11 + 16/11*i = 0 for i.
-1, 2
Let f(x) = -2*x**2 + 15*x + 9. Suppose 0 = -3*l + 4*l + 6. Let u(r) = -r**2 + 8*r + 5. Let n(j) = l*f(j) + 11*u(j). Determine o, given that n(o) = 0.
1
Let d(b) be the second derivative of -8*b**6/15 - 11*b**5/5 + b**4 + 32*b**3/3 - 8*b**2 + 6*b. Determine t, given that d(t) = 0.
-2, 1/4, 1
Let i(r) be the second derivative of -5*r**7/21 + 5*r**6/12 - r**5/8 + 33*r. Factor i(c).
-5*c**3*(c - 1)*(4*c - 1)/2
Let b(q) be the third derivative of 0 + 0*q**4 + 0*q + 1/90*q**5 + 0*q**3 + 8*q**2. Factor b(y).
2*y**2/3
Let u be ((-24)/(-20))/((-4)/(-10)). Factor 2*c**2 + 2*c**2 + 0*c**4 - u*c**2 - c**4.
-c**2*(c - 1)*(c + 1)
Let j(a) be the second derivative of -3*a - 1/100*a**5 + 1/15*a**4 - 1/6*a**3 + 1/5*a**2 + 0. Factor j(u).
-(u - 2)*(u - 1)**2/5
Suppose -42 + 94 = 26*b. Determine j, given that 0 - 1/3*j - 1/3*j**b = 0.
-1, 0
Let q(v) be the third derivative of v**5/30 + 10*v**2. Find h, given that q(h) = 0.
0
Let i(p) be the first derivative of 1/24*p**6 + 0*p - 1/8*p**2 + 3 - 1/10*p**5 + 0*p**4 + 1/6*p**3. Factor i(w).
w*(w - 1)**3*(w + 1)/4
Let m(o) be the second derivative of -o**7/420 - o**6/90 - o**5/60 + 2*o**3/3 - 3*o. Let k(v) be the second derivative of m(v). Determine h so that k(h) = 0.
-1, 0
Let p(u) be the third derivative of u**6/540 - u**5/135 + u**4/108 - 7*u**2. Let p(o) = 0. Calculate o.
0, 1
Let j(q) = -q**3 + 9*q**2 + q - 9. Let h(z) = -2*z**3 + 14*z**2 + 2*z - 14. Let d(p) = 5*h(p) - 8*j(p). Factor d(r).
-2*(r - 1)*(r + 1)**2
Let h(q) be the third derivative of 0 + 0*q**3 + 1/180*q**5 - 1/144*q**4 + 0*q - q**2 - 1/720*q**6. Let h(z) = 0. Calculate z.
0, 1
Suppose -6 = 8*c - 6. Factor 2*a**4 + c + 2*a**2 + 3*a**3 + 1/2*a**5 + 1/2*a.
a*(a + 1)**4/2
Suppose 0 = t + 3*o - 29, 2*t - 2*o = -6*o + 54. Suppose 0 = -v - 3*g - 13, v - g + 6*g = -t. Factor -3*w**2 - w**4 + v*w**4 - 2*w**4 - 3*w**3 - w.
-w*(w + 1)**3
Suppose 0*x = -x + n - 10, 2*x = -2*n - 4. Let w be ((-39)/169)/(x/4). Factor 0*c - 2/13*c**2 - 6/13*c**3 + 0 - 6/13*c**4 - w*c**5.
-2*c**2*(c + 1)**3/13
Let l = -64 + 35. Let m be l/(-8) + (-9)/(-24). Suppose -4/5*d**4 + m*d**3 + 8/5*d**2 - 2*d - 2*d**5 - 4/5 = 0. What is d?
-1, -2/5, 1
Let t(x) be the third derivative of 0 + 1/3*x**3 + 0*x + 1/108*x**4 + x**2 - 1/270*x**5 + 1/1620*x**6. Let v(c) be the first derivative of t(c). Factor v(z).
2*(z - 1)**2/9
Let r(n) be the first derivative of n**3/9 + n**2/3 - 1. Factor r(u).
u*(u + 2)/3
Let a(d) be the second derivative of -d**5/180 - d**2 - 3*d. Let f(i) be the first derivative of a(i). Factor f(r).
-r**2/3
Let c(b) be the second derivative of b**4/16 - b**3/2 + 41*b. Determine i, given that c(i) = 0.
0, 4
Let u(t) be the second derivative of -t**4/4 - 3*t**3/2 + 15*t**2 - 18*t + 1. Factor u(h).
