 d(q) = 0.
-2, -1
Let g(x) = -7*x**2 - 8*x - 16. Let o(h) = -6*h**2 - 9*h - 15. Let t(z) = -3*g(z) + 4*o(z). Let t(w) = 0. Calculate w.
-2
Let j(t) = -t**2 + 6*t + 10. Let w = 3 - -4. Let n be j(w). Factor c**5 + 8*c**4 + n*c**3 - 13*c**3 - 3*c**5 + 4*c**2.
-2*c**2*(c - 2)*(c - 1)**2
Let y(x) = x**4 + x**3 + x**2 + x - 1. Let i(f) = 4*f**4 - 6*f**3 + 18*f**2 + 28*f - 3. Let s(r) = -4*i(r) + 12*y(r). Find z, given that s(z) = 0.
-1, 0, 5
Let h(i) be the third derivative of -i**7/1470 - i**6/168 - 2*i**5/105 - i**4/42 + 8*i**2. Suppose h(z) = 0. What is z?
-2, -1, 0
Let d = 27/22 + -8/11. Let x be 4/(-18) + (-52)/(-72). What is b in 1/2*b**3 - x*b - 1/2*b**2 + d = 0?
-1, 1
Let h = -7/15 + 13/15. Suppose 7*r - 6 = 8. Suppose 2/5*m**3 - h*m**r + 0 + 0*m = 0. What is m?
0, 1
Let g(z) be the third derivative of -z**5/120 - z**4/32 - z**3/24 - 8*z**2. Suppose g(u) = 0. Calculate u.
-1, -1/2
Let x = 4 + 5. Suppose -3*l = -3 - x. Factor -49/2*j**l + 10*j - 2 - 35*j**3 + 3/2*j**2.
-(j + 1)**2*(7*j - 2)**2/2
Let l(b) be the first derivative of -2/3*b**2 + 1 + b + 1/9*b**3. Factor l(h).
(h - 3)*(h - 1)/3
Let q(f) be the second derivative of 16/3*f**3 + 0 - 4/3*f**4 + 0*f**2 + 1/10*f**5 - 5*f. Suppose q(w) = 0. What is w?
0, 4
Suppose 64/3*v + v**2 + 7 = 0. What is v?
-21, -1/3
Let o(f) = 3*f**3 + 2*f**3 - 201*f - 2 + 2*f**2 + 196*f. Let z(m) = 14*m**3 + 5*m**2 - 15*m - 6. Let q(p) = -17*o(p) + 6*z(p). Factor q(a).
-(a + 1)**2*(a + 2)
Find a such that -a**5 - 3*a**2 - a**2 - a**2 + 4 + 3*a**4 + a**3 - 2*a**2 = 0.
-1, 1, 2
Let o(l) be the second derivative of -l**6/90 - l**5/30 - l**4/36 + l. Solve o(h) = 0 for h.
-1, 0
Let g(i) be the third derivative of i**2 + 0*i - 1/3*i**3 - 1/20*i**6 + 0 - 7/30*i**5 - 5/12*i**4. Determine b, given that g(b) = 0.
-1, -1/3
Let y(u) be the first derivative of -u**6/135 - 2*u + 5. Let b(q) be the first derivative of y(q). Suppose b(x) = 0. Calculate x.
0
Let t(s) be the third derivative of 0*s**4 + 2*s**2 + 0 - 1/27*s**3 + 1/270*s**5 + 0*s. Determine w, given that t(w) = 0.
-1, 1
Let y(r) be the second derivative of -r**7/63 - r**6/15 - r**5/15 + r**4/9 + r**3/3 + r**2/3 + r. Factor y(i).
-2*(i - 1)*(i + 1)**4/3
Let -20/3 + 20/3*g + 5*g**2 - 5/3*g**4 - 10/3*g**3 = 0. What is g?
-2, 1
Let q(i) be the second derivative of 0*i**2 + 1/80*i**5 + 3*i + 1/6*i**3 + 1/12*i**4 + 0. Factor q(m).
m*(m + 2)**2/4
Let r(k) be the second derivative of 0 - 1/12*k**4 - 3*k + 0*k**2 - 1/2*k**3. Let r(d) = 0. Calculate d.
-3, 0
Let p(k) be the first derivative of 2*k**3/15 + 4*k**2/5 + 6*k/5 - 7. Determine s so that p(s) = 0.
-3, -1
Let t(j) = j**3 + j**2 - 5*j + 1. Let v(b) = -5*b**3 - 3*b**2 + 21*b - 4. Let g(k) = 9*t(k) + 2*v(k). Factor g(w).
-(w - 1)**3
Let y(p) be the third derivative of -p**2 - 1/24*p**5 - 1/3*p**3 + 0*p + 1/6*p**4 + 1/240*p**6 + 0. Factor y(m).
