- u*h**3 - j*h**2.
-h*(h + 1)*(h + 2)/2
Let r(v) = -v**5 + v**3 + 2*v**2 + v. Let l(y) = -10*y**5 + y**4 + 7*y**3 + 18*y**2 + 11*y. Let q(a) = 2*l(a) - 22*r(a). Factor q(d).
2*d**2*(d - 2)*(d + 1)*(d + 2)
Let c(i) be the third derivative of 0*i**3 + 12*i**2 + 0 + 0*i + 1/48*i**4 + 1/80*i**5. Determine v so that c(v) = 0.
-2/3, 0
Let a(y) be the third derivative of -507*y**6/70 + 104*y**5/7 - 157*y**4/168 + y**3/42 + y**2 + 67. Find w such that a(w) = 0.
1/78, 1
Let h = 23 + -18. Suppose h*d = -t + 15, 9 = -t - 0*d + 3*d. Determine x, given that -3/2*x**3 - 7/2*x**5 + 0*x - x**2 + t + 6*x**4 = 0.
-2/7, 0, 1
Let f(r) = -3*r**2 - 64*r - 10. Let o(x) = -22*x**2 - 447*x - 75. Let l(v) = 15*f(v) - 2*o(v). Let l(j) = 0. Calculate j.
-66, 0
Factor 7/3*t**2 - 1/3*t**3 + 8/3*t + 0.
-t*(t - 8)*(t + 1)/3
Let s be 2/5 + ((-15)/636)/5. Let k = s + 1/212. Solve -1/5*z - 1/5*z**3 + 0 + k*z**2 = 0.
0, 1
Let c be 2/(-8) + 365/80*4. What is g in 20 + 4*g**2 - 4 - 2*g - c*g = 0?
1, 4
Let y(o) be the second derivative of o**5/6 + 41*o**4/72 + 11*o**3/18 + o**2/12 + 691*o. Factor y(t).
(t + 1)**2*(20*t + 1)/6
Let h be (160/336)/(222/21 + -10). Factor 0 - 1/3*l + h*l**4 - 3/2*l**3 + 7/6*l**2 - 1/6*l**5.
-l*(l - 2)*(l - 1)**3/6
Let j = -14 - -20. Let x be j/6 - (-2 + 0). Suppose 43*w - 139*w - 2*w**x - 58 - 24*w**2 - 70 = 0. Calculate w.
-4
Let t(d) be the second derivative of 0 - 1/8*d**6 - 1/56*d**7 - 1/4*d**3 - 27/80*d**5 + 0*d**2 - 20*d - 7/16*d**4. Factor t(l).
-3*l*(l + 1)**3*(l + 2)/4
Let l(b) be the third derivative of -b**9/24192 - b**8/4032 - b**7/2016 + 7*b**5/20 + 31*b**2. Let y(h) be the third derivative of l(h). Factor y(g).
-5*g*(g + 1)**2/2
Let g(x) be the first derivative of x**4/14 - 2*x**3/21 - 9*x**2/7 + 18*x/7 + 127. Suppose g(y) = 0. Calculate y.
-3, 1, 3
Let i(c) be the second derivative of c**8/47040 + c**7/8820 - c**6/5040 - c**5/420 - 25*c**4/12 - 10*c. Let w(z) be the third derivative of i(z). Factor w(q).
(q - 1)*(q + 1)*(q + 2)/7
Let t(m) be the first derivative of -4*m**5/5 - m**4/2 + m**2 - 2*m - 11. Let l(u) = 13*u**4 + 6*u**3 - 7*u + 7. Let k(a) = 2*l(a) + 7*t(a). Factor k(j).
-2*j**3*(j + 1)
Let d(r) be the first derivative of 2*r**5/25 - 4*r**4/5 - 16*r**3/15 + 96*r**2/5 + 288*r/5 + 27. Solve d(c) = 0.
-2, 6
Let i(z) be the second derivative of z**6/6 + z**5 - 65*z**4/12 - 10*z**3/3 + 30*z**2 + 38*z. Determine l so that i(l) = 0.
-6, -1, 1, 2
Suppose 4*l = 3*c + 2*l - 20, l = -4*c + 45. Solve -3 + 1 + c*b - 8*b**2 + 0 = 0 for b.
1/4, 1
Let p(y) be the second derivative of 3*y - 1/20*y**4 - 7/10*y**3 + 0*y**2 - 12. Factor p(z).
-3*z*(z + 7)/5
Let r(i) be the first derivative of -9*i + 13 - 1/3*i**3 - 3*i**2. Factor r(j).
-(j + 3)**2
Let c(z) = -z**2 - 8*z - 2. Let q be c(-7). Solve -3*k**4 + 2*k**q + 210 - 210 - 2*k**2 - 2*k**3 + 5*k**4 = 0.
