.
2
Let b(c) = -10*c**3 - 22*c**2 - 17*c - 12. Let a be 28/((-7)/(14/(-4))). Let x(m) = 3*m**3 + 7*m**2 + 6*m + 4. Let u(p) = a*x(p) + 4*b(p). Factor u(w).
2*(w + 1)*(w + 2)**2
Let v(y) = -6*y**5 + 6*y**4 + 4*y**3 + 4*y + 4. Let c(l) = 13*l**5 - 13*l**4 - 9*l**3 - 9*l - 9. Let j(x) = 4*c(x) + 9*v(x). Solve j(a) = 0.
0, 1
Let f(v) be the third derivative of -v**5/20 + v**4/8 + v**3 + 23*v**2. Factor f(r).
-3*(r - 2)*(r + 1)
Let t(n) = n - 6. Let b be t(9). Determine z so that 0*z**3 + 6*z**2 - 3*z - 6 - 2*z**b + 3*z**3 + 2*z**3 = 0.
-2, -1, 1
Let m(y) be the second derivative of y + 1/3*y**2 + 2/9*y**3 + 0*y**4 + 0 - 1/15*y**5 - 1/45*y**6. Let m(u) = 0. Calculate u.
-1, 1
Suppose z = 2*d - 6, -5*d = -z - 13 - 2. Let b(g) be the first derivative of -g**4 + z*g**2 + 2 - 1/3*g**3 + 0*g + 1/5*g**5 + 2/3*g**6. Solve b(j) = 0 for j.
-1, -1/4, 0, 1
Suppose 4*w + 5 = -w. Let g be -5 + w + 3 - -5. Suppose -4*i**3 + 2*i**2 + 2*i**3 + 2*i + g*i = 0. What is i?
-1, 0, 2
Let w(p) be the first derivative of -p**3 + 0*p + 0*p**2 - 1/160*p**5 + 2 - 1/480*p**6 + 1/16*p**4. Let a(b) be the third derivative of w(b). Factor a(s).
-3*(s - 1)*(s + 2)/4
Let n(v) be the first derivative of -4*v + 1 - 2*v**2 - 1/3*v**3. Factor n(w).
-(w + 2)**2
Let f(r) = r**2 - 14*r - 30. Let i be f(16). Let m(w) be the first derivative of -1/3*w - 1/9*w**3 + 1/3*w**2 - i. Suppose m(k) = 0. What is k?
1
Let -3*u**4 + 35*u + 16*u**3 - 2*u**4 - 10 + 9*u**3 - 45*u**2 = 0. Calculate u.
1, 2
Suppose 3*k = -12, 2*k = 4*a + 7 - 23. Suppose 0*o - 3 = 5*o + 3*v, a = -o - 2*v. Let -8/9*f**2 - 2/9*f**3 + o - 8/9*f = 0. What is f?
-2, 0
Let k(g) = g**2 + g + 1. Let l(p) = -4*p**2 - 12*p - 2. Let n(w) = -4*k(w) - 2*l(w). Factor n(x).
4*x*(x + 5)
Let h(z) be the second derivative of -z**5/60 + z**4/9 - 2*z**3/9 + 12*z. Suppose h(v) = 0. What is v?
0, 2
Let k(q) = -q**2 - 20*q - 19. Let y be k(-19). Let v(x) be the first derivative of 0*x + 3 + y*x**2 - 2/9*x**3. Factor v(h).
-2*h**2/3
Let k = -15 - -15. Let v(z) be the first derivative of 0*z + k*z**2 + 1/20*z**5 - 1 + 0*z**3 - 1/16*z**4. Factor v(g).
g**3*(g - 1)/4
Let x(o) = -12*o**3 + 8*o**2 + 12*o + 8. Suppose -2*z - 14 = -12. Let d(u) = -u**3 + u**2 + u + 1. Let k(c) = z*x(c) + 8*d(c). Find v such that k(v) = 0.
-1, 0, 1
Let n = 1 - -3. Let a(h) be the third derivative of 0*h**3 + n*h**2 + 0 + 1/60*h**4 + 0*h - 1/300*h**5 - 1/600*h**6. Suppose a(o) = 0. Calculate o.
-2, 0, 1
Suppose 3*z = 2*z + 3. Suppose -12*w + 27*w**2 - z*w + 3 - w - 2*w = 0. What is w?
1/3
Suppose 0 = r + 5*z - 14, r - 6 = z - 2*z. Let s be (1 - 0) + (-1 - -2). Factor 6*d - 6*d**s - 3*d**2 - r + 3.
-(3*d - 1)**2
Let s(c) be the second derivative of -c**6/90 - c**5/60 + c**4/12 + c**3/18 - c**2/3 - 32*c. Determine y, given that s(y) = 0.
