7*a**2. What is w in q(w) = 0?
-2, -1
Find p, given that -3/5*p**3 - 9/5*p - 3/5 - 9/5*p**2 = 0.
-1
Let k(i) be the first derivative of -i**7/1260 + i**6/540 + i**5/180 - i**4/36 - i**3 - 2. Let w(o) be the third derivative of k(o). Find s such that w(s) = 0.
-1, 1
Let q be 90/21 + (-8)/28. Let n be -2 + (-4)/(q/(-4)). Factor 0*r + 0*r**n + 4/5*r**4 - 2/5*r**5 + 0 - 2/5*r**3.
-2*r**3*(r - 1)**2/5
Let o be 132/77*(-42)/4. Let h = -18 - o. Factor 2/7*g + h + 2/7*g**3 - 4/7*g**2.
2*g*(g - 1)**2/7
Suppose 5*o - 4 = 11, -4*o = 3*u - 27. Factor 5/2*y**4 + 0*y**2 + 0 - 7/2*y**u + y**3 + 0*y.
-y**3*(y - 1)*(7*y + 2)/2
Let j be (4/3)/(2/(-21)). Let q be 1 + j/(-6) + -2. Factor 1/3*a**4 + q*a**3 + 2*a**2 + 4/3*a + 1/3.
(a + 1)**4/3
Determine j, given that -9*j - j**5 + 2*j**4 + 8*j + 2*j**5 - 2*j**2 = 0.
-1, 0, 1
Let v be -3 - (-10)/(20/7). Factor -v*l**2 + 0 + 1/2*l**4 + 1/4*l - 1/4*l**5 + 0*l**3.
-l*(l - 1)**3*(l + 1)/4
Factor -2/15 + 2/5*z - 2/5*z**2 + 2/15*z**3.
2*(z - 1)**3/15
What is l in -2/11*l**2 + 8/11 + 0*l = 0?
-2, 2
Suppose -10/7*j + 4/7 + 8/7*j**2 - 2/7*j**3 = 0. Calculate j.
1, 2
Let f(q) = 20*q**2 - 2*q. Let o(n) = 59*n**2 - 6*n. Let g(a) = -17*f(a) + 6*o(a). Let d(v) = -5*v**2 + v. Let w(t) = -8*d(t) - 3*g(t). Factor w(k).
-2*k*(k + 1)
Let j(f) be the third derivative of -f**6/10 + f**5/3 - f**4/3 - 7*f**2. Factor j(s).
-4*s*(s - 1)*(3*s - 2)
Let n(z) be the second derivative of -z**4/6 - 2*z**3/3 - z**2 + z. Factor n(x).
-2*(x + 1)**2
Solve -2/