. Let n(b) be the first derivative of 9*b - 2*b**3 - 1 + 1/2*b**6 - 9/2*b**4 - 3/5*b**5 + 15/2*b**x. Solve n(z) = 0.
-1, 1, 3
Suppose 2*n = p - 2*p - 6, 3*n + 9 = 2*p. Factor -58*j + 3 + p + 3*j**2 + 52*j.
3*(j - 1)**2
Let l(g) be the first derivative of -22/5*g**2 - 6 - 5/4*g**4 - 8/5*g - 14/3*g**3. Factor l(a).
-(a + 2)*(5*a + 2)**2/5
Suppose -111*y**3 + 90*y**3 + 5*y**4 + 7 - 2*y**4 - 39*y + 45*y**2 + 5 = 0. Calculate y.
1, 4
Solve -75 - 3/4*h**2 + 15*h = 0 for h.
10
Let b = 5837 - 5834. Factor 0*u**2 + 2/3 - 1/3*u**b + u.
-(u - 2)*(u + 1)**2/3
Suppose -14*t**2 + 15*t**4 + 16*t**3 - 12*t**3 - 6*t**2 - 4*t**3 - 5*t**5 = 0. Calculate t.
-1, 0, 2
Let f be (-121 + 118)*(0 + -1). Solve -2/3*o**2 - 4/9*o + 0 - 2/9*o**f = 0 for o.
-2, -1, 0
Let r(y) be the second derivative of y**5/10 - y**4/6 - 56*y**3/3 + 241*y. Find p, given that r(p) = 0.
-7, 0, 8
Let h(a) be the second derivative of 5*a**7/42 + 17*a**6/6 + 103*a**5/4 + 445*a**4/4 + 240*a**3 + 270*a**2 + 29*a. Solve h(j) = 0 for j.
-6, -3, -1
Suppose -1/2*l**3 + 1/2*l + 5/2 - 5/2*l**2 = 0. What is l?
-5, -1, 1
Let h(o) = o**3 + 25*o**2 + 25*o + 24. Let k be h(-24). Let u be (-4)/8 - 10/(-4). Let 0*b**3 - 1/3*b**4 + k*b + 1/3*b**u + 0 = 0. What is b?
-1, 0, 1
Let v = 1 + -1. Let k = -1/833 - -837/3332. Solve 1/4*j + v + 0*j**2 - k*j**3 = 0 for j.
-1, 0, 1
Let z(d) be the second derivative of -d**5/330 + 3*d**4/44 - 8*d**3/33 - 16*d**2 - 33*d. Let h(m) be the first derivative of z(m). Factor h(y).
-2*(y - 8)*(y - 1)/11
Let m(f) be the second derivative of f**7/168 - f**6/12 + 5*f**5/16 + 5*f**4/12 - 10*f**3/3 - 8*f**2 + 73*f. Suppose m(z) = 0. Calculate z.
-1, 4
Let c = -1/52 + 215/364. Factor 1/7*a**2 + c*a**4 + 0*a - 5/7*a**3 + 0.
a**2*(a - 1)*(4*a - 1)/7
Let -162/5*s**5 + 1104/5*s - 1628/5*s**3 + 2088/5*s**2 - 306*s**4 + 128/5 = 0. What is s?
-8, -2, -2/9, 1
Let o be (-330)/(-70) - (-6)/21. Let c(y) be the first derivative of 4 + 0*y + 1/30*y**o + 1/3*y**2 + 0*y**3 - 1/8*y**4. Determine a, given that c(a) = 0.
-1, 0, 2
Suppose l = -5*p + 5, -2*l + 1 = p - 0*p. Let d(t) be the third derivative of t**2 - 1/60*t**5 + 0 + 0*t**4 + l*t**3 + 0*t + 1/120*t**6. Factor d(u).
u**2*(u - 1)
Let a(s) be the third derivative of s**7/2940 - s**6/630 + 11*s**3/3 + 13*s**2. Let j(t) be the first derivative of a(t). Suppose j(l) = 0. Calculate l.
0, 2
Factor 8*n**2 - 21*n**4 + 44 - 8*n**4 - 4*n**5 - 67*n**3 - 21*n**3 - 23*n**4 + 92*n.
-4*(n - 1)*(n + 1)**3*(n + 11)
Let s(k) be the first derivative of -k**4/6 - 4*k**3/9 + k**2/3 + 4*k/3 - 47. What is v in s(v) = 0?
-2, -1, 1
Determine m so that 4*m**2 + 5 - 63 + 4*m + 10 - 5*m + 17*m = 0.
-6, 2
Let n(o) be the second derivative of 0 + 0*o**2 - 1/14*o**3 - 12*o - 1/28*o**4. Factor n(v).
-3*v*(v + 1)/7
Solve -33*t**2 - 4*t**3 - 4*t**4 + t**3 - 3*t**3 + 113*t**2 + 2*t**3 = 0 for t.
