2*w + 13.
w*(w + 2)
Let g(i) be the first derivative of i**3/9 + i**2/3 - i + 14. Find z, given that g(z) = 0.
-3, 1
Let z(q) = -4*q**3 + 8*q**2 - 9*q. Let w(k) = 12*k**3 - k**2 + 1. Let t be w(1). Let n(a) = 10*a**3 - 20*a**2 + 22*a. Let p(c) = t*z(c) + 5*n(c). Factor p(u).
2*u*(u - 1)**2
Let k(l) be the first derivative of -8/9*l**2 + 10/27*l**3 - 8 - 8/9*l. Factor k(y).
2*(y - 2)*(5*y + 2)/9
Let g = 780/77 - 102/11. Factor 10/7*c**2 - 2/7*c**3 - 2*c + g.
-2*(c - 3)*(c - 1)**2/7
Let m be ((-24)/(-63))/((-84)/(-18) - 4). What is i in 0*i + 0 + 8/7*i**2 + m*i**3 = 0?
-2, 0
Let h(w) be the first derivative of -w**6/60 - w**5/10 + 4*w**3/3 - 3*w**2/2 - 1. Let j(r) be the second derivative of h(r). Suppose j(f) = 0. What is f?
-2, 1
Let l(q) be the third derivative of -q**11/997920 + q**9/60480 + q**8/30240 - q**5/20 - 5*q**2. Let z(i) be the third derivative of l(i). Factor z(d).
-d**2*(d - 2)*(d + 1)**2/3
Solve l**3 - 3*l**3 + 4*l**2 + 2*l**2 - 4 - 2*l**4 + 2*l = 0.
-2, -1, 1
Factor 1 - 6 + 12*f + 2*f**2 - 9.
2*(f - 1)*(f + 7)
Let h(y) be the third derivative of y**6/48 - y**5/30 - 7*y**4/240 + y**3/30 + 36*y**2. Determine k so that h(k) = 0.
-2/5, 1/5, 1
Let g(p) be the first derivative of p**9/1512 - p**8/840 - p**7/420 + p**6/180 - 2*p**3 + 5. Let x(u) be the third derivative of g(u). Factor x(r).
2*r**2*(r - 1)**2*(r + 1)
Let t(h) = -h**2 - h + 1. Let s(b) = 5*b**2 - 1 + 2 + 8*b + 0*b**2 - 7. Let z(y) = s(y) + 6*t(y). Factor z(q).
-q*(q - 2)
Let y = 13 + -11. Let w(o) be the first derivative of 2 - 2*o - 9/4*o**4 + 7/5*o**5 + 9/2*o**y - 5/3*o**3. Find q, given that w(q) = 0.
-1, 2/7, 1
Suppose 5*m + 25 = 5*v, -110*m + 113*m = 4*v - 15. Let 2*p**4 + 2*p**3 + 2/3*p**2 + v*p + 2/3*p**5 + 0 = 0. What is p?
-1, 0
Let h = 547/456 + -22/19. Let a(n) be the third derivative of 0 - 1/32*n**4 + 0*n - 1/480*n**6 + 2*n**2 + h*n**3 + 1/80*n**5. Find z such that a(z) = 0.
1
Let y be 6/(-24) - (-17)/4. Determine v so that 22*v**2 + 4*v - 12*v**5 - 99*v**5 + 15*v**5 - 112*v**y + 10*v**3 - 8*v = 0.
-1, -2/3, 0, 1/4
Suppose 12 = -0*s - 2*s. Let f = s + 6. Factor -6*v**4 + 6*v**2 + f + 4*v**3 + 0 + 2*v - 6*v.
-2*v*(v - 1)*(v + 1)*(3*v - 2)
Let h(y) = -y**3 + y**2 - y - 1. Let k(r) = 8*r**3 - 2*r**2 + 8*r + 6. Let s(c) = 6*h(c) + k(c). Factor s(m).
2*m*(m + 1)**2
Suppose -3/5*j**4 + 0 + 3/5*j**2 + 0*j + 0*j**3 = 0. What is j?
-1, 0, 1
Let o(j) be the second derivative of -j**9/5040 + j**8/560 - j**7/210 - j**4/6 + 2*j. Let b(f) be the third derivative of o(f). Suppose b(p) = 0. What is p?
0, 2
Let h be 4 - (-1)/180*-719. Let j(k) be the third derivative of k**2 - 1/9*k**3 - 1/36*k**4 + 0 + h*k**6 + 0*k + 1/90*k**5. Factor j(m).
2*(m - 1)*(m + 1)**2/3
Let l(c) = 3*c**4 - 20*c**3 - 5*c**2 + 22*c - 2. Let b(m) = 5*m**4 - 40*m**3 - 10*m**2 + 45*m - 5. Let x(d) = -2*b(d) + 5*l(d). Factor x(v).
