)*(o + 2)/5
Let v(z) = z**2 + 2*z + 1. Let g be v(-4). Let s(a) = 12*a**2 - 16*a - 7. Let b(m) = -3*m**2 + 4*m + 2. Let k(y) = g*b(y) + 2*s(y). Solve k(l) = 0 for l.
-2/3, 2
Let b(g) be the first derivative of 2*g**5/15 + 2*g**4/3 + 10*g**3/9 + 2*g**2/3 + 4. Let b(z) = 0. What is z?
-2, -1, 0
Let w(z) = 31*z**5 + 10*z**4 - 21*z**3 - 11*z**2 - 11. Let c(a) = -6*a**5 - 2*a**4 + 4*a**3 + 2*a**2 + 2. Let n(k) = 11*c(k) + 2*w(k). Factor n(h).
-2*h**3*(h + 1)*(2*h - 1)
Solve 12/5*u + 0 + 3/5*u**2 = 0 for u.
-4, 0
Suppose 64/5 + 4/5*n**2 + 32/5*n = 0. What is n?
-4
Let n(v) = 13*v**2 - 12*v + 2. Let f(t) = 7*t**2 + 2 - 6*t - 6*t + 0 + 5*t**2. Let i(p) = 5*f(p) - 6*n(p). Factor i(x).
-2*(3*x - 1)**2
What is j in 6 - 2*j**2 + 7*j**3 - 8*j + 2 - 3*j**3 - 2*j**3 = 0?
-2, 1, 2
Let x be (-18)/(-36)*(-1 - (2 + -7)). Factor 2*h**3 + 18/5*h + 4/5 + 24/5*h**x.
2*(h + 1)**2*(5*h + 2)/5
Let l(q) = 5*q**2 - 7*q. Let v(s) = -9*s**2 + 13*s. Let p(t) = 5*l(t) + 3*v(t). Suppose p(a) = 0. Calculate a.
0, 2
Suppose 3*c = 6*c. Let 0*p + p + c*p - 2*p + p**3 = 0. What is p?
-1, 0, 1
Let b(v) be the third derivative of -4*v**2 + 0 - 1/36*v**4 + 0*v + 1/18*v**3 + 1/180*v**5. Factor b(o).
(o - 1)**2/3
Let k(w) be the third derivative of -w**7/4620 + w**6/1980 - 5*w**3/3 + 11*w**2. Let o(p) be the first derivative of k(p). Determine u so that o(u) = 0.
0, 1
Let b(x) be the second derivative of 0*x**2 + 0 - 1/18*x**4 + 1/30*x**5 - 1/63*x**7 - 3*x + 1/45*x**6 + 0*x**3. Solve b(y) = 0 for y.
-1, 0, 1
Let a = -473 - -476. Factor 2*v**2 + 1/2*v**5 - 3*v**a + 0 - 1/2*v**4 + 4*v.
v*(v - 2)**2*(v + 1)*(v + 2)/2
Let b(t) be the second derivative of 4/3*t**3 + 4/5*t**5 + 0*t**2 + 2/15*t**6 - 5*t + 0 + 5/3*t**4. Solve b(a) = 0 for a.
-2, -1, 0
Suppose -2*f + 9 = 1. Suppose 0 = 4*m + 4*k + 16, 2*k = f*m - 0*m - 14. Determine a so that -7/2*a + 5/2*a**2 + m = 0.
2/5, 1
Suppose -i + 0 = m - 9, -2*m + 13 = i. Factor 0*s - 2/7*s**4 + 2/7*s**3 + 2/7*s**2 + 0 - 2/7*s**i.
-2*s**2*(s - 1)*(s + 1)**2/7
Factor -2/9*s**5 - 2/3*s**4 + 2/9 + 4/9*s**2 - 4/9*s**3 + 2/3*s.
-2*(s - 1)*(s + 1)**4/9
Let q(z) be the third derivative of 0*z + 0 + 3*z**2 + 1/840*z**8 - 1/450*z**5 + 0*z**3 - 1/300*z**6 + 1/1575*z**7 + 0*z**4. Let q(f) = 0. Calculate f.
-1, -1/3, 0, 1
Let t(m) be the second derivative of m**7/21 + 2*m**6/5 + 7*m**5/5 + 8*m**4/3 + 3*m**3 + 2*m**2 - 10*m. Factor t(b).
2*(b + 1)**4*(b + 2)
Let n(u) be the first derivative of 5*u**4/4 - 10*u**3/3 + 5*u**2/2 + 41. Factor n(z).
5*z*(z - 1)**2
Let h(g) be the second derivative of -g**6/40 - 3*g**5/20 - g**4/4 + 2*g**2 - 3*g. Let y(p) be the first derivative of h(p). Solve y(d) = 0.
-2, -1, 0
Let h(w) = 1 + 0 + w**2 + 2*w - 3*w. Suppose 4*t + 33 = -3*l, -3*l - 6 = -l. Let v(s) = -2*s**2 + 2*s - 5. Let r(z) = t*h(z) - 2*v(z). Factor r(x).