-5, 0, 4
Let n = 315 - 313. Factor 2/5 - 2/15*l**n + 4/15*l.
-2*(l - 3)*(l + 1)/15
What is y in -11/3*y**3 - 13/3*y**2 + 11/3*y + 1/3*y**4 + 4 = 0?
-1, 1, 12
Let s(t) be the first derivative of -22*t**5/15 - 43*t**4/3 - 38*t**3 - 76*t**2/3 + 40*t/3 + 900. Determine g, given that s(g) = 0.
-5, -2, -1, 2/11
Determine c so that 20/11*c + 1/11*c**2 - 21/11 = 0.
-21, 1
Suppose -7*z + 19*z + 7*z = 38. Let 0 + 3/5*b**4 + 12/5*b**3 + 0*b + 12/5*b**z = 0. Calculate b.
-2, 0
Determine w, given that 6348/5*w + 4/5*w**3 - 276/5*w**2 - 48668/5 = 0.
23
Let w = -1 - -5. Suppose -16 = -y - w*b, 0 = -y - 9*b + 4*b + 19. Factor 0*f**y + 2*f**4 - 3*f**2 + f**4.
3*f**2*(f - 1)*(f + 1)
Suppose 5*w - 60 = -w. Suppose 2*y + 3*y = w. Solve -y*k**2 + 4*k**3 + k**3 - 3*k**3 = 0 for k.
0, 1
Let n be -17*(550/80 + -7) + -3 + 1. Let 11/8*d**2 - n + 9/8*d - 5/4*d**4 - 9/8*d**3 = 0. What is d?
-1, 1/10, 1
Let l(h) = -h**3 + 4*h**3 - 2*h**2 - h + 5 - 4*h**3 - 3. Let j be l(-2). Let 0*q**2 - 6*q**2 + 4*q**j + 2*q**2 + 0*q - 2*q**5 + 2*q = 0. What is q?
-1, 0, 1
Let h(g) be the third derivative of -1681*g**6/72 - 287*g**5/12 + 50*g**4 - 250*g**3/9 - 172*g**2. Let h(o) = 0. What is o?
-1, 10/41
Let m(y) be the second derivative of 2*y**7/21 + 2*y**6/3 + 8*y**5/5 + 4*y**4/3 + 173*y. Factor m(n).
4*n**2*(n + 1)*(n + 2)**2
Let q = 23 - 13. Determine r so that -12 + q*r + 6*r + 0*r - 4*r**2 = 0.
1, 3
Suppose 39*c**3 + 288*c**4 + 193*c**2 - 151*c**2 - 291*c**4 = 0. Calculate c.
-1, 0, 14
Let m = -28180/11 - -2562. Find r, given that 6/11*r + 0 - m*r**3 - 4/11*r**2 = 0.
-3, 0, 1
Factor -19*w + w + 14*w + 72 + 3*w**2 - 13*w - 25*w.
3*(w - 12)*(w - 2)
Find d, given that 0 - 2/19*d**2 - 30/19*d = 0.
-15, 0
Let l(u) be the second derivative of 4*u**3 + 2*u**2 - 6/5*u**5 - 25*u - 1/3*u**4 + 0. Let l(j) = 0. What is j?
-1, -1/6, 1
Let y be (-2)/(-10) + -3*(-60)/450. Factor -1/5*c**5 + y*c**4 - 1/5 - 2/5*c**2 - 2/5*c**3 + 3/5*c.
-(c - 1)**4*(c + 1)/5
Let m = 49 + -47. Solve m*s**2 + 0*s**2 + 7*s - s = 0.
-3, 0
Let o(k) be the first derivative of k**8/210 + k**7/84 - 7*k**6/180 - k**5/30 + 20*k**3/3 - 9. Let g(i) be the third derivative of o(i). Factor g(v).
2*v*(v - 1)*(v + 2)*(4*v + 1)
Suppose 5/2*y**3 - 8*y**2 - 6*y + 8 + 1/2*y**5 + 3*y**4 = 0. What is y?
-4, -2, 1
Suppose -3*l + 12 = p - 11, -9 = l - 3*p. Let w be 0/1 + l + -2. Factor -4*s**3 + 2*s**4 + w*s - 4*s**4 - 2*s**4 + 4*s**2.
-4*s*(s - 1)*(s + 1)**2
Let 58*a + 8*a**4 - 54*a + 2*a**5 - 6*a**5 - 8*a**2 + 0*a**5 = 0. Calculate a.
-1, 0, 1
Let i(x) = -x**3 - 10*x**2 - 20*x - 12. Let w be i(-8). Let n = w - 20. What is y in n - 1/4*y**3 - 3/4*y**4 + 1/2*y + 3/4*y**2 - 1/4*y**5 = 0?