5*v*(v - 4)*(v - 1)*(v + 1)
Let g(h) be the third derivative of -h**7/70 - h**6/16 - h**5/40 + h**4/8 - 4*h**2. What is s in g(s) = 0?
-2, -1, 0, 1/2
Let p(f) = -7*f - 11. Let a be p(-12). Suppose 16*u**4 - 18*u + 44*u + 56*u**3 + a*u**2 + 10 + 16*u - 1 = 0. What is u?
-1, -3/4
Let x be ((-66)/36)/11*4/(-1). Factor -x*m + 0 - 2/3*m**2.
-2*m*(m + 1)/3
Let t(c) = -8*c**5 + 4*c**3 + 6*c**2 - 8*c + 6. Let o(h) = h**5 - h**2 + h - 1. Suppose 12 = -3*w + 5*w. Let v(g) = w*o(g) + t(g). Factor v(z).
-2*z*(z - 1)**2*(z + 1)**2
Let a(p) = -3*p**2. Let f be a(-1). Let l(k) = k**2 + k - 2. Let s be l(f). Factor 2*m**3 - m**3 - 2*m**5 + m**5 - m**s + m**2.
-m**2*(m - 1)*(m + 1)**2
Let p(t) be the third derivative of -t**6/360 - t**5/36 - t**4/9 - 2*t**3/9 + 9*t**2. Solve p(z) = 0 for z.
-2, -1
Factor -10*f**4 - 2*f**4 - 6*f**2 + 10*f**3 + 5*f**3 + 3*f**5.
3*f**2*(f - 2)*(f - 1)**2
Find d, given that 0*d - 2/11*d**2 + 2/11 = 0.
-1, 1
Let k = 6 + -6. Suppose -4*i + 3*i = k. Factor -42/5*s**4 + 0 + i*s - 8*s**3 - 8/5*s**2.
-2*s**2*(3*s + 2)*(7*s + 2)/5
Let b be 1*-2 - (-801)/387. Let a = b - -123/86. Factor -a*j**2 + 2 - 2*j.
-(j + 2)*(3*j - 2)/2
Let v = 18 + -20. Let h be 1 + 1/(v/(-2)). Factor 1/4*k - 1/4*k**h - 1/4*k**3 + 1/4.
-(k - 1)*(k + 1)**2/4
Let v(m) be the second derivative of 0*m**3 + 0*m**4 + 1/20*m**6 - m + 0*m**2 + 0 - 3/40*m**5. Factor v(w).
3*w**3*(w - 1)/2
Let h(w) be the third derivative of -w**5/210 + w**3/21 + 5*w**2. Factor h(z).
-2*(z - 1)*(z + 1)/7
Let q(a) be the first derivative of -a**6/120 + a**5/30 - a**4/24 + a**2/2 - 3. Let o(c) be the second derivative of q(c). Factor o(d).
-d*(d - 1)**2
Suppose -q - 2*b + 2 = 4*q, 5*q = 2*b + 18. Let o be (4/(-6))/((-42)/18). Determine c, given that 0 - o*c + 2/7*c**q = 0.
0, 1
Let n = 3996/5 - 796. Let h be (-2)/4*2*0. Let -4/5*s**2 + h + n*s**4 - 2/5*s**3 + 0*s - 2*s**5 = 0. Calculate s.
-2/5, 0, 1
Factor 3*n - 4*n**2 + 8*n**2 - 7*n**2.
-3*n*(n - 1)
Let k(w) be the first derivative of -w**6/3 - 8*w**5/5 - 3*w**4 - 8*w**3/3 - w**2 - 6. Solve k(u) = 0 for u.
-1, 0
Let a = 787/147 - 1/49. Solve 10/3*m**3 + a*m**2 + 8/3*m + 2/3*m**4 + 0 = 0 for m.
-2, -1, 0
Let c = -390 - -392. Suppose -1/4*z + 1/2 - 1/4*z**c = 0. Calculate z.
-2, 1
Let q(y) = 6*y**2 - 2*y - 2. Let t(x) = -25*x**2 + 7*x + 9. Let k(n) = -9*q(n) - 2*t(n). Factor k(l).
-4*l*(l - 1)
Let t(p) = -4*p - 5. Let h be t(-3). Suppose -h*g - 16 = -11*g. What is w in -2/5*w**5 - 12/5*w**3 - 2/5*w + 8/5*w**g + 8/5*w**2 + 0 = 0?
0, 1
Suppose -8 = -4*c - 0. Suppose -w - c = -7. Factor -1/2*l**3 + 1/2*l**w + 0*l + 1/2*l**2 - 1/2*l**4 + 0.
l**2*(l - 1)**2*(l + 1)/2
Let g(r) = 2*r**2 - 3*r + 2. Let c be g(2). Suppose -s - 1 + c = 0. Find l such that 0 - 1/2*l + 0*l**2 + l**s - 1/2*l**5 + 0*l**4 = 0.