-3*(h - 2)*(h + 5)
Suppose 0 = -5*c - 0*c. Let n = 0 - c. Let n*j + j**2 + 2*j - j = 0. Calculate j.
-1, 0
Let m(y) = 5*y**2 - 13*y - 3. Let l(s) = 4*s**2 - 12*s - 2. Let r(d) = -3*l(d) + 2*m(d). Factor r(k).
-2*k*(k - 5)
Factor -5*o**3 - 2*o**4 - 7*o**4 + 4*o**4.
-5*o**3*(o + 1)
Let d(m) be the third derivative of 0*m**3 + 0*m**4 + 1/40*m**6 + 1/20*m**5 + 0 + 0*m + 3*m**2. Factor d(o).
3*o**2*(o + 1)
Let x(u) be the third derivative of -u**6/40 + 29*u**5/20 - 28*u**4 + 98*u**3 + 2*u**2 - 3. Factor x(l).
-3*(l - 14)**2*(l - 1)
Find k, given that -7/9*k**4 + 0*k - 5/9*k**2 - 11/9*k**3 + 0 - 1/9*k**5 = 0.
-5, -1, 0
Let v be (-6)/2 + -8 + 11. Factor 2*i**2 + 42*i - i**2 - 40*i + v*i**2.
i*(i + 2)
Let 2/13*w**3 + 0 - 2/13*w**2 + 0*w = 0. What is w?
0, 1
Let z(p) = p + 4. Let g be z(0). Suppose 2*k + g = 4*k. Let 1/2*j + j**k - 1/2 = 0. What is j?
-1, 1/2
Let z be ((-16)/(-4) - -1) + -3. Factor 117*g**3 + 4*g + 91*g**4 - 5*g**4 + 40*g**z - 5*g**4.
g*(g + 1)*(9*g + 2)**2
Let f be (-1)/4 + (-1)/(-2). Factor f + 1/2*g + 1/4*g**2.
(g + 1)**2/4
Let h be (-1)/(-2)*(12 + 6). Factor 9*g**3 - 2*g**5 + 14*g**2 + 4*g + 4*g**5 + h*g**3 + 10*g**4.
2*g*(g + 1)**3*(g + 2)
Let g(u) be the third derivative of -1/180*u**6 + 0*u + 1/30*u**5 + 2*u**2 + 1/3*u**3 + 0 - 1/12*u**4. Let v(h) be the first derivative of g(h). Factor v(b).
-2*(b - 1)**2
Solve 5*f**3 - 15 - f**5 - 1 + 8*f - 7*f**3 + 20*f**2 - f**5 - 8*f**4 = 0 for f.
-2, 1
Suppose -4*q = -2*o - 8, -2*o + 4*q = -q + 6. Let h = o - -10. Let -2/5*k + 2*k**h + 0 = 0. Calculate k.
0, 1/5
Let l(v) be the first derivative of v**6/180 - v**4/12 + 2*v**3 + 1. Let y(j) be the third derivative of l(j). Factor y(r).
2*(r - 1)*(r + 1)
Let j be (-52)/195 + (5/3 - 1). Factor -j*q**2 - 8/5 + 8/5*q.
-2*(q - 2)**2/5
Factor -4*i**2 + i**4 + 67*i**3 - 71*i**3 - 2*i**4.
-i**2*(i + 2)**2
Let i(m) = -5*m**4 - m**3 - m**2 - 5*m - 3. Let a(v) = -4*v**4 - 4*v - 2. Let n(q) = -3*a(q) + 2*i(q). Factor n(t).
2*t*(t - 1)**2*(t + 1)
Let m(x) = 3*x**2 + 18*x + 5. Let d be m(-6). Let r(n) be the second derivative of -2*n + 1/70*n**d + 8/21*n**3 + 0 + 4/7*n**2 + 5/42*n**4. Solve r(w) = 0.
-2, -1
Let q(m) be the third derivative of -m**6/440 - m**5/132 - m**4/132 - 34*m**2. Solve q(b) = 0 for b.
-1, -2/3, 0
Let z(f) be the second derivative of -f**9/1008 + f**7/280 + f**3/3 - f. Let b(x) be the second derivative of z(x). Factor b(k).
-3*k**3*(k - 1)*(k + 1)
Let g(i) be the third derivative of i**8/336 + i**7/280 - i**6/96 - i**5/80 + i**4/96 - i**2. Determine z so that g(z) = 0.
-1, 0, 1/4, 1
Let v(g) be the second derivative of -g**4/42 - 4*g**3/21 - 4*g**2/7 - 21*g. Factor v(s).
