 = -4*t(x) + 15*w(x). Find m such that r(m) = 0.
0, 2
Suppose -2*p - l + 31 = 0, 5*p - 78 = -0*l - 3*l. Suppose 0 = -3*m - 3*j + p, -13 = -3*m - j + 12. Factor t**3 + 0*t - m*t**4 + 0*t + 3*t**3.
-2*t**3*(5*t - 2)
Let t(f) = f**2 + 2*f + 1. Let q(z) = 1 + z**2 - 3 - 3*z**2 - 4*z. Suppose -7*m = -2*m - 10. Let o(c) = m*q(c) + 5*t(c). Factor o(u).
(u + 1)**2
Suppose -b + 2*h + 1 = 5, 5*h + 1 = -3*b. Let o be (-4)/((-2)/(b + 4)). Let 0*w**2 + w - 1/2*w**o - w**3 + 1/2 = 0. What is w?
-1, 1
Suppose z = 3*z. What is x in 35*x**3 - x - 5*x**2 - 44*x**3 + z*x**2 - 7*x**4 - 2*x**5 = 0?
-1, -1/2, 0
Suppose -3*u + 2*u + 5 = 3*v, -3*v + 5*u = -29. Factor -14*l**v + 2*l + 12*l**3 + 0*l.
-2*l*(l - 1)*(l + 1)
Suppose -h = b - 9, -3*h + 3*b = h - 1. Let n(r) be the second derivative of 25/6*r**h + 0 + 10/3*r**3 + 3*r + r**2. Factor n(l).
2*(5*l + 1)**2
Factor -2*s**2 + 2*s**4 - 2*s + 3 + s**3 + s**3 - 3.
2*s*(s - 1)*(s + 1)**2
Let h(l) = -160*l**2 + 352*l + 104. Let b(s) = 29*s**2 - 64*s - 19. Let g(w) = -28*b(w) - 5*h(w). Factor g(t).
-4*(t - 3)*(3*t + 1)
Let p(c) be the first derivative of c**6/8 + 3*c**5/10 - c**3/2 - 3*c**2/8 - 14. Factor p(x).
3*x*(x - 1)*(x + 1)**3/4
Let f(l) = -l + 24. Let y be f(22). Let w be 2/56 + (-1)/(-4). Determine i so that -w*i**y - 2/7*i**3 + 0*i + 0 = 0.
-1, 0
Solve 2/3*l + 2*l**3 + 2*l**2 + 2/3*l**4 + 0 = 0 for l.
-1, 0
Let c = 2 - -2. Let y be ((-28)/10)/((-39)/65). Find w such that 10/3*w**2 + 0 + 2/3*w + 4/3*w**5 + 6*w**3 + y*w**c = 0.
-1, -1/2, 0
Suppose -5*m - f + 10 = 0, m = -0*m - f + 2. Factor -8*t**3 - 5*t**m + 7*t - 9*t**4 - 9*t + 24*t**3.
-t*(t - 1)**2*(9*t + 2)
Let n(i) be the second derivative of -i**5/110 + i**4/66 + i. Find j, given that n(j) = 0.
0, 1
Factor 0*w - 3/5*w**2 + 3/5.
-3*(w - 1)*(w + 1)/5
Let m(r) be the second derivative of r**4/12 - 2*r. Let o(g) = -3*g + 2. Let s(a) = -m(a) - o(a). Factor s(c).
-(c - 2)*(c - 1)
Let v = -41/3 + 55/4. Let w(c) be the third derivative of -1/30*c**5 + 2*c**2 + 1/3*c**3 + 0 + v*c**4 + 0*c - 1/60*c**6. What is p in w(p) = 0?
-1, 1
Let g(m) = -m**3 + m - 1. Let c(y) = y**5 - 9*y**4 + 33*y**3 - 56*y**2 + 47*y - 15. Let s(h) = -2*c(h) - 2*g(h). Determine p so that s(p) = 0.
1, 2
Let o(b) = -b**3 - 3*b**2 - 6*b - 6. Let j be o(-2). Suppose -2/9*y**3 + 0*y**j + 2/9*y + 0 = 0. What is y?
-1, 0, 1
Let a = 8/9 + -7/18. Let -3/2*x**2 + a*x**3 - 1/2 + 3/2*x = 0. Calculate x.
1
Let p = 5 - 5. Suppose 3*b = 3*a + 12, 0 = -2*b - a + 5 - 3. Factor 1/2*t**3 + p*t + 0 + 1/2*t**b.
t**2*(t + 1)/2
Let m(n) = n**3 + 4*n**2 - n. Let a be m(-3). Factor 0*j - 12*j - 1 - a*j - 35 - 4*j**2.
-4*(j + 3)**2
Let k(c) be the second derivative of c**7/273 + c**6/195 - c**5/26 + c**4/26 + 2*c - 16. Factor k(y).