-2, -1, 1
Let y(q) be the first derivative of 3/8*q**4 + 0*q**2 + 3/20*q**5 + 0*q + 5 + 1/4*q**3. Find h, given that y(h) = 0.
-1, 0
Let w(h) be the first derivative of -1/5*h**5 + 3 - h + h**4 - 2*h**3 + 2*h**2. Factor w(n).
-(n - 1)**4
Find l such that 4/3*l + 2/9*l**2 + 10/9 = 0.
-5, -1
Let v(x) = 3*x**3 - 8*x**2 + 3*x - 7. Let a(k) = k + 12. Let g be a(-9). Let n(b) = -b**3 + 4*b**2 - b + 3. Let d(j) = g*v(j) + 7*n(j). Factor d(r).
2*r*(r + 1)**2
Let t(b) be the first derivative of b**6/160 + b**5/240 - b**4/32 - b**3/24 + b**2 - 4. Let p(m) be the second derivative of t(m). Find o such that p(o) = 0.
-1, -1/3, 1
Factor 0 + 0*m**2 - 2/3*m**3 + 2/3*m.
-2*m*(m - 1)*(m + 1)/3
Suppose -15 + 0 = -5*k. Factor 11*l**2 - 5*l**k - 56*l + 16 + 33*l**2 - 5*l**3.
-2*(l - 2)**2*(5*l - 2)
Let u(v) be the first derivative of -4*v**6/9 + 16*v**5/15 + 23*v**4/6 - 38*v**3/9 - 55*v**2/3 - 50*v/3 + 9. Factor u(g).
-2*(g + 1)**3*(2*g - 5)**2/3
Let r(c) = -10*c**2 - c**3 + 2 + c + c + 8*c**2. Let v be r(-3). Factor 0*m**4 - 1/2*m**3 + 0 + 0*m**2 + 1/4*m + 1/4*m**v.
m*(m - 1)**2*(m + 1)**2/4
Let b = 8 + -4. Factor b - 8*u + 2*u**2 + 9 - 5.
2*(u - 2)**2
Suppose 0*z + z = 4*a - 7, -4*a = -3*z + 3. Let j(y) be the first derivative of 2 - 3*y**4 + 9/5*y**5 + 2*y**2 - 2/3*y**a + y. Suppose j(w) = 0. What is w?
-1/3, 1
Let t(k) be the second derivative of k**7/1680 - k**6/720 - 2*k**3/3 + 3*k. Let m(y) be the second derivative of t(y). Solve m(u) = 0.
0, 1
Let l(f) be the first derivative of 2*f**5/55 + f**4/11 - 10. Solve l(u) = 0 for u.
-2, 0
Let f = 5 + -3. Suppose 0 = f*z - 3 - 1. Factor -z*t + 0*t**2 + 0*t**4 + 6*t**2 + 2*t**4 - 6*t**3.
2*t*(t - 1)**3
Let h = 4 - 3. Let w(r) be the first derivative of h - 4*r**2 + 6*r - 2*r + 0*r**3 + r**3 + 0*r. Factor w(z).
(z - 2)*(3*z - 2)
Suppose -28 = 3*u - 4*u. Suppose 2*w = 6*w - u. Factor -2*t - 6*t**2 + 2*t**5 + 3*t**2 - 4*t**4 + w*t**2.
2*t*(t - 1)**3*(t + 1)
Let a(i) be the third derivative of -2209*i**5/150 - 47*i**4/15 - 4*i**3/15 + 2*i**2 + 2. Factor a(v).
-2*(47*v + 2)**2/5
Suppose -1/6*k**4 + 0 - 1/6*k - 1/2*k**2 - 1/2*k**3 = 0. Calculate k.
-1, 0
Let l(f) = f - 4. Let p be l(4). Let 1 + 2*x**2 + 0*x**2 + p*x**2 - 4*x + 1 = 0. Calculate x.
1
Let i be 0/(3 - (-2 + 2)). Let j(q) be the third derivative of -1/6*q**4 - 7/60*q**6 + i + 3/10*q**5 + 0*q + 0*q**3 + 2*q**2. Let j(d) = 0. Calculate d.
0, 2/7, 1
Let y = -61/15 - -22/5. Suppose -y*u**2 - 4/3 - 4/3*u = 0. Calculate u.
-2
Let s(w) = w**3 - 4*w**2 - 5*w - 1. Let p be s(5). Let m = p - -3. Factor -5*b**2 + 0*b**2 - m + 3*b**2 + 4*b.
-2*(b - 1)**2
Let l = 29641/57 - 520. Let i = l - -37/57. Solve 4/3*g + i*g**4 + 10/3*g**2 + 8/3*g**3 + 0 = 0 for g.
-2, -1, 0
Suppose 0*x = 4*m + 4*x - 12, -5*x - 17 = m. Suppose 4*s + 0 - 28 = 0. Factor m*k**3 + s*k**4 - 2*k + 1 - 2 + 2*k**5 - k**2 + 3*k**2.
