**4. Suppose t(l) = 0. What is l?
-1, 0
Let z = -80 + 242/3. Let o(s) be the first derivative of 2 - z*s**3 - 2*s + 2*s**2. Suppose o(j) = 0. Calculate j.
1
Let i(d) = -d**3 + 8*d**2 - 7*d + 5. Let q be i(7). Let a = 7 - q. Solve 0*k - 2/7*k**a + 0 + 2/7*k**3 = 0 for k.
0, 1
Let h(t) be the third derivative of t**6/60 - t**4/24 + t**3/6 - 2*t**2. Let z be h(1). Factor -z + u**2 - u + 2.
u*(u - 1)
Let u(o) = o**2 - o - 1. Let v be u(-2). Factor 12*b**4 + 17*b**3 - 9*b**v - 38*b**3 + 18*b**3.
-3*b**3*(b - 1)*(3*b - 1)
Let y = 964/1125 + 4/125. Factor -10/9*p**2 - 8/3*p - y.
-2*(p + 2)*(5*p + 2)/9
Let o be 0 - -1 - (7 + -9). Let u(y) be the first derivative of 1/8*y**4 - 3/4*y**2 - 3 + 0*y**o - y. Let u(k) = 0. Calculate k.
-1, 2
Let s = 7 - 4. Determine i, given that -2*i - 7*i - i**5 - 20*i**2 - 20*i**s - i - 2 - i**5 - 10*i**4 = 0.
-1
Let o(x) = x**2 - 8*x + 6. Let h be o(7). Let d = h - -5. Solve 3*a**3 + 6*a**4 + 3*a**d - 5*a**2 + a + 0*a**4 = 0.
-1, 0, 1/3
Let h be -1*(-3 - (-1 - -1)). Let k be 6/9 + h/9. Factor -1 - 2*l**3 + l**3 + l**2 + k.
-l**2*(l - 1)
Suppose 9*u = 37*u. Factor u + 2/3*k**3 + 0*k**2 - 2/3*k.
2*k*(k - 1)*(k + 1)/3
What is u in 0 - 6*u - 6*u**2 - 3/2*u**3 = 0?
-2, 0
Let h(q) be the third derivative of -q**7/70 - 7*q**6/40 - 3*q**5/4 - 9*q**4/8 + 5*q**2 - 1. Factor h(t).
-3*t*(t + 1)*(t + 3)**2
Let q(y) be the third derivative of y**8/26880 - y**7/3360 + y**6/960 - y**5/480 - y**4/8 - y**2. Let h(p) be the second derivative of q(p). Factor h(t).
(t - 1)**3/4
Let r(w) be the second derivative of -7*w**6/180 + w**5/10 - w**4/18 + 9*w**2/2 - 7*w. Let q(h) be the first derivative of r(h). What is y in q(y) = 0?
0, 2/7, 1
Find k such that -3*k**4 + 0 + 22*k**3 + k - 10*k**3 - 3 + 11*k - 18*k**2 = 0.
1
Factor -3/5*c**4 + 6/5*c**3 + 0*c**2 + 0 + 0*c.
-3*c**3*(c - 2)/5
Let l = -15 + 27. Let n be 2/7 - l/(-7). Let -1/2*f + 0 + 2*f**n - 3/2*f**3 = 0. What is f?
0, 1/3, 1
Let r(y) = y - 3. Let c = 16 - 11. Let t be r(c). Factor -a**3 + a - a**t + 5*a - 4*a.
-a*(a - 1)*(a + 2)
Let d(t) = -t**3 - t**2 - 3*t + 1. Let n(v) = -v**3 - v. Let s(y) = d(y) - 2*n(y). Suppose s(c) = 0. Calculate c.
-1, 1
Let b(s) be the second derivative of s**4/20 - s**3/5 + 3*s**2/10 + 10*s. Factor b(f).
3*(f - 1)**2/5
Factor 2/11*q**4 + 6/11*q**3 + 0*q + 0 + 4/11*q**2.
2*q**2*(q + 1)*(q + 2)/11
Let i(n) be the second derivative of -3*n**5/20 + n**4/4 + n**3 + 12*n. Factor i(j).
-3*j*(j - 2)*(j + 1)
Suppose 3*u + 0*u = 12. Suppose -13 = u*y - 7*y - 2*n, -18 = -2*y + n. Factor 4*f - y*f - 2*f**2 - f + 2*f**3.
2*f*(f - 2)*(f + 1)
Let x(u) be the second derivative of u**4/90 + u**3/15 + 2*u**2/15 - 3*u. Factor x(k).