-1, 0, 1
Factor -n**2 - 3 - 2*n + 3*n + 8*n - 11.
-(n - 7)*(n - 2)
Let t(y) = -370*y**3 + 440*y**2 + 145*y - 145. Let m(v) = 3 + 13*v - 41*v**3 - 3 + 49*v**2 - 16 + 3*v. Let s(g) = 35*m(g) - 4*t(g). Factor s(x).
5*(x - 1)*(3*x - 2)*(3*x + 2)
Let y(r) be the second derivative of -7*r**4/18 - 187*r**3/9 + 18*r**2 - 3*r + 4. Let y(d) = 0. Calculate d.
-27, 2/7
Let m(f) = f. Let z be m(1). Let i be 1/(-3)*z + (-392)/(-420). What is l in -6/5 - 18/5*l**4 + i*l**5 + 42/5*l**3 - 48/5*l**2 + 27/5*l = 0?
1, 2
Suppose 0 = 106*c - 11339 + 11021. Factor 15/2*d**2 + 5/2*d**4 + 15/2*d**c + 5/2*d + 0.
5*d*(d + 1)**3/2
Let x(w) be the third derivative of w**7/1680 - 17*w**6/160 - w**5/480 + 17*w**4/32 + 865*w**2. Factor x(a).
a*(a - 102)*(a - 1)*(a + 1)/8
Let v(u) = -5*u - 12*u - 11 + u**2 + 24*u + u**2. Let h(f) = -f**2 - 2*f + 4. Let z = 4 + -8. Let n(x) = z*v(x) - 11*h(x). Factor n(o).
3*o*(o - 2)
Let s(b) be the first derivative of 0*b**2 + 0*b**4 + 4/3*b - 15 + 4/15*b**5 - 8/9*b**3. Factor s(n).
4*(n - 1)**2*(n + 1)**2/3
Suppose 3*o = -0 + 90. Factor -20*c + 40 - 5*c**3 + 3*c**3 - o*c**2 + 7*c**3 + 5*c**4.
5*(c - 2)*(c - 1)*(c + 2)**2
Let r(f) be the third derivative of 0*f - 3/40*f**5 + 1/16*f**6 + 5/84*f**7 + 0 + 0*f**3 + 1/48*f**4 - 5*f**2. Factor r(t).
t*(t + 1)*(5*t - 1)**2/2
Let y(r) = r**3 + 8*r**2 - 11*r - 16. Let w(u) = -u**2 + 6*u + 7. Let s be w(-2). Let z be y(s). Factor 4/3*p**z + 0 - 2*p**3 + 2/3*p**5 + 0*p + 0*p**4.
2*p**2*(p - 1)**2*(p + 2)/3
Factor 69 - 50*a + 8 + 48 + 5*a**2.
5*(a - 5)**2
Let q = 10 - 6. Suppose -6 = q*x - 18. Factor 15*c**3 + 12*c**4 - 20*c**5 - 3*c**3 - 4*c**x.
-4*c**3*(c - 1)*(5*c + 2)
Let s be (-4)/14*(1 - (-264)/(-55) - -1). Factor -2/5 - 2/5*f**4 - 2/5*f - 2/5*f**5 + s*f**3 + 4/5*f**2.
-2*(f - 1)**2*(f + 1)**3/5
Solve 65/3*u**4 + 72*u**2 - 3*u**5 + 16/3 - 176/3*u**3 - 112/3*u = 0.
2/9, 1, 2
Let p(z) be the first derivative of 8/3*z**3 + 2/3*z - 5/2*z**2 + 9 + 4/3*z**4. What is d in p(d) = 0?
-2, 1/4
Factor -22*l - 48*l + 13*l + 5*l - l**2 - 676.
-(l + 26)**2
Let y(m) be the first derivative of m**5/10 + m**4/6 - 2*m**3 - 7*m + 23. Let h(p) be the first derivative of y(p). Factor h(s).
2*s*(s - 2)*(s + 3)
Let n be (-2)/(-7) + (-95)/(-35). Let v = 0 - -2. Factor -4*o**n - v - 9*o - 2*o**2 + 3*o**3 + 4*o**2 + 10*o.
-(o - 2)*(o - 1)*(o + 1)
Suppose -4/5*c**2 - 1/5*c**3 + 0*c + 0 = 0. What is c?
-4, 0
Factor -1/5*y**2 + 2 + 9/5*y.
-(y - 10)*(y + 1)/5
Solve 3*g - 3/2 + 9/2*g**2 = 0 for g.
-1, 1/3
Let c(t) be the second derivative of -2*t**2 + 0 - 3/2*t**4 - 7/3*t**3 - 1/2*t**5 - 1/15*t**6 - 2*t. Let c(w) = 0. Calculate w.
-2, -1
Let j be (14/30 - -1) + (-76)/95. Suppose 2/3 + 2/3*k**3 - 2/3*k - j*k**2 = 0. What is k?
