t -l + q*l**2 + 1 = 0.
2
Factor 15/4*h + 3/4*h**2 + 3.
3*(h + 1)*(h + 4)/4
Let w(x) be the first derivative of 3*x**6 + 22*x**5/5 + x**4 - 104. Determine b so that w(b) = 0.
-1, -2/9, 0
Let w(r) be the second derivative of 3*r**5/20 - 7*r**4/4 - 4*r**3 - 76*r. Solve w(g) = 0 for g.
-1, 0, 8
Suppose 0*y + 2*y = -0*y. Let u(n) be the first derivative of y*n**2 - 2/3*n + 2/9*n**3 - 5. Factor u(w).
2*(w - 1)*(w + 1)/3
Let k(b) be the second derivative of b**6/45 + b**5/30 - b**4/18 - b**3/9 - 80*b. Suppose k(r) = 0. Calculate r.
-1, 0, 1
Let l(t) be the second derivative of -t**6/285 + t**5/95 + 10*t**4/57 + 8*t**3/19 + 142*t. Suppose l(w) = 0. Calculate w.
-2, 0, 6
Let c be (7/2 - 3)*(-11 - 7). Let n = c + 9. Suppose -2/3*w**2 + 0*w - 2/3*w**3 + n = 0. Calculate w.
-1, 0
Determine m so that 4/5*m**4 - 4/5*m**2 + 0 - 8/5*m + 8/5*m**3 = 0.
-2, -1, 0, 1
Let t = 19322/13 + -1486. Find r such that -74/13*r + t - 1080/13*r**3 + 36*r**2 + 432/13*r**4 = 0.
1/6, 2
Let q(w) = -5*w + 4. Let f be q(0). Factor -8*z**3 + 54*z**4 - 58*z**4 - 4 + 8*z + 4*z**2 + f.
-4*z*(z - 1)*(z + 1)*(z + 2)
Suppose -2*b - 6 = -5*b. Let n be 1/(b/14) - 3. Factor -6 + 10 - n*x**2 - 2*x + 8*x.
-2*(x - 2)*(2*x + 1)
Let a(v) = -2*v**4 - 2*v**3 - 2*v**2 + 2*v + 4. Let x(i) = -i + 0*i - i**2 + 9*i**2 - 9*i**2. Let g(p) = -a(p) + 8*x(p). Factor g(s).
2*(s - 2)*(s + 1)**3
Factor 2/9*z**2 - 22/9*z + 20/9.
2*(z - 10)*(z - 1)/9
Let j(p) = -p**2 - 4*p + 3. Let i be ((-2)/(-5))/(1/(-10)). Let n be j(i). Factor -6*c**2 + 3*c**5 + 3*c**4 + 5*c - n*c**3 + 3*c**2 - 5*c.
3*c**2*(c - 1)*(c + 1)**2
Let y = -274069/9 - -30453. Determine f so that 14/9*f**2 + y*f**3 + 4/9*f - 2/9 = 0.
-1, 1/4
Determine y, given that 0 - 12*y - 1/2*y**4 - 7*y**2 + 9/2*y**3 = 0.
-1, 0, 4, 6
Let g(l) be the second derivative of -2/11*l**2 + 1/110*l**5 + 0 - 1/33*l**3 + 1/33*l**4 - 34*l. Factor g(m).
2*(m - 1)*(m + 1)*(m + 2)/11
Suppose 0 = -4*w - 4*k - 24, 1 = 4*w - 5*k - 29. Factor -1/6*x**2 + 1/6*x**4 + w*x + 1/6*x**5 - 1/6*x**3 + 0.
x**2*(x - 1)*(x + 1)**2/6
Let k(f) be the second derivative of f**6/135 - f**5/90 - f**4/18 + f**3/27 + 2*f**2/9 - 74*f. Solve k(j) = 0.
-1, 1, 2
Factor -23/2*r**2 + 1/8*r**3 + 91/8*r + 0.
r*(r - 91)*(r - 1)/8
Suppose -31*x = -28*x. Let p(l) be the third derivative of -1/4*l**4 + x*l**3 - 3/20*l**5 - 9*l**2 + 0 - 1/40*l**6 + 0*l. Suppose p(w) = 0. Calculate w.
-2, -1, 0
Let o = -7/419 + 31481/3352. Let a(d) be the first derivative of -12*d**2 + 12 - 6*d + o*d**4 - 5/2*d**3. Determine i so that a(i) = 0.
-2/5, 1
Suppose -3*n = -5*n + 4. Let q be 718/7 + (-3 - -13 - 16). Factor q*l**n + 208/7*l + 16/7.
4*(13*l + 2)**2/7
Let y(q) be the first derivative of -3*q**4/22 - 14*q**3/11 + 3*q**2/11 + 42*q/11 + 19. Factor y(z).