(m - 2)**2*(m - 1)/2
Let k(p) be the first derivative of 2*p**3/3 - 17*p**2 - 42. Let k(y) = 0. What is y?
0, 17
Let v(c) = 3*c**2 + c + 2. Let l(y) = -4*y**2 - 2*y - 3. Let j(x) = -2*l(x) - 3*v(x). Suppose j(q) = 0. What is q?
0, 1
Let j be 6/4*(-80)/(-30). Let y be (-1 - -5)/j - -1. Factor -2/3*l**y - 4/3*l - 2/3.
-2*(l + 1)**2/3
Suppose -t + 3 = -0*t. What is r in -20*r**2 - 3*r - 3*r**4 + 17*r + 32*r**4 + 25*r**4 - 2 - 36*r**t + 54*r**5 = 0?
-1, 1/3
Factor 28 + 35*u - 3*u**2 - 2*u**2 + 3*u - u**2.
-2*(u - 7)*(3*u + 2)
Let v(g) be the first derivative of -3/8*g**4 - 7 + 3/8*g**2 + 0*g**5 + 1/8*g**6 + 0*g + 0*g**3. Solve v(h) = 0.
-1, 0, 1
Let j(f) be the first derivative of -2*f**5/25 + 2*f**3/3 - 8*f/5 + 3. Let j(m) = 0. What is m?
-2, -1, 1, 2
Let h(a) = 5*a**2 - 13*a + 29. Let w(g) = -36*g**2 + 90*g - 202. Let k(i) = -44*h(i) - 6*w(i). What is z in k(z) = 0?
4
Let c(i) be the third derivative of -i**8/1848 + i**7/231 - i**6/66 + i**5/33 - 5*i**4/132 + i**3/33 + 30*i**2. Factor c(w).
-2*(w - 1)**5/11
Let d(w) be the first derivative of 0*w - 4 - 4/21*w**3 + 0*w**2 + 1/7*w**4. Solve d(i) = 0 for i.
0, 1
Suppose 25/2 + 1/2*n**2 + 5*n = 0. What is n?
-5
Let i(d) be the second derivative of d**5/50 - d**4/6 + 7*d**3/15 - 3*d**2/5 - 13*d. Factor i(t).
2*(t - 3)*(t - 1)**2/5
Let r = 8 - 4. Factor 3*i + 4*i**3 - 9*i - 1 + 2*i - 2*i**r + 3.
-2*(i - 1)**3*(i + 1)
Let a(t) be the second derivative of -t**8/1512 + t**7/945 + 3*t**2/2 - 2*t. Let m(v) be the first derivative of a(v). Factor m(i).
-2*i**4*(i - 1)/9
Let r(o) be the second derivative of o**7/36 + 11*o**6/45 + 4*o**5/5 + 47*o**4/36 + 41*o**3/36 + o**2/2 + 6*o. Factor r(y).
(y + 1)**3*(y + 3)*(7*y + 2)/6
Let q be (-196)/(-315) - (-4)/(-10). Let t(m) = m**3 + 12*m**2 + 10*m - 11. Let g be t(-11). Let g*u**3 + 2/9*u**2 + 0*u + 0 - q*u**4 = 0. What is u?
-1, 0, 1
Factor 8/3*f**2 + 4/3*f**4 - 26/9*f**3 + 0 - 2/9*f**5 - 8/9*f.
-2*f*(f - 2)**2*(f - 1)**2/9
Let i(f) be the first derivative of 2*f**3/27 + 4*f**2/9 + 8*f/9 + 12. Let i(j) = 0. Calculate j.
-2
Suppose -1 = 3*p + 5*j, -5*p - 4*j = -0*p - 7. Factor 0 + m - 3/4*m**p + m**2.
-m*(m - 2)*(3*m + 2)/4
Suppose -3*b = -9 - 3. Suppose b*f = 3*f + 10. Let 20*g**5 + 2*g - 3*g**4 + 0*g**4 - 12*g**3 - f*g**3 + 3*g**2 = 0. Calculate g.
-1, -1/4, 0, 2/5, 1
Let j be 11/2 + (-3)/6. Suppose j*a = -2*q - 1 + 7, -a + q = -4. Let -1 - y**2 + y + a*y - y = 0. What is y?
1
Let j(p) be the first derivative of p**4/14 - 2*p**3/7 - 4*p**2/7 + 4. Determine a so that j(a) = 0.
-1, 0, 4
Let l(v) = v**2 - 13*v + 2. Let f be l(13). Let s(a) be the first derivative of -1/2*a**2 + 1/6*a**3 + 1/2*a + f. Factor s(u).
(u - 1)**2/2
Factor 2/3 - 5/3*u**3 + 3*u**2 - 7/3*u + 1/3*u**4.