-2, -1, 0, 1
Let g(v) be the third derivative of -2*v**3 + 0*v**4 + 0 + 22*v**2 + 3/20*v**5 + 0*v + 1/40*v**6. Factor g(n).
3*(n - 1)*(n + 2)**2
Factor -8*j**2 - 8*j**2 + 2*j**3 + 6*j + 5*j**2 + j**2 + 4*j**2 - 2.
2*(j - 1)**3
Let g = -92 + 159. Let o = g + -67. Factor o + 1/4*r - 1/4*r**2.
-r*(r - 1)/4
Let t(g) = -14*g**2 + 146*g - 35. Let s(w) = 5*w - 34. Let k be s(8). Let a(c) = -15*c**2 + 147*c - 36. Let p(n) = k*t(n) - 7*a(n). Find r, given that p(r) = 0.
2/7, 7
Let c(m) be the first derivative of -3*m**4/4 + 75*m**3 + 114*m**2 + 994. Factor c(u).
-3*u*(u - 76)*(u + 1)
Determine u, given that 0*u**3 - 45*u - 21*u**2 - 14*u**2 - 5*u**2 + 5*u**3 = 0.
-1, 0, 9
Factor -1/6*i**2 + 103/3 - 101/6*i.
-(i - 2)*(i + 103)/6
Suppose -4*c - 5*v = -97, -4*c + 0*c = -5*v - 127. Factor 45*s**2 - c + 10 - 43*s**2.
2*(s - 3)*(s + 3)
Factor -190 - 73 + 116 - 168*o - 48*o**2.
-3*(4*o + 7)**2
Let m be (-1)/(-5) + (-36)/(-8). Let z = -16/5 + m. Solve z*y**3 + y**4 + 0*y - y**2 + 0 = 0.
-2, 0, 1/2
Let c(d) be the second derivative of -d**5/480 - d**4/96 - d**3/48 + 35*d**2/2 - 3*d. Let g(a) be the first derivative of c(a). Factor g(o).
-(o + 1)**2/8
Let h = 4 - 7. Let g = -90 + 93. Let t(i) = 2*i - 2. Let r(p) = p**3 - p**2 + p - 1. Let j(b) = g*r(b) + h*t(b). Solve j(o) = 0.
-1, 1
Let -4/7*d**3 + 48/7 - 4*d**2 - 16/7*d = 0. Calculate d.
-6, -2, 1
Factor -18/5*o**2 - 12/5*o + 3/5*o**4 + 24/5 + 3/5*o**3.
3*(o - 2)*(o - 1)*(o + 2)**2/5
Let t = -1664 - -1666. Let c(x) be the third derivative of 0*x + 10*x**t + 5/72*x**4 + 1/180*x**5 + 2/9*x**3 + 0. Suppose c(s) = 0. What is s?
-4, -1
Let f(r) = -7*r**4 - 11*r**3 - 13*r**2 + 21*r + 24. Let p(t) = -8*t**4 - 12*t**3 - 15*t**2 + 21*t + 25. Let o(s) = -7*f(s) + 6*p(s). Solve o(k) = 0.
-3, -1, 2
Factor -22*i**2 + 275*i**3 - 551*i**3 + 64*i - 56 + 278*i**3.
2*(i - 7)*(i - 2)**2
Suppose -15*v**4 + 5*v**5 - 35*v**4 + 39*v**3 + 4*v**3 - 3*v**3 + 50*v**2 - 45*v = 0. Calculate v.
-1, 0, 1, 9
Let q(a) be the first derivative of 3*a**5/5 - 93*a**4/4 + 255*a**3 - 675*a**2/2 + 32. Find k, given that q(k) = 0.
0, 1, 15
Let u be -3*((-55)/66 + -4). Suppose -25/2 - 65/2*x - 3/2*x**3 + u*x**2 = 0. Calculate x.
-1/3, 5
Let w(i) = -2*i**3 + 23*i**2 + 14*i - 24. Let f be w(12). Let u(y) be the first derivative of f*y**2 - 1/6*y**3 - 4 + 1/2*y. Factor u(p).
-(p - 1)*(p + 1)/2
Let k = -3/4790 + 19169/14370. Factor 1/6*m**4 - 2*m - k + 1/2*m**3 - 1/3*m**2.
(m - 2)*(m + 1)*(m + 2)**2/6
Let x(q) = -2*q**3 - q**2 - 9*q - 9. Let a be x(-6). Let n be -1*(-6)/(-2) - a/(-77). Factor 14/11*g - n*g**2 - 8/11*g**4 - 2/11 + 26/11*g**3.
-2*(g - 1)**3*(4*g - 1)/11
Let c(a) be the second derivative of 2*a**7/27 + 5*a**6/27 - 32*a**5/45 - 52*a**4/27 + 32*a**3/27 + 16*a**2/9 - 12*a + 1. Solve c(g) = 0.
-2