-6*(z - 1)*(z + 1)*(z + 7)/11
Let h = 3925 + -3923. Factor 396/5*f - 108/5 - 363/5*f**h.
-3*(11*f - 6)**2/5
Let c(z) = -z**4 + 8*z**3 + 8*z**2 - 12*z + 14. Let n(q) = -q**3 - 2. Let v(f) = 2*c(f) + 14*n(f). Suppose v(h) = 0. What is h?
-3, 0, 2
Let l(i) = i + 27. Let y be 4*2/8*-25. Let v be l(y). Factor -8/3*n - 4/3*n**3 - 4*n**v + 0.
-4*n*(n + 1)*(n + 2)/3
Let t = 626 - 624. Let m = 15 + -15. Factor 1/4*l**t - 1/4*l**4 + m - 1/4*l + 1/4*l**3.
-l*(l - 1)**2*(l + 1)/4
Let u be 2 - (6/3 + -2). Factor 11*d**u + 9*d**2 + 12*d**2 - 16*d + 4*d**4 - 20*d**3.
4*d*(d - 2)**2*(d - 1)
Let a = 53 + -49. Let m(d) = 5*d**2 + 5*d - 6. Let v(g) = -g**2 - g. Let i(w) = a*v(w) + m(w). Factor i(u).
(u - 2)*(u + 3)
Let t(i) = 16*i - 11. Let c be 14/(-49) + (-116)/(-14). Let x be t(c). Factor -15*q + x*q**3 + 7 + 3 - 112*q**3.
5*(q - 1)**2*(q + 2)
Let f(c) = -c**2 - 56*c - 663. Let y be f(-17). Find h such that y*h - 8/5*h**3 - 4/5*h**2 + 0 - 4/5*h**4 = 0.
-1, 0
Let l(t) be the first derivative of 0*t**2 + 1/600*t**6 + 5 + 4/3*t**3 + 0*t**4 - 1/200*t**5 + 0*t. Let j(a) be the third derivative of l(a). Factor j(v).
3*v*(v - 1)/5
Let v(h) = -h**2 + 11*h + 12. Let n be v(9). Let d(o) = 35*o**2 - 100*o + 875. Let g(a) = a**2 + a + 1. Let m(z) = n*g(z) - d(z). Solve m(i) = 0.
13
Factor 0*r + 10/7*r**3 + 2/3*r**2 + 2/21*r**5 + 6/7*r**4 + 0.
2*r**2*(r + 1)**2*(r + 7)/21
Let i(p) be the second derivative of -p**8/47040 + p**7/8820 - p**6/5040 + p**4/12 + 9*p. Let k(u) be the third derivative of i(u). Factor k(s).
-s*(s - 1)**2/7
Let k(g) = 9*g + 24. Let b be k(10). Solve -b*w**3 + 57*w - 6*w**3 + 72*w**2 - 9*w**5 + 57*w**4 - 9*w - 48 = 0.
-2/3, 1, 2
Let o(k) be the first derivative of k**4/4 + 5*k**3/3 - 5*k**2/2 + 8*k + 12. Let c be o(-6). Let 3/2 - 27/4*f**c + 21/4*f = 0. Calculate f.
-2/9, 1
Find t such that t - 15 - 1/4*t**3 + 15/4*t**2 = 0.
-2, 2, 15
Let a(v) be the first derivative of -v**6/120 - v**5/20 - v**4/8 - v**3/6 - 3*v**2/2 - 13. Let p(f) be the second derivative of a(f). Factor p(y).
-(y + 1)**3
Let -12*a**2 + 21/2 + 9*a - 9*a**3 + 3/2*a**4 = 0. Calculate a.
-1, 1, 7
Let c(g) be the first derivative of 0*g**3 - 24 + 1/12*g**4 + 0*g**2 + 0*g. Suppose c(a) = 0. What is a?
0
Let h(n) be the third derivative of -n**7/140 + n**6/60 + 31*n**5/120 - 3*n**4/4 - 3*n**3 - 8*n**2 - 8*n. Suppose h(q) = 0. What is q?
-3, -2/3, 2, 3
Let w(b) be the second derivative of -35/6*b**3 + 15*b**2 + 0 - 37*b - 5/42*b**7 - 5/2*b**4 + 0*b**6 + 2*b**5. Determine l so that w(l) = 0.
-3, -1, 1, 2
Let k(d) be the third derivative of -d**6/180 - 7*d**5/90 - 25*d**4/144 - d**3/6 + 61*d**2. Let k(g) = 0. Calculate g.
-6, -1/2
Factor 99*v**2 + 7*v + 3*v - 8 + 5*v**3 - 76*v**2.