-2*(s + 2)**2/7
Let u(n) be the second derivative of -n**6/90 - n**5/15 - n**4/36 + n**3/3 - 8*n. Solve u(p) = 0 for p.
-3, -2, 0, 1
Let j(s) be the third derivative of s**7/11340 - s**6/648 + s**5/135 + s**4/24 - 3*s**2. Let z(i) be the second derivative of j(i). Find o such that z(o) = 0.
1, 4
Let v(s) be the third derivative of 1/16*s**5 + 1/112*s**8 + 0*s + 1/160*s**6 - 1/32*s**4 - 1/35*s**7 - 1/8*s**3 + 5*s**2 + 0. What is u in v(u) = 0?
-1/2, 1
Factor 0 - 2/13*f - 2/13*f**2.
-2*f*(f + 1)/13
Let f(r) be the third derivative of r**7/525 - r**6/100 - 3*r**5/50 - r**4/12 - 16*r**2. Find l, given that f(l) = 0.
-1, 0, 5
Let o(c) = c + 10. Let s = -15 + 8. Let r be o(s). Factor 2*u - u**4 + u**2 - 3*u**2 + r*u**4 - 2*u**3.
2*u*(u - 1)**2*(u + 1)
Let y(l) be the third derivative of -l**9/7560 + l**8/1680 + l**4/24 - 3*l**2. Let n(c) be the second derivative of y(c). Factor n(w).
-2*w**3*(w - 2)
Let l(b) be the first derivative of -b**6/60 - b**5/10 - b**4/6 - b**2 - 2. Let i(p) be the second derivative of l(p). Factor i(d).
-2*d*(d + 1)*(d + 2)
Let l(j) = -4*j + 35. Let t be l(8). Let r(b) be the third derivative of 0 + 0*b**t + 0*b**4 + 0*b**5 + 2*b**2 + 0*b + 1/600*b**6. Factor r(k).
k**3/5
Let z(x) be the third derivative of -x**9/6480 - x**8/1260 - 11*x**7/7560 - x**6/1080 + x**4/8 - x**2. Let j(b) be the second derivative of z(b). Factor j(m).
-m*(m + 1)**2*(7*m + 2)/3
Let v(c) be the second derivative of c**7/294 - c**6/70 - c**5/140 + c**4/28 + 17*c. Factor v(k).
k**2*(k - 3)*(k - 1)*(k + 1)/7
Let d(k) be the first derivative of -k**6/36 - k**5/30 + k**4/8 + k**3/18 - k**2/6 + 28. Determine v, given that d(v) = 0.
-2, -1, 0, 1
Suppose -2*n - 7*z + 16 = -10*z, -5*z = 5*n + 10. Let -2/11*t**n + 12/11*t - 18/11 = 0. What is t?
3
Let l(d) = -3 + d - 2*d**2 - 3*d - 1 + 1. Let r(y) = y**2. Let x(s) = l(s) + 3*r(s). Let x(g) = 0. Calculate g.
-1, 3
Let c be (-18)/(-4) - 8/2. Let v(q) be the first derivative of 0*q**5 + 0*q + 2 + 0*q**3 - c*q**2 + 1/2*q**4 - 1/6*q**6. Suppose v(h) = 0. What is h?
-1, 0, 1
Let n(s) be the second derivative of -s**5/100 + s**4/15 - s**3/6 + s**2/5 - s. Factor n(w).
-(w - 2)*(w - 1)**2/5
Let y = 201 + -601/3. Factor -2/3*r**3 + 0*r**2 - 1/3*r**4 + y*r + 1/3.
-(r - 1)*(r + 1)**3/3
Let y(o) be the first derivative of -1/18*o**6 + 0*o**5 + 6 - 2/9*o**3 + 1/4*o**4 + 0*o**2 + 0*o. Factor y(w).
-w**2*(w - 1)**2*(w + 2)/3
Let a(f) be the second derivative of -5*f**4/6 - f**3/3 + 4*f**2 - 8*f. Let a(h) = 0. Calculate h.
-1, 4/5
Let k(n) = n - 8. Let q be k(8). Let f = 3 + q. Suppose g**2 + f*g**3 - g**3 - g**3 = 0. What is g?
-1, 0
Let m(j) be the third derivative of -j**6/300 + j**5/75 + j**4/20 - 2*j**2. Suppose m(h) = 0. Calculate h.
-1, 0, 3
Let q(y) = -y**2 + 1. Let i(m) = -7*m**4 - 2*m**3 + 25*m**2 - 8*m - 8. Let l = -12 + 8. Let r(j) = l*q(j) -