-2*(x - 2)*(x + 1)
Let b be 8/(-6*(-2)/6). Let 2/7*f**5 - 2/7*f**3 + 2/7*f**b - 2/7*f**2 + 0 + 0*f = 0. What is f?
-1, 0, 1
Let q(i) be the third derivative of 1/36*i**4 + 0 + i**2 - 2/9*i**3 + 1/90*i**5 + 0*i. Factor q(k).
2*(k - 1)*(k + 2)/3
Let c = 4988/5 - 994. Let c + 2/5*l**2 + 12/5*l = 0. What is l?
-3
Factor -6*r**3 + 7*r**4 + 4*r - 2*r**4 - 2*r**2 + 2*r**5 - 3*r**4.
2*r*(r - 1)**2*(r + 1)*(r + 2)
Suppose 0 = 18*x - 2*x. Factor x + 3/4*d**3 + 1/4*d**2 + 3/4*d**4 + 0*d + 1/4*d**5.
d**2*(d + 1)**3/4
Let j = 5 - 3. Factor j*d**3 - 3*d**2 + d**2 + 0*d**2.
2*d**2*(d - 1)
Let l = -155 - -161. Let q(s) be the second derivative of 0 - 3/10*s**l + 0*s**2 + 0*s**5 + 1/4*s**4 + 0*s**3 + 1/7*s**7 - 2*s. Find z such that q(z) = 0.
-1/2, 0, 1
Let i(h) = 9 + 2*h - 3*h + 1 + 5. Let w be i(11). What is s in 0 + 1/4*s - 1/4*s**3 + 1/4*s**2 - 1/4*s**w = 0?
-1, 0, 1
Suppose 0 = c - 6 + 3. Suppose d - 2*d + 2 = 0. What is k in 0*k**d + 0*k + 0 + 1/3*k**c = 0?
0
Let w(r) = -41*r**2 - 19*r + 6. Let g(x) = 40*x**2 + 20*x - 4. Let l(z) = 5*g(z) + 4*w(z). Determine i so that l(i) = 0.
-1/3
Let s(g) = 2*g - 3. Let w be s(3). Let j be w/20 + (-1)/(-4). Determine b, given that 6/5*b + 8/5*b**2 - j = 0.
-1, 1/4
Let z = 2 - -2. Suppose 2 = -3*f - z. Let t(l) = l**4 - l**3. Let d(u) = -6*u**4 + 2*u**2. Let w(g) = f*t(g) - d(g). Factor w(m).
2*m**2*(m + 1)*(2*m - 1)
Let d be (-17)/(-6) + 24/(-16). Let k(f) be the first derivative of -5/2*f**2 - 1 - d*f**3 - f. Factor k(v).
-(v + 1)*(4*v + 1)
Let t(b) be the first derivative of -2*b**5/15 - 2*b**4/3 - 66. Factor t(u).
-2*u**3*(u + 4)/3
Suppose -15*x = 35*x + 12*x. Factor -t + x + 7/2*t**2 + 2*t**3.
t*(t + 2)*(4*t - 1)/2
Let y(n) = -4*n - 1. Let c be ((-2)/6*-3)/(-1). Let k be y(c). What is o in -3*o**2 - 4*o + 0*o - k*o**2 = 0?
-2/3, 0
Let q(j) be the first derivative of 3*j**5/10 + 5*j**4/6 - 4*j**3/3 - 4*j**2 - 3*j - 2. Let x(o) be the first derivative of q(o). Solve x(v) = 0.
-2, -2/3, 1
Let u(y) be the third derivative of y**5/135 + y**4/12 + 4*y**3/27 - 26*y**2. Factor u(m).
2*(m + 4)*(2*m + 1)/9
Let 7*l**2 + 5*l**2 - 3*l**5 - 9*l**4 + 9*l - 9*l = 0. What is l?
-2, 0, 1
Let h(x) = -8*x**4 + 8*x**3 + 16*x**2 - 16*x - 12. Let u(c) = 9*c**4 - 8*c**3 - 17*c**2 + 16*c + 11. Let s(f) = -5*h(f) - 4*u(f). Factor s(k).
4*(k - 2)**2*(k + 1)**2
Find f, given that -2*f**2 + 12*f**2 + 0*f**3 - 6*f**3 + f**3 = 0.
0, 2
Let a(q) = -q**2 + 6*q - 1. Let l(m) = -3*m**2 + 19*m - 2. Let r(s) = 21*a(s) - 6*l(s). Factor r(p).
-3*(p - 3)*(p - 1)
Let r be -2 - 3*(-5)/6. Factor -3/2*x + r*x**3 + 0*x**2 + 1.
(x - 1)**2*(x + 2)/2
Let l(c) be the first derivative of -3*c**5/40 + 15*c**4/32 - 9*c**3/8 + 21*c**2/16 - 3*c/4 + 18. Factor l(t).