(v + 1)*(v + 4)*(5*v - 2)
Let n(g) be the first derivative of 4*g**5/25 + 4*g**4/5 - 8*g**3/5 - 72*g**2/5 - 108*g/5 + 113. Factor n(j).
4*(j - 3)*(j + 1)*(j + 3)**2/5
Let k(h) = -4*h - 150. Let p be k(-38). Let f(n) be the first derivative of 4 + 1/6*n**6 + 0*n**p - 1/4*n**4 - 1/3*n**3 + 1/5*n**5 + 0*n. Factor f(m).
m**2*(m - 1)*(m + 1)**2
Let t be ((-8)/(-12))/((-1)/(-3)). Suppose 23 - 1 = 5*n + 3*i, -20 = -t*n - 4*i. Let -512/5*j**4 + 32/5*j - 2/5 - 192/5*j**n + 512/5*j**3 = 0. Calculate j.
1/4
Let u be 1/(-1) - (4/((-40)/14))/1. Suppose 4/5*j + 0*j**2 + u*j**4 - 4/5*j**3 - 2/5 = 0. Calculate j.
-1, 1
Let x(g) be the second derivative of -1/48*g**4 + 0*g**2 + 7/6*g**3 - 9*g - 1/720*g**6 + 0 - 1/120*g**5. Let w(y) be the second derivative of x(y). Factor w(z).
-(z + 1)**2/2
Let v(k) be the third derivative of -k**5/60 + 29*k**4/24 - 38*k**2 - 2*k. Suppose v(x) = 0. What is x?
0, 29
Let z(w) be the third derivative of -w**7/840 - 3*w**6/160 - w**5/10 - w**4/6 - 143*w**2. Factor z(a).
-a*(a + 1)*(a + 4)**2/4
Let c be 19/228*75*(-6)/(-5). Find b, given that -55/2*b**3 + 0*b + 10*b**4 + 0 - c*b**2 = 0.
-1/4, 0, 3
Let z(r) be the first derivative of 1/23*r**2 - 10/69*r**3 + 2/23*r**4 - 5 + 0*r. Suppose z(u) = 0. Calculate u.
0, 1/4, 1
Let n be 3 + (2 - -2)/4. Factor -n*k**2 - 14*k - 69 - 23*k - 127 - 19*k.
-4*(k + 7)**2
Suppose 14/5*s**4 - 22*s**2 + 0 + 2/5*s**5 - 6/5*s**3 + 20*s = 0. Calculate s.
-5, 0, 1, 2
Suppose 9*b - 8*b = -11*b. Let m(v) be the first derivative of 3*v**5 + 5 + 0*v + b*v**3 + 3/2*v**4 + 0*v**2. Factor m(l).
3*l**3*(5*l + 2)
Let j(b) be the first derivative of -16*b**2 - 15 + 4/3*b**3 + 64*b. Find t such that j(t) = 0.
4
Let m(c) be the third derivative of c**7/2520 + c**6/144 + c**5/30 + 9*c**4/8 - 16*c**2. Let o(h) be the second derivative of m(h). Factor o(r).
(r + 1)*(r + 4)
Let x(z) be the first derivative of 2*z**7/735 - z**6/210 - 3*z**2/2 - 4. Let o(d) be the second derivative of x(d). Factor o(y).
4*y**3*(y - 1)/7
Suppose 12 = -20*d + 18*d. Let u be (-3 + 15)*(-2)/d. Find i such that -10 + u*i**2 + 1 - 4*i + 1 = 0.
-1, 2
Let u(r) be the third derivative of r**7/140 + r**6/20 - r**5/40 - r**4/4 - 70*r**2. Factor u(h).
3*h*(h - 1)*(h + 1)*(h + 4)/2
Let x(b) be the second derivative of 0 + 1/6*b**3 + b**2 + 7*b - 1/20*b**5 - 1/6*b**4. Factor x(h).
-(h - 1)*(h + 1)*(h + 2)
Let f(u) be the second derivative of -u**6/8 - 7*u**5/5 - 33*u**4/8 + 9*u**3 + 3*u**2/2 - 18*u. Let p(h) be the first derivative of f(h). Factor p(j).
-3*(j + 3)**2*(5*j - 2)
Let v(h) be the third derivative of -18*h**2 - 1/945*h**7 + 0 - 1/54*h**5 + 0*h**3 + 0*h + 0*h**4 - 1/90*h**6. Determine r, given that v(r) = 0.
-5, -1, 0
Suppose 5*v - 13 = 7. Suppose 0 = v*h + b - 5, -2 = -2*h - 4*b - 10. Suppose 2*a**3 + a**2 - h*a**3 + a**4 - 4*a**3 + 6*a**