2*y**2*(y - 1)**2*(y + 3)/13
Let g(v) be the second derivative of -v**6/120 + v**5/40 - v**3/12 + v**2/8 + v. Suppose g(i) = 0. Calculate i.
-1, 1
Let t(q) be the first derivative of 0*q**4 + 0*q**2 + q**3 + 5 - 3/5*q**5 + 0*q. Factor t(d).
-3*d**2*(d - 1)*(d + 1)
Let n = 14 - 10. Suppose 2 = -b + n. What is s in 1 + 0 - 5*s**2 + s**3 - s + 4*s**b = 0?
-1, 1
Suppose -16/7*u**2 - 2/7*u - 32/7*u**3 + 0 = 0. What is u?
-1/4, 0
Suppose -w = 3*x - 6, 5*x = 3*x + 10. Let s = 11 + w. Factor c**3 + 2*c**4 - 5*c**4 + 4*c**4 - c - c**s.
c*(c - 1)*(c + 1)**2
Let u(d) be the third derivative of -d**7/945 - d**6/90 - d**5/30 + 2*d**2 + 6*d. Factor u(v).
-2*v**2*(v + 3)**2/9
Let y(m) be the first derivative of m**8/1680 - m**6/360 - 4*m**3/3 + 3. Let w(x) be the third derivative of y(x). Factor w(q).
q**2*(q - 1)*(q + 1)
Determine h so that -4*h**2 - 17*h - 1375 + 79 + 20*h - 147*h = 0.
-18
Let n(o) be the second derivative of 0 + 1/18*o**4 - 1/15*o**5 - 1/45*o**6 + 0*o**2 + 2/9*o**3 - o. Suppose n(g) = 0. Calculate g.
-2, -1, 0, 1
Let g(k) be the second derivative of k**10/7560 + k**9/945 + k**8/420 - k**4/12 + 7*k. Let i(x) be the third derivative of g(x). Find p such that i(p) = 0.
-2, 0
Let r = -31 + 34. Let m(l) be the first derivative of -l - 2 + 1/2*l**2 - 1/12*l**r. Find d such that m(d) = 0.
2
Let g(x) be the third derivative of x**5/75 - 7*x**4/120 - x**3/15 + 10*x**2. Factor g(q).
(q - 2)*(4*q + 1)/5
Let x(r) = 9*r**4 - 25*r**3 + 31*r**2 - 23*r + 13. Let i(j) = 10*j**4 - 26*j**3 + 30*j**2 - 22*j + 14. Let f(d) = 5*i(d) - 6*x(d). Factor f(c).
-4*(c - 2)*(c - 1)**3
Let w(c) = -8*c**2 - 16*c - 3. Let t(n) = -4*n**2 - 8*n - 2. Let s(f) = 5*t(f) - 2*w(f). Factor s(p).
-4*(p + 1)**2
Let a = -2 + 2. Let g(r) be the first derivative of a*r**2 + 2/21*r**3 + 0*r + 3 + 1/14*r**4 - 1/21*r**6 - 2/35*r**5. Factor g(t).
-2*t**2*(t - 1)*(t + 1)**2/7
Let z(u) be the second derivative of -u**8/3360 + u**7/1260 + u**6/360 - u**5/60 + u**4/2 - 5*u. Let g(b) be the third derivative of z(b). Factor g(j).
-2*(j - 1)**2*(j + 1)
Let s(f) = -8*f**3 + 4*f**2 + 4*f + 6. Let r(p) = -p**3 + p + 1. Let b(z) = -6*r(z) + s(z). Solve b(j) = 0 for j.
0, 1
Let u(y) = y**3 - 3*y - 5*y**2 - 3 + y + 3*y. Let r be u(5). Factor -r*o + 3*o**2 + o**2 - 2 + 0*o**2 + 2*o**3 - 2*o**2.
2*(o - 1)*(o + 1)**2
Let q(c) = -7*c**3 - 3*c**2 + 2*c - 1. Let k be q(-3). Let z = k - 1393/9. What is g in 4/9*g + 2/9 + z*g**2 = 0?
-1
Let c(l) be the third derivative of 1/20*l**5 - 2/3*l**3 + 0*l**4 - 2*l**2 + 0 + 0*l + 1/120*l**6. Factor c(w).
(w - 1)*(w + 2)**2
Find a, given that -52*a + 0*a**2 + 21*a - 55 - 5*a**2 - 29*a = 0.
-11, -1
Let d(m) = m + 5. Let l be d(-3). Let p(i) be the first derivative of 2 + 2/9*i**3 + 2/3*i + 2/3*i**l. Suppose p(z) = 0. What is z?