(u - 2)*(u - 1)**3/3
Factor 10 - 20*k**2 + 3*k + 2*k + 5*k**2.
-5*(k - 1)*(3*k + 2)
Let g(w) be the first derivative of w**4/2 - 2*w**3 + 2*w**2 - 19. Let g(a) = 0. What is a?
0, 1, 2
Suppose 3*r + r**2 + 4*r**3 - 2 + r**4 - 13*r**3 + 6*r**3 = 0. Calculate r.
-1, 1, 2
Let -2*r**2 + 3*r + r**2 - 2*r**2 + 0*r**2 = 0. Calculate r.
0, 1
Factor 0 + 2/5*n + 2/15*n**3 - 8/15*n**2.
2*n*(n - 3)*(n - 1)/15
Let p(x) be the first derivative of 8*x**4/9 - 16*x**3/9 + x**2 - 2*x/9 + 5. Factor p(d).
2*(d - 1)*(4*d - 1)**2/9
Let c(g) be the first derivative of -7*g**6/720 - g**5/120 + 4*g**3/3 + 6. Let t(p) be the third derivative of c(p). Factor t(u).
-u*(7*u + 2)/2
Let l be ((-15)/9)/(-5)*-6. Let k be l/(-10) - (-8)/60. Factor o**2 + 0 + o**3 + k*o**4 + 1/3*o.
o*(o + 1)**3/3
Factor -1/4*b**2 + 1/4*b**3 + 0 - 1/2*b.
b*(b - 2)*(b + 1)/4
Suppose -29 = -3*z - i - 12, 0 = 3*z + 5*i - 37. Let h(w) be the first derivative of 2 + 1/5*w**5 - 1/6*w**6 - 1/2*w**2 + 1/2*w**z - 2/3*w**3 + w. Factor h(t).
-(t - 1)**3*(t + 1)**2
Let u(v) be the third derivative of 1/1470*v**7 - 1/84*v**4 + 0 + 0*v**5 + 1/420*v**6 - 1/42*v**3 + 0*v + v**2. Suppose u(n) = 0. What is n?
-1, 1
Let y(m) = m + 5. Let g be y(-5). Suppose -r = -g*r. Find n, given that 2/3*n**3 + 0 + r*n + 0*n**2 = 0.
0
Let z(y) be the third derivative of 0*y - 2*y**2 + 0*y**5 + 0*y**4 + 0 + 0*y**3 - 1/660*y**6. What is s in z(s) = 0?
0
Suppose 0 = -4*a - 0*a. Let d be 3 + 2 + (-18)/4. Let i**3 + 0 + 0*i**2 + d*i**4 - 5*i**5 + a*i = 0. What is i?
-2/5, 0, 1/2
Let u = 119/3 + -39. Find s, given that -2/3*s**2 + 2/3*s**5 + 0 - u*s**3 + 0*s + 2/3*s**4 = 0.
-1, 0, 1
Let s = 1766/7 - 250. Solve 0 - 10/7*o**5 + s*o**4 - 4/7*o**2 + 0*o - 2/7*o**3 = 0 for o.
-2/5, 0, 1
Let q = 1070 + -3176/3. Let m(j) be the first derivative of 4*j - q*j**3 - 7*j**4 + 3 - j**2. Factor m(x).
-2*(x + 1)*(2*x + 1)*(7*x - 2)
Let b(n) be the first derivative of -n**4/12 - n**3/9 + 1. Solve b(d) = 0.
-1, 0
Let y(n) be the first derivative of 0*n + 0*n**2 - 1/6*n**3 - 3 - 1/8*n**4. Factor y(t).
-t**2*(t + 1)/2
Let i = 12 + -12. Let q(c) be the second derivative of 0*c**2 + 1/3*c**3 + 1/6*c**4 - 3/5*c**5 + c + i. Factor q(y).
-2*y*(2*y - 1)*(3*y + 1)
Let b = 1 + 0. Let a be (2 - 9)*-1*b. Factor -q**3 + 10*q**2 + 3 + 2*q + a*q**3 - 18*q**4 - 3.
-2*q*(q - 1)*(3*q + 1)**2
Suppose 3*s - 9 = 5*n, -2 = -2*n - s + 1. Let z be 5*(n - (-9)/15). Let 4/7*f**z + 0*f**2 - 2/7*f**4 - 4/7*f + 2/7 = 0. What is f?
-1, 1
Let g(y) be the third derivative of y**8/30240 - y**7/2520 + y**6/540 - y**5/20 - y**2. Let k(f) be the third derivative of g(f). Solve k(a) = 0 for a.
1, 2
Suppose -7*o - 151 = 59. Let w be ((-16)/20)/(12/o). What is f in 235/2