= 5 - r. Let x(s) = u*c(s) - l(s). Let x(v) = 0. What is v?
0
Let y(a) be the first derivative of 4/5*a**5 + 0*a**4 - a**2 - 4/3*a**3 + 1/3*a**6 - 2 + 0*a. Factor y(i).
2*i*(i - 1)*(i + 1)**3
Let l(c) = c - 8. Let j be l(9). Let n be j/(-2) - 9/(-2). Find s such that 5*s**3 + s**2 - 2*s**n - 3*s**3 + 3*s**2 = 0.
-1, 0, 2
Let n(x) be the second derivative of 9*x + 1/54*x**4 + 0*x**2 - 1/90*x**5 - 1/135*x**6 + 1/27*x**3 + 0. Suppose n(i) = 0. Calculate i.
-1, 0, 1
Factor -14/3 - 5/3*k**2 + 37/3*k.
-(k - 7)*(5*k - 2)/3
Let z(g) be the first derivative of 3*g**4/28 + 2*g**3/7 - 3*g**2/2 + 12*g/7 - 7. Factor z(o).
3*(o - 1)**2*(o + 4)/7
Let 1/2 + 0*t - 1/2*t**2 = 0. What is t?
-1, 1
Let n = 50 - 46. Let r(a) be the second derivative of -1/18*a**3 - 4*a + 1/60*a**5 + 0*a**n + 0*a**2 + 0. Solve r(z) = 0.
-1, 0, 1
Let i(j) be the first derivative of 3/8*j**4 - 1 + j - 1/3*j**3 - 3/4*j**2. Find x such that i(x) = 0.
-1, 2/3, 1
Let h(k) be the first derivative of -k**2 - 2/3*k - 2/3*k**3 - 1/6*k**4 - 5. What is w in h(w) = 0?
-1
Factor 6*u - 8*u + 20*u**2 - 5*u**3 - 13*u.
-5*u*(u - 3)*(u - 1)
Suppose -5*c = -k + 20, -c + 3*c + 8 = 2*k. Suppose 2/3*m**5 + 0*m + 2*m**3 + 2*m**4 + k + 2/3*m**2 = 0. What is m?
-1, 0
Let a(i) be the third derivative of i**2 + 1/20*i**5 - 3/8*i**4 + i**3 + 0 + 0*i. Solve a(b) = 0 for b.
1, 2
Let r = 31/48 + -5/16. Find w, given that 0 + 0*w + r*w**2 = 0.
0
Let x(i) = -28*i**3 + 50*i**2 + 14*i + 2. Let o(j) = j**2 - j + 1. Let y(p) = -2*o(p) + x(p). Factor y(g).
-4*g*(g - 2)*(7*g + 2)
Let g(t) be the third derivative of 2*t**5/75 + t**4/15 + t**3/15 - 2*t**2. Factor g(i).
2*(2*i + 1)**2/5
Factor -3/7*l**4 + 0*l + 3/7*l**5 + 0 - 3/7*l**3 + 3/7*l**2.
3*l**2*(l - 1)**2*(l + 1)/7
Let k(d) = -d**2 - 4*d + 11. Let w = 20 + -18. Let c(q) = -12*q**2 - 51*q + 144. Let m(n) = w*c(n) - 27*k(n). Factor m(u).
3*(u - 1)*(u + 3)
Let v(q) be the first derivative of q**5/80 - q**3/24 + 2*q - 3. Let k(g) be the first derivative of v(g). Determine x so that k(x) = 0.
-1, 0, 1
Let o(l) be the first derivative of -3*l**4/16 + l**3/4 + 5. Factor o(g).
-3*g**2*(g - 1)/4
Let y be 1*(-2 - 0)*(-3)/2. Let j(s) be the first derivative of 0*s**2 - 2/3*s + 2/9*s**y - 4. Factor j(v).
2*(v - 1)*(v + 1)/3
Let z(t) be the first derivative of t**7/252 + t**6/36 + t**5/15 + t**4/18 + 5*t + 8. Let g(p) be the first derivative of z(p). Suppose g(r) = 0. What is r?
-2, -1, 0
Let d(j) = 4*j**3 + 2*j**2 + 3*j - 3. Let w(o) = 17*o**3 + 8*o**2 + 13*o - 13. Let s(q) = -26*d(q) + 6*w(q). Solve s(b) = 0.
-2, 0
Let a(n) be the second derivative of 0 - 9/2*n**2 + 7*n - n**3 - 1/12*n**4. Factor a(z).
-(z + 3)**2
Suppose 8*s - 3*s = 10. Factor s*a**3 + 3*a - a**3 + 5*a**2 + 68 - 77.