-1, 0, 1
Find x, given that -3*x**2 + 12*x - 117*x**4 - 4*x**2 + 121*x**4 + 3*x**2 - 12*x**3 = 0.
-1, 0, 1, 3
Suppose -d - 21 = -4*d. Factor -3*n - d + 7 - 3*n**2.
-3*n*(n + 1)
Suppose -3*c = l - 12 - 6, 0 = 5*l + c - 20. What is w in -5*w**2 + 4*w**2 + l*w**2 - 2*w = 0?
0, 1
Suppose 2*n + 9*n = 0. Let t(s) be the third derivative of 0*s**3 + n + 3*s**2 - 1/240*s**6 + 0*s**4 - 1/120*s**5 + 0*s. Factor t(r).
-r**2*(r + 1)/2
Let a(s) = 23*s**3 - 7*s**2 + 7*s. Let g(c) = 12*c**3 - 3*c**2 + 4*c. Let i be 4/6 - (-66)/(-18). Let x(y) = i*a(y) + 5*g(y). What is r in x(r) = 0?
0, 1/3
Let x = -299/30 - -10. Let b(c) be the second derivative of 0*c**2 - x*c**4 + 0 + 0*c**3 + 1/50*c**5 - 2*c. Factor b(g).
2*g**2*(g - 1)/5
Let q(u) be the second derivative of 0*u**2 + 0*u**3 + 5*u + 0 + 1/10*u**5 - 1/6*u**4. Factor q(k).
2*k**2*(k - 1)
Let i(v) = -21*v**3 + 3*v**2 + 12*v - 3. Let r(n) = -5*n**3 + n**2 + 3*n - 1. Let h(o) = 2*i(o) - 9*r(o). Factor h(u).
3*(u - 1)**2*(u + 1)
Factor -f**2 + 5 - 2*f**2 + 4 - 5*f - f.
-3*(f - 1)*(f + 3)
Let q(t) be the second derivative of t**9/25200 + t**8/11200 - t**4/12 + 3*t. Let m(p) be the third derivative of q(p). Determine o, given that m(o) = 0.
-1, 0
Let g(t) = 25*t**3 + 40*t**2 + 25*t - 50. Let o(k) = -k**3 - 1. Let l(z) = g(z) + 20*o(z). Factor l(q).
5*(q - 1)*(q + 2)*(q + 7)
Let b(m) be the first derivative of 42/5*m**5 + 3 + 4*m**3 + 49/18*m**6 + 2/3*m**2 + 0*m + 109/12*m**4. Factor b(y).
y*(y + 1)**2*(7*y + 2)**2/3
Let w(g) be the second derivative of 0 - g + 1/30*g**5 + 1/3*g**3 + g**2 - 1/6*g**4. Let p(h) be the first derivative of w(h). Suppose p(y) = 0. What is y?
1
Let s be 342/(-30)*(-5)/2. Let j = 29 - s. Factor -1/2*u**4 + 0*u**3 + 0 + j*u**2 + 1/4*u**5 - 1/4*u.
u*(u - 1)**3*(u + 1)/4
Let y(f) = 3*f - 10. Let j be y(4). Suppose 3 - 3 + 3*b**3 - j*b**3 = 0. Calculate b.
0
Let o = 475 + -473. Factor -1/2 - 2*n**o - 1/4*n**5 + 7/4*n + 1/2*n**4 + 1/2*n**3.
-(n - 1)**4*(n + 2)/4
Suppose 5*k = -2*t + 6 - 18, 4*t = 5*k + 36. Let w be ((-1)/t)/(-3 - -2). Suppose -1/4*b - 1/2*b**2 - w*b**3 + 0 = 0. What is b?
-1, 0
Let u(j) be the third derivative of -j**6/660 + j**4/132 - 35*j**2. Suppose u(a) = 0. Calculate a.
-1, 0, 1
Suppose -25 = -4*j - j. Suppose -7*q = -j*q. What is i in 27/2*i**4 + 45*i**3 + q + 12*i + 42*i**2 = 0?
-2, -2/3, 0
Suppose -16 = -5*z + 4. Let i be z + (0 - 1 - 3). Suppose -g**3 + 4/3*g + 4/3*g**2 + i = 0. Calculate g.
-2/3, 0, 2
Let s(c) = 60*c**2 + 31*c - 11. Let y(d) = 15*d**2 + 8*d - 3. Let q(v) = -2*s(v) + 9*y(v). Factor q(z).
5*(z + 1)*(3*z - 1)
Let q(r) be the third derivative of -1/35*r**7 + 0*r**5 + 0*r**6 - 5/112*r**8 + 