-1
Suppose -2*g = -g - 3. Suppose g*m = -a + 11, -m + a + 12 = 3*a. Let -8 + 5*r**3 - 3*r**3 + 0*r**3 + 6*r**m = 0. What is r?
-2, 1
Suppose 2*q = -4*b - 4, 2*q = -3*q + 5*b + 20. Factor 7*w**4 + 4*w**2 - q*w**4 - 7*w**3 + w**2 - 3*w**2.
w**2*(w - 1)*(5*w - 2)
Let d(z) be the second derivative of -7*z**6/15 - 19*z**5/10 + z**4 + 28*z**3/3 - 8*z**2 - z. Suppose d(g) = 0. What is g?
-2, 2/7, 1
Let p(y) be the first derivative of 2/15*y**5 + 1 - 4/3*y**2 + 4/3*y**3 - 2/3*y**4 + 2/3*y. Factor p(r).
2*(r - 1)**4/3
Let x(t) = 9*t**5 - 5*t**4 + 13*t**3 - 13*t**2. Let m(f) = 4*f**5 - 2*f**4 + 6*f**3 - 6*f**2. Let j be 2/4*-8 - 2. Let l(k) = j*x(k) + 13*m(k). Factor l(h).
-2*h**4*(h - 2)
Let y(o) be the third derivative of -7*o**2 + 0*o - 1/30*o**6 + 0*o**4 - 1/210*o**7 + 0 + 0*o**3 - 1/15*o**5. Find a, given that y(a) = 0.
-2, 0
Factor 0 + 0*n + 0*n**3 - 1/4*n**2 + 1/4*n**4.
n**2*(n - 1)*(n + 1)/4
Let w(h) be the first derivative of h**8/1344 - h**7/210 + h**6/160 + h**5/60 - h**4/24 - 3*h**2/2 - 1. Let m(s) be the second derivative of w(s). Factor m(o).
o*(o - 2)**2*(o - 1)*(o + 1)/4
Let c(m) = -m + 11. Let r be c(8). Factor -o**3 - o + 3*o**r - 2*o**3 + 4*o**2 - 2 + 3*o**3.
(o + 1)**2*(3*o - 2)
Let k = 5 + -3. Suppose 0 = 2*y + 4*w - 20, 6*y - 2*y = 2*w. Determine j so that -4*j**k + 2*j + 2*j**4 - y*j + 2 = 0.
-1, 1
Let k(j) = j**3 - 2*j**2 - 5*j + 3. Let c(a) = -3*a**3 + 5*a**2 + 15*a - 9. Let t(i) = 3*c(i) + 8*k(i). Solve t(x) = 0 for x.
-3, 1
Let o be (-3 - (-5 - -3))/(-18). Let v(k) be the second derivative of -o*k**3 - 1/6*k**2 + 1/60*k**5 + 0 + k + 1/36*k**4. Find q, given that v(q) = 0.
-1, 1
Let r(o) = 10*o**5 + 14*o**4 - 6*o**3 + 6*o**2 - 6*o. Let t(m) = -m**5 - m**4 + m**3 - m**2 + m. Let h(y) = r(y) + 6*t(y). Solve h(i) = 0 for i.
-2, 0
Determine c, given that 32/3 + 32/3*c - 8/3*c**3 + 0*c**2 - 2/3*c**4 = 0.
-2, 2
Let n(p) be the first derivative of 2*p**3/33 - 2*p**2/11 - 6*p/11 - 26. Factor n(m).
2*(m - 3)*(m + 1)/11
Let -9 + 3*i**4 + 6*i**3 + 6*i**3 - i**2 - 12*i + 7*i**2 = 0. Calculate i.
-3, -1, 1
Determine d, given that 0 - 4/5*d**4 - 12/5*d**3 + 0*d - 8/5*d**2 = 0.
-2, -1, 0
Let s(x) = -x**2 + 12*x - 24. Let b be s(3). Suppose 0*f + 0 + 2/9*f**b - 2/9*f**4 + 4/9*f**2 = 0. What is f?
-1, 0, 2
Let p = 67 - 64. Determine j so that 136/3*j + 220/3*j**2 + 16/3 - 1092*j**4 - 310*j**p - 882*j**5 = 0.
-2/3, -1/3, -2/7, 1/3
Let n be (-3 - -3)/(-1*1). Let w(j) be the first derivative of 1/12*j**4 - 1/6*j**2 + 0*j**3 + n*j - 4. Factor w(t).
t*(t - 1)*(t + 1)/3
Let j(l) be the third derivative of l**8/1176 + 2*l**7/735 - l**6/105 - l**5/105 + l**4/28 - l**2. Suppose j(h) = 0. Calculate h.
-3, -1, 0, 1
Let d = 259/15 + -83/5. Factor 2/3*o**2 - d*o - 4/3.
2*(o - 2)*(o + 1)/3
Let o(c) be