(a - 1)*(a + 3)**2
Let y(b) be the third derivative of b**8/6720 - b**7/840 + b**6/360 - b**4/6 - 10*b**2. Let h(q) be the second derivative of y(q). Factor h(i).
i*(i - 2)*(i - 1)
Let h be (-4)/(-2)*(-2 - (-36)/8). Determine o, given that 1/2*o**2 + 0 - 1/2*o**h + 0*o - 3/2*o**3 + 3/2*o**4 = 0.
0, 1
Let u = -5 + 7. What is l in 8 + 6*l**3 - 4*l**3 - 6*l**u - 3 + 1 - 2*l = 0?
-1, 1, 3
Suppose -2*q**2 + q - 6*q - 3*q + 12 - 2*q**2 = 0. Calculate q.
-3, 1
Let a(o) be the third derivative of -o**9/60480 + o**8/20160 + o**7/5040 - o**6/720 + o**5/30 - 3*o**2. Let v(j) be the third derivative of a(j). Factor v(w).
-(w - 1)**2*(w + 1)
Let v(n) be the third derivative of n**5/4 + 5*n**4/6 + 5*n**3/6 - n**2. Suppose v(w) = 0. What is w?
-1, -1/3
Suppose 0 = -k - 8 + 1. Let w be -1 + k/((-7)/6). Factor -10*l**4 + 3*l**w - 2*l + 2*l - 4*l + 4*l**2 + 7*l**3.
l*(l - 2)*(l - 1)**2*(3*l + 2)
Factor -2/3*t**4 + 2/3*t**2 + 1/3*t + 0 - 1/3*t**5 + 0*t**3.
-t*(t - 1)*(t + 1)**3/3
Let q(t) = -6*t**2 + 2*t - 6. Let b(w) = 5*w**2 - 2*w + 5. Let z(c) = 5*b(c) + 4*q(c). Determine i, given that z(i) = 0.
1
Let i(f) be the first derivative of f - 1 + 1/42*f**4 - 2/21*f**3 + 1/7*f**2. Let j(d) be the first derivative of i(d). Solve j(s) = 0.
1
Let l(y) be the third derivative of -2*y**7/175 - y**6/40 + 3*y**5/100 + y**4/8 + y**3/10 - 19*y**2. Solve l(a) = 0.
-1, -1/4, 1
Suppose 24 = -4*f + 60. Factor -5*b**3 - b**2 - 6*b**2 - f*b - 5*b**2 - 2.
-(b + 1)**2*(5*b + 2)
Let a(y) be the third derivative of -y**5/180 - y**4/72 + 7*y**2. Factor a(m).
-m*(m + 1)/3
Let z(p) be the second derivative of p**6/120 + p**5/80 - p**4/24 + 10*p. Factor z(l).
l**2*(l - 1)*(l + 2)/4
Let j(d) = 8*d**2 + 7*d - 4. Let i(x) = 4*x**2 + 4*x - 2. Let m(q) = 11*i(q) - 6*j(q). Factor m(r).
-2*(r - 1)*(2*r + 1)
Find z such that -9/2 + 3/2*z**2 + 3*z = 0.
-3, 1
Factor 8/7*t - 4/7 - 3/7*t**2.
-(t - 2)*(3*t - 2)/7
Let a(k) = k**2 + 4*k + 13. Let s be a(-6). Let y be 15/s + (-21)/60. Factor 1/2*j - 1/2*j**3 + 0*j**2 - y + 1/4*j**4.
(j - 1)**3*(j + 1)/4
Suppose 2*y - 12 = -2*y. Determine q so that -q**2 - y - q**2 + 5*q**2 = 0.
-1, 1
Let f(h) be the second derivative of 7*h**6/90 + 23*h**5/60 + 3*h**4/4 + 13*h**3/18 + h**2/3 - 34*h. Find s, given that f(s) = 0.
-1, -2/7
Let b(t) be the second derivative of 2*t + 0*t**2 + 1/66*t**4 + 0 - 2/33*t**3. Factor b(j).
2*j*(j - 2)/11
Let l(n) be the first derivative of -7*n**6/15 + 52*n**5/25 - 17*n**4/5 + 32*n**3/15 + n**2/5 - 4*n/5 - 8. Factor l(w).
-2*(w - 1)**4*(7*w + 2)/5
Let h(x) be the first derivative of -x**3/2 + 3*x**2/2 - 3*x/2 + 25. What is o in h(o) = 0?
1
Let y(r) = -r**3 - 7*r**2 + 7*r - 5. Let b be y(-8). Let b*f - 6*f**2 - 7*f - f**2 + 3*f**2 = 0. Calculate f.
-1, 0
Suppose -5*z + 10*z = 5. Let s be (4 - 4)/(z + 1). Factor 2/7*t**2 + s - 2/7*t**3 + 0*t.