2*(k + 1)*(k + 2)/15
Let r = -29/44 - -10/11. Factor 0 + 0*i - 1/4*i**3 + 1/4*i**5 - r*i**2 + 1/4*i**4.
i**2*(i - 1)*(i + 1)**2/4
Suppose -3*c = 10 - 25. Let z(u) be the first derivative of 0*u**2 + 1/15*u**3 + 1 + 0*u + 0*u**4 - 1/25*u**c. Factor z(g).
-g**2*(g - 1)*(g + 1)/5
Let z be -3 + 3 - 8/(-2). Find g such that 0*g**2 + 9*g**2 - 8*g**z + 3*g**3 - 9*g**4 + 8*g**4 - 3*g = 0.
-1, 0, 1/3, 1
Suppose 120 = 2*y + 2*y. Suppose -y = -6*j + j. Factor 6*n**2 - 17*n**2 - j*n - 3 + 8*n**2.
-3*(n + 1)**2
Let u(c) = c**4 - c**3 + c**2 + c - 2. Let d(p) = 4*p**4 + 2*p**2 + 2*p**3 + p**3 - 5 - p**4 - 6*p**3 + 3*p. Let g(v) = -4*d(v) + 10*u(v). Factor g(j).
-2*j*(j - 1)**2*(j + 1)
Let h(c) = -2*c**3 + 0 - 2*c**2 + 1 - c**2. Let m be h(-2). Factor -50*w**4 + 8*w**2 - 5*w + m*w.
-2*w**2*(5*w - 2)*(5*w + 2)
Suppose 5*f - 2*l + l - 15 = 0, -9 = -3*f - 5*l. Let j(i) = i**2 - 21*i - 16. Let s be j(22). Find h such that -f*h - 3*h**2 + 6*h**2 + 0*h + s*h = 0.
-1, 0
Factor 2*v**2 - 4*v**3 + 7*v**4 - 2*v**4 + 0*v**3 - 3*v**4.
2*v**2*(v - 1)**2
Factor 2 + 14*a - 4*a + 0 - 7*a**3 - 3*a + 3*a**2 - 5*a**4.
-(a - 1)*(a + 1)**2*(5*a + 2)
Let u = -447 + 6709/15. Let f = u - -2/105. Suppose -6/7*o**3 - 6/7*o**4 - f*o**2 + 0*o - 2/7*o**5 + 0 = 0. Calculate o.
-1, 0
Factor 2/5*i + 0 + 0*i**2 - 2/5*i**3.
-2*i*(i - 1)*(i + 1)/5
Let v(l) = -13*l**3 - 17*l**2 - 9*l - 9. Let b(r) = 3*r**3 + 4*r**2 + 2*r + 2. Let x = 1 - -1. Let i(o) = x*v(o) + 9*b(o). Find h such that i(h) = 0.
-2, 0
Let s(g) = -g. Let x(y) = -5*y**2 + 15*y - 1. Let a(f) = 3*s(f) + x(f). Let p(d) = d**2 - 3*d. Let n(m) = -2*a(m) - 9*p(m). Factor n(r).
(r + 1)*(r + 2)
Let g = 20/9 - 31/18. Find m such that -5*m**3 - 1/2 - g*m**5 - 5*m**2 - 5/2*m**4 - 5/2*m = 0.
-1
Let o(i) = i. Let s be o(0). Suppose -4*u - 2*u = s. Solve 2/7*l**4 + u - 4/7*l**3 + 0*l + 2/7*l**2 = 0.
0, 1
Let r(z) be the third derivative of z**6/60 - 2*z**5/15 + z**4/3 + 46*z**2. Factor r(t).
2*t*(t - 2)**2
Suppose 2*s + 0*s - 6 = 0. Let b be 20*s/(54/3). Let -4/3 - 14/3*k - b*k**2 = 0. Calculate k.
-1, -2/5
Suppose 4/7*k**3 + 32/7*k**2 + 16/7*k - k**4 - 16/7 - 2/7*k**5 = 0. What is k?
-2, 1/2, 2
Let u be 0*(-4)/(-8)*1. Let y(k) be the second derivative of 2/5*k**5 + 0*k**2 + 3*k + 1/3*k**3 + u - 5/6*k**4. What is h in y(h) = 0?
0, 1/4, 1
Let l(f) be the third derivative of -1/168*f**8 + 1/30*f**6 + 2*f**2 + 0*f**5 - 1/12*f**4 + 0*f**3 + 0*f**7 + 0*f + 0. Find d such that l(d) = 0.
-1, 0, 1
Let a(i) = i**2 + 27*i + 126. Let w be a(-21). Factor -6/7*z**2 - 6/7*z**3 + w - 2/7*z - 2/7*z**4.
-2*z*(z + 1)**3/7
Suppose 2*o + 0 - 4 = 0. Let s(f) be the first derivative of -3/16*f**4 + 1/4*f**5 + 0*f**2 - o + 0*f - 1/6*f**3. Let s(x) = 0. Calculate x.