-1, 1
Let o(k) be the third derivative of 0*k**4 + 0*k**3 + 5 + 1/1260*k**7 - 1/36*k**5 + 1/80*k**6 + 0*k - 2*k**2. Factor o(r).
r**2*(r - 1)*(r + 10)/6
Suppose 5*b - 6*b = 0. Let r be 1*((0 - b) + 2). Factor 2*w**5 + w**4 + w**3 + 0*w**5 + r*w**2 - 3*w**2 - 3*w**5.
-w**2*(w - 1)**2*(w + 1)
Let c(j) be the first derivative of j**5/20 + j**4/4 + j**3/3 - 21*j + 11. Let a(d) be the first derivative of c(d). Factor a(b).
b*(b + 1)*(b + 2)
Let g(c) be the second derivative of c**4/108 - c**3/9 + 74*c. Suppose g(o) = 0. Calculate o.
0, 6
Let w(j) = 2*j**2 + 30*j + 21. Let t be w(-14). Let d = -62/9 - t. Factor 2/9*b**5 - 7/9*b**4 - 2/9*b + d + 8/9*b**3 - 2/9*b**2.
(b - 1)**4*(2*b + 1)/9
Let a(r) be the second derivative of -2*r**7/21 - 4*r**6/15 + 2*r**5/5 + 4*r**4/3 - 2*r**3/3 - 4*r**2 - 86*r. Find j such that a(j) = 0.
-2, -1, 1
Suppose -10 = -5*l + 2*n, -3*l + 6 = 2*n - 0. Let z be (-5 + 4)/((-10)/l). Factor -3/5*q**2 + 1/5*q**3 - 2/5 + z*q**4 - q.
(q - 2)*(q + 1)**3/5
Let u(y) be the second derivative of y**6/15 - 12*y**5/5 + 92*y**4/3 - 160*y**3 + 400*y**2 - 123*y. What is r in u(r) = 0?
2, 10
Let o = 677/2763 + -7/307. What is a in 0 + 2/3*a**3 - 2/9*a**4 - 2/3*a**2 + o*a = 0?
0, 1
Suppose -11*t + 448 = -3*t. Let i = t + -111/2. Let 3/2*n**2 + 0 + i*n**4 + 1/2*n + 3/2*n**3 = 0. Calculate n.
-1, 0
Let f be (-4)/(-5*2/(-20)). Let s be (-5)/1*8/f. Factor 82*u + 3*u**4 - 87*u + 7*u**4 + 5*u**s - 10*u**2.
5*u*(u - 1)*(u + 1)**3
Let r(k) be the second derivative of k**5/60 - 5*k**4/12 + 25*k**3/6 - 13*k**2 - 5*k. Let g(v) be the first derivative of r(v). Factor g(d).
(d - 5)**2
Let f(y) = -1 - 3 - 8 - 3*y. Let a be f(-5). Let 10*b**3 + 5*b**2 + 2*b**a + 13*b**2 + 3*b**4 + 12*b + 3 + 0*b**4 = 0. What is b?
-1
Let m = -1047 - -1051. Let i(p) be the second derivative of 1/18*p**3 + 1/4*p**5 - 9*p + 0 + 0*p**2 + 1/10*p**6 + 7/36*p**m. What is d in i(d) = 0?
-1, -1/3, 0
Let w(v) be the first derivative of 0*v**3 + 5/4*v**4 + 0*v**2 + 5 + 0*v. Solve w(f) = 0 for f.
0
Suppose 15*m - 11*m = -16. Let b be 2 + m + 5 + -1. Factor -2/7 - 2/7*k**b + 4/7*k.
-2*(k - 1)**2/7
Let d(w) be the third derivative of 0*w**4 + 0 + 1/8*w**6 + 0*w**3 - 22*w**2 + 0*w + 2/15*w**7 + 1/30*w**5. Solve d(k) = 0 for k.
-2/7, -1/4, 0
Let g(v) be the first derivative of -v**4/8 - 7*v**3/6 + 49*v**2/4 + 55*v/2 - 212. Find z, given that g(z) = 0.
-11, -1, 5
Let c(x) = 3*x**3 - 35*x**2 - 150*x - 245. Let p(w) = -6*w**3 + 227 + 150*w + 36*w**2 + 17 + 2*w**3. Let u(a) = 6*c(a) + 5*p(a). Factor u(m).
-2*(m + 5)**3
Let d(m) = -m**3 - 6*m**2 - 2*m. Let o(v) = v**2 + v + 4. Let n(s) = -1. Let a(r) = -3*n(r) - o(r). Let h(x) = -3*a(x) + d(x). Solve h(t) = 0.
-3, -1, 1
Factor -11/4*b**2 + 10*b - 3 - 3/4*b