-2*t**2*(t - 1)/7
Let d(c) be the first derivative of 2/7*c + 7 + 1/7*c**3 - 1/2*c**2. Factor d(a).
(a - 2)*(3*a - 1)/7
Let n(y) be the first derivative of 24*y**5/25 - 27*y**4/10 + 12*y**3/5 - 3*y**2/5 + 30. Solve n(a) = 0 for a.
0, 1/4, 1
Let j(i) be the first derivative of -i**6/10 + 3*i**4/5 + 4. Solve j(r) = 0.
-2, 0, 2
Let w(c) be the first derivative of -c**5/20 + 7*c**4/16 - 4*c**3/3 + 3*c**2/2 + 1. Factor w(x).
-x*(x - 3)*(x - 2)**2/4
Let b(a) be the third derivative of a**7/280 - a**5/40 + 4*a**3/3 + 2*a**2. Let l(c) be the first derivative of b(c). Factor l(u).
3*u*(u - 1)*(u + 1)
Let a(s) be the second derivative of -s**5/30 + s**3/3 - 2*s**2/3 + s. Factor a(w).
-2*(w - 1)**2*(w + 2)/3
Suppose 6*k - k - 25 = 0. Suppose -k*n - 5*u - 5 = 0, 18 + 2 = 4*n - 4*u. Solve n + 25*q**2 + 13*q + 3*q + 19*q**3 + q**5 + 2 + 7*q**4 = 0 for q.
-2, -1
Let g(k) = k + 2. Let r be g(-2). Factor r*c + 0*c**2 - c**2 + 2*c.
-c*(c - 2)
Let w(t) be the third derivative of 0*t - 1/135*t**5 + 0*t**3 - 1/540*t**6 + 0 - 6*t**2 + 1/36*t**4. Find z such that w(z) = 0.
-3, 0, 1
Let b(r) be the first derivative of -r**3/15 - 3*r**2/5 - 8*r/5 + 15. Factor b(p).
-(p + 2)*(p + 4)/5
Suppose 0 = 3*b - 0*b - 6. Determine t so that 2*t**4 - 2*t**b + 5*t - 5*t + 0*t = 0.
-1, 0, 1
Let t(c) = c**3 + 1. Let j(s) = 9*s**4 - 6*s**3 - 27*s**2 + 27*s - 9. Suppose -5*g - 8 = 7. Let n(b) = g*t(b) - j(b). Solve n(w) = 0 for w.
-2, 1/3, 1
Let d(z) = -z + 1. Let t(o) = 5*o**2 + 55*o + 120. Let l(a) = 5*d(a) + t(a). Factor l(c).
5*(c + 5)**2
Let r(n) be the second derivative of n**6/15 + n**5/10 - n**4/3 + 11*n. Let r(f) = 0. What is f?
-2, 0, 1
Let c(b) be the first derivative of 2*b**3/15 - b**2/5 - 4*b/5 - 8. Factor c(g).
2*(g - 2)*(g + 1)/5
Let x(n) = n**2 - 7*n + 8. Let z be x(6). Factor -z + c**2 + c - 2*c + c - c.
(c - 2)*(c + 1)
Let k(b) be the third derivative of -b**6/48 + b**5/12 + 5*b**4/16 - 30*b**2. Factor k(z).
-5*z*(z - 3)*(z + 1)/2
Let o(v) = 11*v**2 - 6*v + 1. Let t(r) = 10*r**2 - 5*r. Let h(f) = -5*o(f) + 6*t(f). Let h(q) = 0. Calculate q.
-1, 1
Let d(s) = 4*s**3 - 12*s**2 - 3*s + 3. Let f(j) = -36*j**3 + 108*j**2 + 28*j - 28. Let l(i) = 28*d(i) + 3*f(i). Factor l(n).
4*n**2*(n - 3)
Let x = 0 + 4. Let c = x + -3. Suppose 2*a - c - 4*a**2 + a + 2*a**2 = 0. What is a?
1/2, 1
Let q(c) be the second derivative of 7/15*c**6 + 3*c + 0*c**2 + 0 + 2/3*c**3 - 7/6*c**4 + 3/10*c**5 - 5/21*c**7. Determine a so that q(a) = 0.
-1, 0, 2/5, 1
Let g(u) be the second derivative of -u**4/6 - 5*u**3/6 - 3*u**2/2 - 4*u. Let r(b) = 3*b**2 + 9*b + 5. Let q(p) = -10*g(p) - 6*r(p). Factor q(w).
2*w*(w - 2)
Let p(c) be the second derivative of -c**9/13608 + c**8/3780 - c**6/810 + c**5/540 + c*