-3*(t - 2)*(t - 1)**3/8
Let t(b) = 2*b - 2. Let u be t(2). Factor 3*q + q**2 - 4*q**u - 3 + 3.
-3*q*(q - 1)
Let a = -5 + 9. Suppose 3 = j - 1. Factor j*k - 2*k**a + 3*k**4 - 2 + k**4 - 4*k**3.
2*(k - 1)**3*(k + 1)
Let a(g) = 3*g + 3. Let r be a(0). Find l, given that -29/2*l**2 - 69/2*l**r + 12*l - 2 + 90*l**4 - 54*l**5 = 0.
-1/2, 1/3, 1/2, 2/3
Let i(t) = -5*t**3 - t**2 + t + 1. Let q be i(-1). Suppose -4*p - 5*f + 1 = -3, 0 = -4*f - 16. Suppose -4*k + q - 2 - 6*k + p*k**2 + 18*k**3 = 0. What is k?
-1, 1/3
Let c(v) = v. Let z(u) be the second derivative of -u**5/10 + u**4/2 - 2*u**3/3 + u**2 + 3*u. Let s(q) = -2*c(q) + z(q). Factor s(j).
-2*(j - 1)**3
Let c(w) be the first derivative of -w**4/2 + 30*w**3 - 675*w**2 + 6750*w + 26. Factor c(g).
-2*(g - 15)**3
Let r(z) be the first derivative of 0*z**3 + 0*z + 1/14*z**4 + 3 + 0*z**2 + 2/35*z**5. Factor r(l).
2*l**3*(l + 1)/7
Let i(b) = b**3 + 12*b**2 + 7*b - 3. Suppose 0 = -2*c - 7 - 15. Let k be i(c). Factor w**2 - w**4 + 41*w - k*w.
-w**2*(w - 1)*(w + 1)
Let a(b) be the third derivative of b**6/24 - b**5/6 - 5*b**4/3 + 41*b**2. Factor a(t).
5*t*(t - 4)*(t + 2)
Let i be ((-4)/1)/(-8 - -6). Let d be (5/(-3))/(i/(-6)). Solve 0*n**3 - 3/5*n**d + 3/5*n**4 + 0*n**2 + 0 + 0*n = 0 for n.
0, 1
Suppose -3*y + 57 = 16*y. Factor -2/3*a**2 + 0 + 0*a + 1/3*a**y.
a**2*(a - 2)/3
Let c = -5 + 6. Suppose -5*r + c = -4. Suppose 0 + 6*k - 3 - 2*k**2 - r = 0. What is k?
1, 2
Let p be ((-1)/2)/(5/(-20)). Let j(s) be the first derivative of 2/3*s + 2/3*s**p - 1 + 2/9*s**3. Factor j(c).
2*(c + 1)**2/3
Let f(i) be the first derivative of -i**8/560 - i**7/150 - i**6/120 - i**5/300 + 3*i**2/2 - 4. Let j(p) be the second derivative of f(p). Factor j(b).
-b**2*(b + 1)**2*(3*b + 1)/5
Let 10*f**3 + 50/9*f**2 + 2/9*f**5 - 500/9*f - 26/9*f**4 + 0 = 0. What is f?
-2, 0, 5
Let i = 8 + -8. Suppose -3*j + 3*m = -18, -j + 5*m - m + 9 = i. Factor -3*f - 3*f**2 + 5*f**2 + j*f - 4.
2*(f - 1)*(f + 2)
Determine x, given that 16/7*x**2 + 0 + 8/7*x + 2/7*x**4 + 10/7*x**3 = 0.
-2, -1, 0
Factor 1/4*w**2 - w + 3/4.
(w - 3)*(w - 1)/4
Let l(b) = b**3 - 6*b**2 + 4*b + 7. Let j be l(5). Determine o so that -3*o**j + 2*o + 5 - 5 + o**3 = 0.
0, 1, 2
Let v(k) = -k**2 + k. Let j be v(0). Let b(l) be the second derivative of j + 2*l + 0*l**2 + 1/50*l**5 - 1/15*l**3 + 0*l**4. Determine h, given that b(h) = 0.
-1, 0, 1
Let k(s) = -s**4 + 3*s**3 - 9*s**2 - 3*s - 5. Let y(a) = 2*a**4 - 4*a**3 + 10*a**2 + 4*a + 6. Let b(g) = 6*k(g) + 5*y(g). Suppose b(c) = 0. What is c?
-1, 0, 1/2, 1
Let x(g) = g - 18. Let z be x(20). Let c be ((-3)/(-2))/((-1)/(-2)). Let -z*l**2 - 15/2*l**c + 9/2*l - 1 = 0. Calculate l.
-1, 1/3, 2/5
Let n be ((-8)/(-12))/((-3)/(-9)). Factor -3*r**5 - 9*r**3 + 27*r**4 + r