i**3 + 19*i**2 - 12*i - 3. Let o(f) = 7*b(f) + 4*q(f). Let o(u) = 0. What is u?
1
Let r = -6 - -6. Factor 2/5*g**2 - 6/5*g + r.
2*g*(g - 3)/5
Let z(a) = a + 1. Suppose -7 = 5*n + 3*p, 4*p = -n - 1 - 14. Let w(m) = -2*m**2 + 3*m - 1. Let t(l) = n*w(l) + z(l). What is x in t(x) = 0?
0, 2
Let h be ((-2)/6)/((-2)/(-6)). Let t(k) = -2*k**2 + k - 1. Let x(j) = -j**2 - 1. Let p(f) = h*x(f) + t(f). Factor p(c).
-c*(c - 1)
Let r = -19 + 23. Suppose i + r*i = 20. Determine h so that -21/4*h**2 + 9/4*h**3 - 1 + i*h = 0.
2/3, 1
Let o(t) = 5*t - 1. Let m be o(1). Suppose 0 = -3*c - 5*v + 6, -2*v - 8 = -2*c - m. Solve -2*d - 6*d**3 + 3*d**c + 4*d**2 + d**2 = 0 for d.
0, 1/3, 1
Let s(m) be the third derivative of 0*m + m**2 + 0*m**3 - 1/168*m**8 + 0 + 0*m**5 + 0*m**7 + 0*m**4 + 1/60*m**6. Factor s(k).
-2*k**3*(k - 1)*(k + 1)
Solve 49 - 49 + u**2 + 5*u**3 = 0 for u.
-1/5, 0
Factor 3/2*y**2 + 27/2 - 9*y.
3*(y - 3)**2/2
Let v(f) be the third derivative of f**6/240 + f**5/24 + f**4/6 + f**3/3 + 17*f**2. Find r such that v(r) = 0.
-2, -1
Let x(q) be the third derivative of 1/72*q**4 + 0 + 0*q - 2*q**2 - 1/3*q**3 - 1/90*q**5 + 1/360*q**6. Let l(s) be the first derivative of x(s). Factor l(u).
(u - 1)*(3*u - 1)/3
Let x = 32 + -28. Solve 0*u**4 - u**2 - 3*u**2 + 8*u**3 + 0*u**2 - 4*u**x = 0.
0, 1
Let t(s) = 4*s**2 - 2*s. Let h(v) = -5*v**2 + 3*v. Let p(x) = 2*h(x) + 3*t(x). Factor p(w).
2*w**2
Let t(x) be the third derivative of x**8/3696 + x**7/462 + x**6/165 + x**5/165 + 10*x**2 - 2. Factor t(b).
b**2*(b + 1)*(b + 2)**2/11
Let y(n) be the second derivative of -n**6/135 + n**5/30 - n**4/27 + 6*n. Factor y(h).
-2*h**2*(h - 2)*(h - 1)/9
Let s(i) be the third derivative of -i**5/300 - i**4/120 + i**3/5 - 12*i**2. Solve s(g) = 0.
-3, 2
Suppose -2*h = 8 - 4, -4*i + 4*h + 20 = 0. Factor -4*s**3 + 2*s**4 - 2*s**2 + 3*s**i + 3*s**3 - 2*s.
2*s*(s - 1)*(s + 1)**2
Let p(q) be the first derivative of 14*q**3/9 - 26*q**2/3 - 16*q/3 - 21. Factor p(m).
2*(m - 4)*(7*m + 2)/3
Find f, given that -13/9*f - 1/9*f**2 + 14/9 = 0.
-14, 1
Suppose 4*o - 2*c = 36 - 26, -c + 1 = o. Determine n, given that 0 - 3/4*n**o + 3/4*n = 0.
0, 1
Let v(b) be the third derivative of -8*b**7/105 + 4*b**6/15 - b**5/3 + b**4/6 + 4*b**2. Factor v(y).
-4*y*(y - 1)*(2*y - 1)**2
Let f(s) = -3*s**2 - 3*s + 3. Let b(x) = -6 + 1 + 3 + 1. Let g = 4 + -3. Let t(c) = g*f(c) - 3*b(c). Factor t(z).
-3*(z - 1)*(z + 2)
Let z = 50 + -110. Let u be 36/z - 13/(-5). What is p in 0 + 1/5*p**3 + 1/5*p - 2/5*p**u = 0?
0, 1
Factor k**2 - 16*k + 5*k**2 - 32 - 6*k**2 - 2*k**2.
-2*(k + 4)**2
What is v in v**2 - 6 + 4 - 46*v + 47*v = 0?