-2/5, 0, 1
Factor -484/5*y**3 - 16/5*y + 0 - 176/5*y**2.
-4*y*(11*y + 2)**2/5
Let k(h) be the first derivative of 5*h**2 - 4*h + 9/2*h**4 - 3 + 32/3*h**3. Factor k(a).
2*(a + 1)**2*(9*a - 2)
Let m(x) be the third derivative of -x**5/90 + x**4/36 + 2*x**2. Factor m(t).
-2*t*(t - 1)/3
Let t(n) be the third derivative of -n**7/3780 - n**6/270 - n**5/45 + n**4/6 + n**2. Let u(r) be the second derivative of t(r). Suppose u(l) = 0. Calculate l.
-2
Let 4/13 - 16/13*g**2 - 6/13*g**3 - 6/13*g = 0. Calculate g.
-2, -1, 1/3
Factor 4/3 - 3*d - 1/3*d**3 + 2*d**2.
-(d - 4)*(d - 1)**2/3
Let p(y) = 2*y**2 - 8*y - 2. Let r(j) = -j**2 - j - 1. Let v(f) = p(f) - 2*r(f). Determine i so that v(i) = 0.
0, 3/2
Let f(m) be the second derivative of -m**7/45 - 2*m**6/15 - m**5/3 - 4*m**4/9 - m**3/3 - 2*m**2/15 + 10*m. Solve f(s) = 0 for s.
-1, -2/7
What is l in 0*l**4 - 4*l**3 + 6*l**3 + l**4 + l**4 = 0?
-1, 0
Let j(k) = k**3 - 22*k**2 - 53*k + 123. Let d be j(24). Find m, given that 0 + 0*m**d + 4/3*m**2 - 4/3*m**4 + 2/3*m - 2/3*m**5 = 0.
-1, 0, 1
Let d(c) be the first derivative of -c**7/5040 + c**6/1080 - c**3/3 - 4. Let v(k) be the third derivative of d(k). Factor v(f).
-f**2*(f - 2)/6
Let g(l) be the second derivative of -l**4/36 - l**3/18 + 2*l. Determine w, given that g(w) = 0.
-1, 0
Let q(a) be the first derivative of -3*a**4/4 - 2*a**3 - 2*a**2 - a - 5. Let l(g) be the first derivative of q(g). What is j in l(j) = 0?
-2/3
Suppose 8*r = 6*r + 8. Let s(l) be the second derivative of 1/90*l**6 + 1/36*l**r - 1/6*l**3 - l + 1/20*l**5 - 1/3*l**2 + 0. What is w in s(w) = 0?
-2, -1, 1
Let o(g) be the second derivative of -g**5/60 - g**4/18 + 2*g. Let o(a) = 0. Calculate a.
-2, 0
Let r(v) be the second derivative of -2*v**6/15 - 3*v**5/5 + 3*v**4 - 10*v**3/3 - 5*v. Factor r(n).
-4*n*(n - 1)**2*(n + 5)
Let m(k) = k + 4. Let v be m(-3). Let w be (-98)/(-40) - v/5. Find z, given that 4*z**3 - 7/2*z**2 - 1/4 + 1/2*z**5 - w*z**4 + 3/2*z = 0.
1/2, 1
Let z = 49/135 + 1/27. Solve 0*q + 2/5*q**2 - z = 0 for q.
-1, 1
Let j be (-4)/(-2) + 0 + 0. Determine x so that 4*x**3 + 0*x**3 + x**3 + 5*x**3 - j*x - 6*x**4 + 6*x**2 - 8*x**5 = 0.
-1, 0, 1/4, 1
Let o(x) be the first derivative of 9*x**5/10 + 21*x**4/4 + 5*x**3/2 - 21*x**2/2 - 12*x + 28. Determine n so that o(n) = 0.
-4, -1, -2/3, 1
Let n(r) be the second derivative of -r**5/20 - r**4/6 + r**3/6 + r**2/2 + 4*r. Let g(c) = -c**2 - c + 1. Let l(u) = -3*g(u) + 3*n(u). Factor l(a).
-3*a*(a - 1)*(a + 2)
Let o(r) = r**3 - 19*r**2 + 20*r - 19. Let d be o(18). Let s = -15 + d. Find n, given that -1/2*n**4 + n**3 - 1/2*n**s + 0*n + 0 = 0.
0, 1
Factor -8/7*o**3 + 8/7*o - 4/7*o**2 + 4/7.
-4*(o - 1)*(o + 1)*(2*o + 1)/7
Find k such that -8/5*k + 8/15 + 2/3*k**2 = 0.
2/5, 2
Let o = 85 + -85. Let v(f) be the first derivative of -4 + 1/12*f**3 - 1/8*f**2 + o*f. Determine n so that v(n) = 0.
0, 1
Suppose -9