(k + 1)**4*(2*k - 1)
Let l be ((-16)/(-50))/(((-220)/50)/(-11)). Let 2/5*h**3 + 0*h**2 + l*h**4 + 0 + 2/5*h**5 + 0*h = 0. Calculate h.
-1, 0
Let n = -31/7 - -169/35. Factor -1/5*j**3 - n + 2/5*j**2 + 1/5*j.
-(j - 2)*(j - 1)*(j + 1)/5
Factor 0*r + 0 - 1/3*r**3 - 1/3*r**2.
-r**2*(r + 1)/3
Let c(r) = r**2 - 3*r - 3. Let k be c(6). Suppose 2*d - 5*q + k = 0, 0 = -5*q + 10 + 5. Let -3/4*h**2 + d + 0*h = 0. Calculate h.
0
Suppose 3*w + 3 - 15 = 0. Let q(n) be the first derivative of -2/15*n**5 + 0*n**w + 1/6*n**2 + 0*n - 2 - 1/18*n**6 + 2/9*n**3. Determine h, given that q(h) = 0.
-1, 0, 1
Let a(u) be the second derivative of u**5/20 + u**4/12 - u**3/3 - 10*u. Let a(q) = 0. What is q?
-2, 0, 1
Suppose -2*n + 4*n + 2*j - 10 = 0, -4*n + j + 45 = 0. Let v be (3/(-6))/(n/(-32)). Suppose -8/5*x - v - 2/5*x**2 = 0. Calculate x.
-2
Let t(b) = 3*b**3 + b**2 + 5*b + 3. Let y(q) = q**3 + 4*q**2 + 4*q + 1. Let l be y(-3). Let k(j) = -j**3 + j**2 - j - 1. Let v(d) = l*k(d) - t(d). Factor v(f).
-(f + 1)**3
Factor 6/11*v - 2/11*v**5 + 4/11*v**2 - 4/11*v**3 + 2/11 - 6/11*v**4.
-2*(v - 1)*(v + 1)**4/11
Suppose 11*s = 15*s - 16. Solve 0*k**2 + 8/9*k**5 + 0 + 2/3*k**s + 0*k - 2/9*k**3 = 0 for k.
-1, 0, 1/4
Let v(n) = 16*n**3 + 44*n**2 + 152*n + 162. Let r(d) = 5*d**3 - 33 + 9*d**2 + 87 + 51*d + 9*d**2 - 3*d**2. Let o(c) = 10*r(c) - 3*v(c). Let o(y) = 0. What is y?
-3
Let s(h) be the second derivative of h**8/560 - h**7/200 + h**6/300 - h**3/2 + 2*h. Let n(p) be the second derivative of s(p). Find x such that n(x) = 0.
0, 2/5, 1
Let a = -89 + 89. Let t(i) be the third derivative of a*i + 0*i**5 + 1/90*i**6 + 0*i**3 - i**2 - 1/35*i**7 + 1/72*i**8 + 0*i**4 + 0. Find f such that t(f) = 0.
0, 2/7, 1
Suppose a = -4*h - 18, 2*a = 4*h + 17 + 7. Suppose 2*p + a*t = 3*p, 3*t = -3*p + 18. Factor -2/3*y**p + 2/3 - 4/3*y + 0*y**2 + 4/3*y**3.
-2*(y - 1)**3*(y + 1)/3
Suppose 0 = -4*q + 3*z + 3, 6*q = 5*q + 2*z - 3. Factor -r**3 + 0*r**3 - r**q - 2*r**2.
-2*r**2*(r + 1)
Let p(u) = -u**2 + 3*u. Suppose -3*n = -0*k + 4*k + 4, 5*k + 10 = -5*n. Let s be p(k). Solve 2*b**2 + 0*b - 4*b**s - 2*b = 0.
-1, 0
Let n(g) be the third derivative of -g**5/75 + g**4/15 - 2*g**3/15 - g**2. Suppose n(d) = 0. Calculate d.
1
Suppose -3*o + 2 = -j - 6*o, 3 = -j - 4*o. Let n be ((-3)/(-2))/(3/4). What is b in n*b**3 + b**4 + j + b - b**2 - b**5 - 2*b - b**2 = 0?
-1, 1
Let f(q) = -q. Let z be f(-3). Suppose -z*k - 2*k + 25 = 0. Factor -2*n**k + 8*n**5 + 9*n**4 + 14*n**3 + 7*n**4 + 4*n**2.
2*n**2*(n + 1)**2*(3*n + 2)
Let i(r) be the second derivative of r**5/50 - r**4/30 + 38*r. Factor i(k).
2*k**2*(k - 1)/5
Determine d, given that 0