-2, 1
Factor 4*v**4 + 0*v + v**2 + 0 + 3/2*v**5 + 7/2*v**3.
v**2*(v + 1)**2*(3*v + 2)/2
Let b(u) be the second derivative of 1/4*u**4 - 3/40*u**6 + 0 + 0*u**3 + 1/56*u**7 - 4*u + 0*u**2 + 0*u**5. Factor b(g).
3*g**2*(g - 2)**2*(g + 1)/4
Let a(t) be the first derivative of t**3/33 - t**2/11 - 11. Let a(v) = 0. Calculate v.
0, 2
Let s = -5 + 10. Let x = s + -9/2. What is l in 0*l**2 + 0*l**4 - 1/2*l**5 + x*l**3 + 0*l + 0 = 0?
-1, 0, 1
Factor 6*h**2 + 2*h + 7*h**2 + 3 - 14*h**2.
-(h - 3)*(h + 1)
Let b(q) be the second derivative of q**7/10080 + q**6/1440 + q**5/480 - q**4/12 - 3*q. Let k(o) be the third derivative of b(o). Factor k(r).
(r + 1)**2/4
Let v(s) be the third derivative of 1/40*s**6 + 0*s + 0*s**3 - 1/4*s**4 - 3/20*s**5 + 1/112*s**8 + 7*s**2 + 0 + 3/70*s**7. Suppose v(g) = 0. What is g?
-2, -1, 0, 1
Let n(s) = -5. Let x(c) = c**2 - 8*c + 1. Let a(o) = 15*n(o) - 5*x(o). Factor a(z).
-5*(z - 4)**2
Let s(l) = -5*l**4 + 3*l**3. Let y(v) = -2*v**4 + v**3. Let u(h) = h**2 - 7*h + 3. Let b be u(6). Let j(i) = b*s(i) + 7*y(i). Determine c so that j(c) = 0.
0, 2
Factor 6/5*x**3 - 7/5*x + 3/5 + 1/5*x**5 - x**4 + 2/5*x**2.
(x - 3)*(x - 1)**3*(x + 1)/5
Let k = 4 + -11/3. Let t(j) be the first derivative of 1/8*j**2 + 0*j - 1 + 5/16*j**4 - 1/10*j**5 - k*j**3. Determine o so that t(o) = 0.
0, 1/2, 1
Suppose 2*d + 2*d - 5*f + 2 = 0, 0 = -2*d - 2*f + 8. Let r(a) be the second derivative of -1/30*a**4 - 2*a + 0 + 0*a**d - 1/50*a**5 + 0*a**3. Factor r(u).
-2*u**2*(u + 1)/5
Let q(h) be the third derivative of -h**8/168 - h**7/105 + h**6/60 + h**5/30 + 3*h**2. What is i in q(i) = 0?
-1, 0, 1
Let r be 3*(-1 - (-5 + 3)). Let g(v) be the first derivative of r*v**3 + 2/3*v - 3 - 23/12*v**4 + 7/15*v**5 - 13/6*v**2. Let g(u) = 0. Calculate u.
2/7, 1
Factor 5*x**2 - x**2 + 3*x**2 - 9*x**2 - 2*x**3.
-2*x**2*(x + 1)
Let w = -33/85 - -10/17. Factor -3/5*s**3 - 1/5*s**4 - w*s**2 + 3/5*s + 2/5.
-(s - 1)*(s + 1)**2*(s + 2)/5
Factor 6*j + 5*j - 6*j + 5*j**2.
5*j*(j + 1)
Let q(d) = d**2 - 7*d + 3. Let c be q(7). Suppose c*v - 8 = v - 4*b, 0 = v - 4*b + 2. Let -9*a**2 - 4*a - 13*a**2 + 8*a**v = 0. What is a?
-2/7, 0
Factor 0*n + 4/3*n**2 + 0 + 2/3*n**3.
2*n**2*(n + 2)/3
Let s(t) be the first derivative of t**6/1440 - t**4/24 - t**3 - 3. Let i(n) be the third derivative of s(n). Factor i(y).
(y - 2)*(y + 2)/4
Let d(n) be the first derivative of -n**6/9 + n**4/6 + 1. Find f, given that d(f) = 0.
-1, 0, 1
Let c(m) be the second derivative of 3/80*m**5 + 3*m + 3/8*m**3 + 0 + 3/8*m**2 + 3/16*m**4. Let c(g) = 0. Calculate g.
-1
Determine n so that 46*n - 5 - 99*n + 10*n**2 + 48*n = 0.
-1/2, 1
Let c(j) be the third derivative of -j**8/1344 + j**7/840 + j**6/480 - j**5/240 - j**2. Factor c(k).
-k**2*(k - 1)**2*(k + 1)/4
Let g(b) be the first derivative of b + 2. Let t(d) = -d**2 - 4*d + 4 - 1 + 0 + 3*d. Let p(o) = 2*g(o) - 2*t(o). Suppose p(f) = 0. What is f?
-2, 1
Let x(q) be the third derivative of -2*q**7/735 - q**6/210 + 33*q**2. Determine w so that x(w) = 0.
-1, 0
Let r(n) = -n**3 + 26*n**2 - 5*n + 2. Let j = -47 - -25. Let y(q) = 2*q**2. Let d(s) = j*y(s) + 2*r(s). Factor d(l).
-2*(l - 2)*(l - 1)**2
Let w(v) = -2*v**2 + 4*v + 3. Let k(n) = -2*n + 4 - n**2 - 2 + 4*n. Let a(t) = -10*k(t) + 6*w(t). Factor a(j).
-2*(j - 1)**2
Let i(p) be the second derivative of -p**7/21 + 8*p**6/45 - 7*p**5/30 + p**4/9 + 12*p. Find t such that i(t) = 0.
0, 2/3, 1
Let h = 5 + -1. Suppose 16 = h*z - 4*v, -4*z - z + 2*v + 14 = 0. Factor 1/2*y**5 + 0 - z*y**2 - 2*y**4 + 1/2*y + 3*y**3.
y*(y - 1)**4/2
Let m(a) = 13*a**3 + 56*a**2 + 59*a - 133. Let s(f) = 32*f**3 + 140*f**2 + 148*f - 332. Let v(r) = 12*m(r) - 5*s(r). Solve v(u) = 0.
-4, 1
What is w in -80*w + 37*w + 2*w**3 + 1 - w**4 + 41*w = 0?
-1, 1
Let o(x) be the second derivative of -1/4*x**4 + 0 - 9/2*x**2 + 1/60*x**5 + 3/2*x**3 + 2*x. Find s, given that o(s) = 0.
3
Suppose -r + 6*c - 2*c = -21, -3*c + 3 = 3*r. Suppose -f = 3*f - 8. Find b such that -1/4*b**3 + 1/4*b**r + 1/4*b**f + 0 - 1/4*b**4 + 0*b = 0.
-1, 0, 1
Let x = 25 - 25. Factor 0*h - 1/5*h**2 + x.
-h**2/5
Let c(l) be the third derivative of 1/20*l**6 + 1/105*l**7 + 0*l**3 - 6*l**2 + 0*l + 1/10*l**5 + 1/12*l**4 + 0. Suppose c(g) = 0. What is g?
-1, 0
Factor -3*h**4 + 662*h**2 - 665*h**2 + h**3 - 7*h**3.
-3*h**2*(h + 1)**2
Let o = -1753/9 - -195. Let 4/9 + o*l - 2/9*l**2 = 0. What is l?
-1, 2
Let q be 51 - 47 - (-1)/((-2)/8). Suppose 2/11*t**3 + 8/11*t**4 - 4/11*t**2 + 0 - 6/11*t**5 + q*t = 0. Calculate t.
-2/3, 0, 1
Let h = -71999/75 + 960. Let b(c) be the third derivative of -1/15*c**3 - 3*c**2 + 0 + 0*c**6 + h*c**5 - 1/525*c**7 + 0*c + 0*c**4. Factor b(y).
-2*(y - 1)**2*(y + 1)**2/5
Let c(r) be the first derivative of -6/5*r**5 + 7/2*r**4 - 2*r**3 + 4*r + 7 - 3*r**2. Factor c(u).
-2*(u - 1)**3*(3*u + 2)
Let s(b) be the third derivative of -b**5/20 + b**4/8 - 7*b**2. Find l, given that s(l) = 0.
0, 1
Suppose 2/9*t**3 + 2*t + 0 - 4/3*t**2 = 0. Calculate t.
0, 3
Let q be (-7)/(-2)*16/28. Let n(r) be the first derivative of -2*r**2 - 2 + q*r**5 + 0*r - 10/3*r**3 + r**4. Find o such that n(o) = 0.
-1, -2/5, 0, 1
Let s(p) be the first derivative of 2*p**3/63 - p**2/7 - 8*p/21 - 5. Find d, given that s(d) = 0.
-1, 4
Let q(w) = -15*w**2 + 44*w + 18. Let i(s) = s. Let p(v) = 5*i(v) - q(v). Factor p(x).
3*(x - 3)*(5*x + 2)
Let i = -1 + 3. Let j be 0*(1 + (-3)/i). Factor 2*o**2 + 4*o + 1 + 2*o**2 + j.
(2*o + 1)**2
Let b(g) be the third derivative of -4*g**2 - 1/96*g**4 + 0 + 1/240*g**5 + 0*g + 0*g**3. Suppose b(q) = 0. What is q?
0, 1
Suppose -5*b - h = -12, 0 = -h - 0*h + 2. Determine r so that -4*r + 5*r**2 - 2*r**b - 2*r - 10 + 1 = 0.
-1, 